results for au:Chakrabarty_I in:quant-ph

- May 26 2017 quant-ph arXiv:1705.09080v1In this brief report, we prove that robustness of coherence (ROC), in contrast to many popular quantitative measures of quantum coherence derived from the resource theoretic framework of coherence, may be sub-additive for a specific class of multipartite quantum states. We investigate how the sub-additivity is affected by admixture with other classes of states for which ROC is super-additive. We show that pairs of quantum states may have different orderings with respect to relative entropy of coherence, $l_{1}$-norm of coherence and ROC and numerically study the difference in ordering for coherence measures chosen pairwise.
- May 22 2017 quant-ph arXiv:1705.07013v1One of the fundamental restrictions that quantum mechanics imposes is the "No deletion Theorem" which tells us that given two identical unknown quantum states, it is impossible to delete one of them. But nevertheless if not perfect, people have tried to delete it approximately. In these approximate deleting processes our basic target is to delete one of the two identical copies as much as possible while preserving the other copy. In this brief report, by using the No communication theorem (NCT) (impossibility of sending signal faster than light using a quantum resource) as a guiding principle, we obtain a bound on the sum of the fidelity of deletion and the fidelity of preservation. Our result not only brings out the complementary relation between these two fidelities but also predicts the optimal value of the fidelity of deletion achievable for a given fidelity of preservation under no signaling constraint. This work eventually saturates the quest for finding out the optimal value of deletion within the NCT framework.
- Mar 06 2017 quant-ph arXiv:1703.01059v1Conditional von Neumann entropy is an intriguing concept in quantum information theory. In the present work, we examine the effect of global unitary operations on the conditional entropy of the system. We start with the set containing states with non-negative conditional entropy and find that some states preserve the non-negativity under unitary operations on the composite system. We call this class of states as Absolute Conditional von Neumann entropy Non Negative class (\textbfACVENN). We are able to characterize such states for $2\otimes 2$ dimensional systems. On a different perspective the characterization accentuates the detection of states whose conditional entropy becomes negative after the global unitary action. Interestingly, we are able to show that this \textbfACVENN class of states forms a set which is convex and compact. This feature enables for the existence of hermitian witness operators the measurement of which could distinguish unknown states which will have negative conditional entropy after the global unitary operation. This has immediate application in super dense coding and state merging as negativity of conditional entropy plays a key role in both these information processing tasks. Some illustrations are also provided to probe the connection of such states with Absolute separable (AS) states and Absolute local (AL) states.
- Feb 08 2017 quant-ph arXiv:1702.02123v2In this work, we exhaustively investigate $1 \rightarrow 2$ local and non local broadcasting of entanglement and correlations (optimal and non-optimal) using asymmetric Pauli cloners, with the most general two qubit state as a resource. We exemplify the broadcasting of entanglement using Maximally Entangled Mixed States and demostrate the variation of broadcasting range with the amount of entanglement in resource state as well as the asymmetry in the cloner. We show that it is impossible to optimally broadcast quantum correlations that go beyond entanglement (Geometric Discord) with the help of these asymmetric Pauli cloning machines. We introduce the concept of asymmetry in correlations to quantify the degree of variation in the amount of correlation present in the output pairs obtained after broadcasting. We also study the problem of $1 \rightarrow 3$ broadcasting of entanglement using non-maximally entangled state (NME) as a resource. We adopt two different strategies : successive application of $1 \rightarrow 2$ optimal cloning machines and application of $1 \rightarrow 3$ optimal cloning machines. Interestingly, we show that $1 \rightarrow 3$ optimal cloner does a better job at broadcasting than the successive application of $1 \rightarrow 2$ cloners. Finally, we create an example to show that there are local unitaries, which when applied on non-maximally entangled state locally give us a better range of broadcasting, that surpasses the best possible range obtained using cloning machines. This result opens up a new direction in exploration of methods to perform broadcasting which may outperform standard broadcasting strategies implemented through cloning transformations.
- Dec 23 2016 quant-ph arXiv:1612.07644v2Steerability is a characteristic nonlocal trait of quantum states lying in between entanglement and Bell nonlocality. A given quantum state is considered to be steerable if it violates a suitably chosen steering inequality. A quantum state which otherwise satisfies a certain inequality can violate the inequality under a global change of basis i.e, if the state is transformed by a nonlocal unitary operation. Intriguingly there are states which preserve their non-violation(pertaining to the said inequality) under any global unitary operation. The present work explores the effect of global unitary operations on the steering ability of a quantum state which live in two qubits. We characterize such states in terms of a necessary and sufficient condition on their spectrum. Such states are also characterized in terms of some analytic characteristics of the set to which they belong. Looking back at steerability the present work also provides a relation between steerability and quantum teleportation together with the derivation of a result related to the optimal violation of steering inequality . An analytic estimation of the size of such non-violating states in terms of purity is also obtained. Interestingly the estimation in terms of purity also gives a necessary and sufficient condition in terms of bloch parameters of the state. Illustrations from some signature class of quantum states further underscore our observations.
- Aug 03 2016 quant-ph arXiv:1608.00847v1Complementarity have been an intriguing feature of physical systems for a long time. In this work we establish a new kind of complimentary relations in the frame work of quantum information processing tasks. In broadcasting of entanglement we create many pairs of less entangled states from a given entangled state both by local and non local cloning operations. These entangled states can be used in various information processing tasks like teleportation and superdense coding. Since these states are less entangled states it is quite intuitive that these states are not going to be as powerful resource as the initial states. In this work we study the usefulness of these states in tasks like teleportation and super dense coding. More precisely, we found out bounds of their capabilities in terms of several complimentary relations involving fidelity of broadcasting. In principle we have considered general mixed as a resource also separately providing different examples like a) Werner like states, b) Bell diagonal states. Here we have used both local and non local cloning operations as means of broadcasting. In the later part of our work, we extend this result by obtaining bounds in form of complimentary relations in a situation where we have used $1-N$ cloning transformations instead of $1-2$ cloning transformations.
- In a recent work, authors prove a yet another no-go theorem that forbids the existence of a universal probabilistic quantum protocol producing a superposition of two unknown quantum states. In this short note, we show that in the presence of closed time like curves, one can indeed create superposition of unknown quantum states and evade the no-go result.
- May 10 2016 quant-ph arXiv:1605.02458v3Quantum coherence (QCh) is considered to be a key ingredient in quantum resource theories and also plays a pivotal role in the design and implementation of various information processing tasks. Consequently, it becomes important for us to create more number coherent quantum states between two labs from a given coherent state shared initially. We call this process as \textbfBroadcasting of Quantum Coherence (QCh). In this work we extensively study the problem of broadcasting of QCh. In order to have a holistic view of broadcasting, we start with a most general representation two qubit mixed state in terms of Bloch vectors. As a cloning transformation we have used universal symmetric optimal Buzek-Hillery (BH) cloner locally as well as non locally. Remarkably, we find that in either of the case it is impossible to do optimal broadcasting of QCh. Further we show in case of non optimal broadcasting it is impossible to increase QCh of the state by both local and non local cloning operations. In non optimal case, apart from general result we consider examples like, a) Werner like states (WLS) and b) Bell diagonal states (BDS) and obtain ranges for broadcasting in terms of input state parameters.
- We introduce a new feature of no-signaling (Bell) non-local theories, namely, when a system of multiple parties manifests genuine non-local correlation, then there cannot be arbitrarily high non-local correlation among any subset of the parties. We call this feature, \textitcomplementarity of genuine multipartite non-locality. We use Svetlichny's criterion for genuine multipartite non-locality and non-local games to derive the complementarity relations under no-signaling constraints. We find that the complementarity relations are tightened for the much stricter quantum constraints. We compare this notion with the well-known notion of \textitmonogamy of non-locality. As a consequence, we obtain tighter non-trivial monogamy relations that take into account genuine multipartite non-locality. Furthermore, we provide numerical evidence showcasing this feature using a bipartite measure and several other well-known tripartite measures of non-locality.
- Dec 08 2015 quant-ph arXiv:1512.01770v3We find a single parameter family of genuinely entangled three qubit pure states, called the maximally Bell inequality violating states (MBV), which exhibit maximum Bell inequality violation by the reduced bipartite system for a fixed amount of genuine tripartite entanglement quantified by the so called tangle measure. This in turn implies that there holds a complementary relation between the Bell inequality violation by the reduced bipartite systems and the tangle present in the three qubit states, not necessarily pure. The MBV states also exhibit maximum Bell inequality violation by the reduced bipartite systems of the three qubit pure states with a fixed amount of genuine tripartite correlation quantified by the generalized geometric measure, a genuine entanglement measure of multiparty pure states, and the discord monogamy score, a multipartite quantum correlation measure from information theoretic paradigm. The aforementioned complementary relation has also been established for three qubit pure states for the generalized geometric measure and the discord monogamy score respectively. The complementarity between the Bell inequality violation by the reduced bipartite systems and the genuine tripartite correlation suggests that the Bell inequality violation in the reduced two qubit system comes at the cost of the total tripartite correlation present in the entire system.
- Nov 30 2015 quant-ph arXiv:1511.08560v2We consider causality respecting (CR) quantum systems interacting with closed timelike curves (CTCs), within the Deutsch model. We introduce the concepts of popping up and elimination of quantum information and use them to show that no-cloning and no-deleting, which are true in CR quantum systems, are no more valid in the same that are interacting with CTCs. We also find limits on the possibility of creation of entanglement between a CR system and a CTC, and the same between two CR systems in the presence of a CTC. We prove that teleportation of quantum information, even in its approximate version, from a CR region to a CTC is disallowed. Interestingly, we find that tweaking the Deutsch model, by allowing the input and output to be not the same, leads to a nontrivial approximate teleportation beyond the classical limit.
- Nov 19 2015 quant-ph arXiv:1511.05796v1In this work, we extensively study the problem of broadcasting of entanglement. In the first part of the work, we reconceptualize the idea of state dependent quantum cloning machine, and in that process we introduce different types of state dependent cloners like static and dynamic state dependent cloners. We derive the conditions under which we can make these cloners independent of the input state. In the broadcasting part, as our resource initial state, we start with general two qubit state and consider specific examples like, non maximally entangled state (NME), Werner like state (WS), and Bell diagonal state (BDS). We apply both state dependent/ state independent cloners, both locally and non-locally, in each of these cases. Incidentally, we find several instances where state dependent cloners outperform state independent cloners in broadcasting. This work gives us a holistic view on the broadcasting of entanglement in various two qubit states, when we have an almost exhaustive sets of cloning machines in our arsenal.
- In the recent years, we have seen that Grover search algorithm (Proceedings, 28th annual ACM symposium on the theory of computing, pp. 212-219, 1996) by using quantum parallelism has revolutionized the field of solving huge class of NP problems in comparisons to classical systems. In this work, we explore the idea of extending Grover search algorithm to approximate algorithms. Here we try to analyze the applicability of Grover search to process an unstructured database with a dynamic selection function in contrast to the static selection function used in the original work (Grover in Proceedings, 28th annual ACM symposium on the theory of computing, pp. 212-219, 1996). We show that this alteration facilitates us to extend the application of Grover search to the field of randomized search algorithms. Further, we use the dynamic Grover search algorithm to define the goals for a recommendation system based on which we propose a recommendation algorithm which uses binomial similarity distribution space giving us a quadratic speedup over traditional classical unstructured recommendation systems. Finally, we see how dynamic Grover search can be used to tackle a wide range of optimization problems where we improve complexity over existing optimization algorithms.
- Mar 23 2015 quant-ph arXiv:1503.05936v2The basic motivation behind this work is to raise the question that whether post selection can be considered a valid physical transformation (on probability space) or not. We study the consequences of both answers set in a device (theory) independent framework, based only on observed statistics. We start with taking up post-selection as an assumption and model the same using independent devices governed by Boolean functions. We establish analogy between the post selection functions and the general probabilistic games in a two party binary input-output scenario. As an observation, we categorize all possible post-selection functions based on the effect on a uniform input probability distribution. We find that post-selection can transform simple no signaling probability distributions to signaling. Similarly, solving NP complete problems is easy independent of classical or quantum computation (in particular we prove that Post RP = NP). Finally, we demonstrate an instance of the violation of the pigeon hole principle independent of underlying theory. As result of our theory independent modeling we conclude that post-selection as an assumption adds power to the underlying theory. In particular, quantum mechanics benefits more with the post-selection assumption, only because it admits a more general set of allowed probabilities as compared to the local hidden variable model. Without the assumption we associate a device independent efficiency factor to quantify the cost of post selection. Our study shows that in the real world post-selection is not efficient enough to be of any advantage. But from an adversarial perspective it is still of significance. As an application, we obtain robust bounds on faking the bell violation in terms of minimum efficiency required using post selection.
- Feb 04 2015 quant-ph arXiv:1502.00857v3It has been suggested that there may exist quantum correlations that go beyond entanglement. The existence of such correlations can be revealed by quantum discord, but not by the conventional measure of entanglement. We argue that a state displays quantumness that can be of local and nonlocal origin. The physical quantity such as the quantum discord probes not only the nonlocal quantumness but also the local quantumness, such as the "local superposition". This can be a reason why such measures are non-zero when there is no entanglement. We consider a generalized version of the Werner state to demonstrate the interplay of local quantumness, nonlocal quantumness, and classical mixedness of a state.
- Dec 01 2014 quant-ph arXiv:1411.7579v1We study the dynamics of quantum dissension for three qubit states in various dissipative channels such as amplitude damping, dephasing and depolarizing. Our study is solely based on Markovian environments where quantum channels are without memory and each qubit is coupled to its own environment. We start with mixed GHZ, mixed W, mixture of separable states, a mixed biseparable state, as the initial states and mostly observe that the decay of quantum dissension is asymptotic in contrast to sudden death of quantum entanglement in similar environments. This is a clear indication of the fact that quantum correlation in general is more robust against the effect of noise. However, for a given class of initial mixed states we find a temporary leap in quantum dissension for a certain interval of time. More precisely, we observe the revival of quantum correlation to happen for certain time period. This signifies that the measure of quantum correlation such as quantum discord, quantum dissension, defined from the information theoretic perspective is different from the correlation defined from the entanglement-separability paradigm and can increase under the effect of the local noise. We also study the effects of these channels on the monogamy score of each of these initial states. Interestingly, we find that for certain class of states and channels, there is change from negative values to positive values of the monogamy score with classical randomness as well as with time. This gives us an important insight in obtaining states which are freely sharable (polygamous state) from the states which are not freely sharable (monogamous). This is indeed a remarkable feature, as we can create monogamous states from polygamous states Monogamous states are considered to have more signatures of quantum ness and can be used for security purpose.
- Nov 18 2014 quant-ph arXiv:1411.4397v3In this work, we extensively study the problem of broadcasting of quantum correlations. This includes broadcasting of quantum entanglement as well as correlations that go beyond the notion of entanglement. It is quite well known from the "No-Broadcasting theorem" that perfect broadcasting of quantum correlation is not possible. However it does not rule out the possibility of partial broadcasting of correlations where we can get lesser correlated states from a given correlated state. In order to have a holistic view of broadcasting, we investigate this problem by starting with most general representation of two qubit mixed states in terms of the Bloch vectors. As a cloning transformation we have used universal symmetric optimal Buzek-Hillery (B-H) cloner both locally and nonlocally. More specifically, we obtain a set of ranges in terms of Bloch vectors for which broadcasting of entanglement will be possible. In addition to the idea of broadcasting of entanglement for general two qubit mixed states, we explore broadcasting of quantum correlations that go beyond entanglement with the help of both local and nonlocal cloners. Remarkably, we find that it is impossible to even partially broadcast such correlations by using both local and nonlocal quantum copying machines. Taking two different types Buzek-Hillery quantum cloners (state dependent and state independent) we analytically prove the impossibility of even partial broadcasting of correlation. Lastly, we generalize this impossibility result for any symmetric or asymmetric cloning machines as well. This result brings out a fundamental difference between the correlation defined from the perspective of entanglement and the correlation measure which claims to go beyond entanglement.
- Oct 28 2014 quant-ph arXiv:1410.7067v2In this brief report we revisit the concept of "quantum dissension", which was introduced as a natural extension of quantum discord for three qubit system. Here we bring in new expression for quantum dissensions and more interestingly we name one such expression as \textitresidual correlation. The basic objective behind the introduction of such a quantity is to capture the extra amount of correlation generated by doing measurement in a correlated system from a situation where we do not bring in a correlated system in the measurement process. Apart from this we also present an operational interpretation of this correlation in context of state merging. Remarkably, we find that for three qubit system if one discards relevant prior information, the change in the cost of state merging ( merging the quantum information of two parties into one) is captured by the \textitresidual correlation. In addition to that we found that this quantity can be negative for mixed states. This indeed opens up a new dimension in the tripartite scenario where we can observe situations where there is a decrease in the cost of state merging on discarding relevant prior information. We claim that this result establishes a re conceptualization of information processing tasks in tripartite situations where we can use suitable measurement and states to bring down the cost of the protocol.
- Feb 12 2014 quant-ph arXiv:1402.2383v2In this work we give a $(n,n)$-threshold protocol for sequential secret sharing of quantum information for the first time. By sequential secret sharing we refer to a situation where the dealer is not having all the secrets at the same time, at the beginning of the protocol; however if the dealer wishes to share secrets at subsequent phases she/he can realize it with the help of our protocol. First of all we present our protocol for three parties and later we generalize it for the situation where we have $(n>3)$ parties. Further in a much more realistic situation, we consider the sharing of qubits through two kinds of noisy channels, namely the phase damping channel (PDC) and the amplitude damping channel (ADC). When we carry out the sequential secret sharing in the presence of noise we observe that the fidelity of secret sharing at the $k^{th}$ iteration is independent of the effect of noise at the $(k-1)^{th}$ iteration. In case of ADC we have seen that the average fidelity of secret sharing drops down to $\frac{1}{2}$ which is equivalent to a random guess of the quantum secret. Interestingly, we find that by applying weak measurements one can enhance the average fidelity. This increase of the average fidelity can be achieved with certain trade off with the success probability of the weak measurements.
- Nov 22 2013 quant-ph arXiv:1311.5378v2In extant quantum secret sharing protocols, once the secret is shared in a quantum network (\textscqnet) it can not be retrieved back, even if the dealer wishes that her secret no longer be available in the network. For instance, if the dealer is part of two \textscqnets, say $\mathcal{Q}_1$ and $\mathcal{Q}_2$ and subsequently finds that $\mathcal{Q}_2$ is more reliable than $\mathcal{Q}_1$, the dealer may wish to transfer all her secrets from $\mathcal{Q}_1$ to $\mathcal{Q}_2$. In this work we address this problem by designing a protocol that enables the source/dealer to bring back the information shared in the network, if desired. Unlike classical revocation, no-cloning-theorem automatically ensures that the secret is no longer shared in the network. The implications of our results are multi-fold. One interesting implication of our technique is the possibility of routing qubits in asynchronous \textscqnets. By asynchrony we mean that the requisite data/resources are intermittently available (but not necessarily simultaneously) in the \textscqnet. For example, we show that a source $S$ can send quantum information to a destination $R$ even though (a) $S$ and $R$ share no quantum resource, (b) $R$'s identity is \em unknown\/to $S$ initially, (c) $S$ herself can be $R$ at a later date and/or in a different location to bequeath her information and (d) the path chosen for routing the secret may hit a dead-end due to resource constraints. Another implication of our technique is the possibility of using \em insecure\/resources. For instance, it may safely store its private information with a neighboring organization without revealing data to the host and losing control over retrieving the data. Putting the two implications together, namely routing and secure storage, it is possible to envision applications like quantum mail (qmail) as an outsourced service.
- Aug 21 2013 quant-ph arXiv:1308.4340v3We quantify the amount of correlation generated between two different output modes in the process of im- perfect cloning and deletion processes. We use three different measures of correlations and study their role in determining the fidelity of the cloning and deletion. We obtain a bound on the total correlation generated in the successive process of cloning and deleting operations. This displays a new kind of complementary relationship between the quantum correlation required in generating a copy of a quantum state and the amount of correlation required in bringing it back to the original state by deleting and vice versa. Our result shows that better we clone (delete) a state, more difficult it will be to bring the state back to its original form by the process of deleting (cloning).
- Oct 05 2012 quant-ph arXiv:1210.1312v4In this work we consider a quantum network consisting of nodes and entangled states connecting the nodes. In evrey node there is a single player. The players at the intermediate nodes carry out measurements to produce an entangled state between the initial and final node. Here we address the problem that how much classical as well as quantum information can be sent from initial node to final node. In this context, we present strong theorems along with proosf, which state that how the teleportation capability of this remotely prepared state is linked up with the fidelities of teleportation of the resource states. Similarly, we analyze the super dense coding capacity of this remotely prepared state in terms of the capacities of the resource entangled states. However, we first obtain the relations involving the amount of entanglement of the resource states with the final state in terms of two different measures of entanglement namely concurrence and entanglement entropy. These relations are quite similar to the bounds obtained in reference \citeGour,Gour1. These results involving the teleportation fidelities and super dense coding capacities have a tremendous future application in the context of determining the amount of quantum and classical information can be sent from a given node to a desired node in a quantum network (QNet).
- Jul 28 2011 quant-ph arXiv:1107.5395v2We introduce the concept of the locally unextendible non-maximally entangled basis (LUNMEB) in $H^d \bigotimes H^d$. It is shown that such a basis consists of $d$ orthogonal vectors for a non-maximally entangled state. However, there can be a maximum of $(d-1)^2$ orthogonal vectors for non-maximally entangled state if it is maximally entangled in $(d-1)$ dimensional subspace. Such a basis plays an important role in determining the number of classical bits that one can send in a superdense coding protocol using a non-maximally entangled state as a resource. By constructing appropriate POVM operators, we find that the number of classical bits one can transmit using a non-maximally entangled state as a resource is $(1+p_0\frac{d}{d-1})\log d$, where $p_0$ is the smallest Schmidt coefficient. However, when the state is maximally entangled in its subspace then one can send up to $2\log (d-1) $ bits. We also find that for $d= 3$, former may be more suitable for the superdense coding.
- Jul 15 2011 quant-ph arXiv:1107.2908v3It is known that there exist non-local correlations that respect no-signaling criterion, but violate Bell-type inequalities more than quantum-mechanical correlations. Such super quantum correlations were introduced as the Popescu-Rohrlich (PR) box. We consider such non-local boxes with two/three inputs and two/three outputs. We show that these super quantum correlations can lead to signaling when at least one of the input bit has access to a word line along a closed time-like curve.
- Dec 28 2010 quant-ph arXiv:1012.5570v3In a realistic situation, the secret sharing of classical or quantum information will involve the transmission of this information through noisy channels. We consider a three qubit pure state. This state becomes a mixed-state when the qubits are distributed over noisy channels. We focus on a specific noisy channel, the phase-damping channel. We propose a protocol for secret sharing of classical information with this and related noisy channels. This protocol can also be thought of as cooperative superdense coding. We also discuss other noisy channels to examine the possibility of secret sharing of classical information.
- Jul 14 2010 quant-ph arXiv:1007.2127v1We utilize quantum discord to charecterize the correlation present in Buzek-Hillery quantum copying machine \citebh (not necessarily universal quantum cloning machine). In other words we quantify the correlation present beetween the original and the replicated copy of the quantum state obtained at the outport port, Interestingly, we find some domain of the machine parameter, for which the quantum disord is non negative even in the mere absence of entanglement. These non zero values of the quantum discord is a strong signature for the presence of non classical correlations. This is one step forward evidence in the support of the fact that quantum discord and entanglement are not synonymous.
- Jul 01 2010 quant-ph arXiv:1006.5784v3We introduce the notion of quantum dissension for a three-qubit system as a measure of quantum correlations. We use three equivalent expressions of three-variable mutual information. Their differences can be zero classically but not so in quantum domain. It generalizes the notion of quantum discord to a multipartite system. There can be multiple definitions of the dissension depending on the nature of projective measurements done on the subsystems. As an illustration, we explore the consequences of these multiple definitions and compare them for three-qubit pure and mixed GHZ and W states. We find that unlike discord, dissension can be negative. This is because measurement on a subsystem may enhance the correlations in the rest of the system. This approach can pave a way to generalize the notion of quantum correlations in the multiparticle setting.
- Jun 10 2010 quant-ph cond-mat.stat-mech arXiv:1006.1856v3In this work, we study quantum correlations in mixed states. The states studied are modeled by a two-qubit system interacting with its environment via a quantum non demolition (purely dephasing) as well as dissipative type of interaction. The entanglement dynamics of this two qubit system is analyzed. We make a comparative study of various measures of quantum correlations, like Concurrence, Bell's inequality, Discord and Teleportation fidelity, on these states, generated by the above evolutions. We classify these evoluted states on basis of various dynamical parameters like bath squeezing parameter $r$, inter-qubit spacing $r_{12}$, temperature $T$ and time of system-bath evolution $t$. In this study, in addition we report the existence of entangled states which do not violate Bell's inequality, but can still be useful as a potential resource for teleportation. Moreover we study the dynamics of quantum as well as classical correlation in presence of dissipative coherence.
- In ordinary quantum theory any mixed state can be purified in an enlarged Hilbert space by bringing an ancillary system. The purified state does not depend on the state of any extraneous system with which the mixed state is going to interact and on the physical interaction. Here, we prove that it is not possible to purify a mixed state that traverses a closed time like curve (CTC) and allowed to interact in a consistent way with a causality-respecting (CR) quantum system in the same manner. Thus, in general for arbitrary interactions between CR and CTC systems there is no universal 'Church of the larger Hilbert space' for mixed states with CTC. This shows that in quantum theory with CTCs there can exist 'proper' and 'improper' mixtures.
- Mar 03 2009 quant-ph arXiv:0903.0248v3In this letter we analyze the efficacy of the entangled output of Pati-Braunstein deletion machine [3] as a teleportation channel. We analyze the possibility of it violating the Bell's inequality. Interestingly we find that for all values of the input parameter$\alpha$ the state does not violate the Bell's inequality but when used as a teleportation channel can give a fidelity higher than the classical optimum (i.e 2/3).
- Jan 29 2009 quant-ph arXiv:0901.4473v2In this work we study a state which is a random mixture of a two qubit subsystem of a $N$-qubit W state and GHZ state. We analyze several possibilities like separability criterion (Peres-Horodecki criterion [14,15]), non violation of Bell's inequality [6]($M(\rho)<1$)and teleportation fidelity [1,2,3,4] ($(F_{max}>{2/3})$) for this state. We also obtain a relationship between $N$ (number of qubits) and $p$ (the classical probability of random mixture) for each of these possibilities. Finally we present a detailed analysis of all these possibilities for $N=3,4,5$ qubit systems. We also report that for N=3 and $p\in(.75,1]$, this entangled state can be used as a teleportation channel without violating Bell's inequality.
- Dec 05 2008 quant-ph arXiv:0812.0967v2Here we described a protocol by which one can broadcast GHZ-type states secretly. We have done this with the help of a cloning machine followed by subsequent measurements. We also made a comparative study of the amount of residual tangle present in these entangled states, obtained as outputs of the measurements.
- Sep 02 2008 quant-ph arXiv:0809.0067v2In this work we describe a protocol by which two of three parties generate two bipartite entangled state among themselves without involving third party, from a non maximal W state or W - type state $|X>=\alpha|001>_{123}+\beta|010>_{123}+\gamma|100>_{123}, \alpha^{2} + \beta^{2} + \gamma^{2} = 1$ shared by three distant partners. Also we have considered the case $\beta=\gamma$, to obtain a range for $\alpha^2$, for which the local output states are separable and non local output states are inseparable. We also find out the dependence of the mixed ness of inseparable states with their amount of inseparability, for that range of $\alpha^2$.
- Apr 17 2008 quant-ph arXiv:0804.2568v1In this work we investigate the problem of secretly broadcasting five qubit entangled state between three different partners We implement the protocol described in ref [16] on three particle W-state shared by three distant partners Alice,Bob and Charlie. The problem is interesting in the sense it is the first attempt to broadcast five qubit entangled state between three parties.
- Mar 25 2008 quant-ph arXiv:0803.3393v3In this work we describe a protocol by which one can secretly broadcast W-type state among three distant partners. This work is interesting in the sense that we introduce a new kind of local cloning operation to generate two W- type states between these partners from a W-type state initially shared by them.
- Dec 11 2007 quant-ph arXiv:0712.1404v2We analyze a possibility of using the two qubit output state from Buzek-Hillery quantum copying machine (not necessarily universal quantum cloning machine) as a teleportation channel. We show that there is a range of values of the machine parameter $\xi$ for which the two qubit output state is entangled and violates Bell-CHSH inequality and for a different range it remains entangled but does not violate Bell-CHSH inequality. Further we observe that for certain values of the machine parameter the two-qubit mixed state can be used as a teleportation channel. The use of the output state from the Buzek-Hillery cloning machine as a teleportation channel provides an additional appeal to the cloning machine and motivation of our present work.
- Jun 28 2007 quant-ph arXiv:0706.4067v1It is a well known fact that an quantum state $|\psi(\theta,\phi)>$ is represented by a point on the Bloch sphere, characterized by two parameters $\theta$ and $\phi$. In a recent work we already proved that it is impossible to partially swap these quantum parameters. Here in this work we will show that this impossibility theorem is consistent with principles like unitarity of quantum mechanics and no signalling principle.
- Jun 13 2007 quant-ph arXiv:0706.1735v2It is known that if one could clone an arbitrary quantum state one could send signal faster than the speed of light. However it remains interesting to see that if one can perfectly self replicate an arbitrary quantum state, does it violate the no signalling principle? Here we see that perfect self replication would also lead to superluminal signalling.
- May 07 2007 quant-ph arXiv:0705.0631v2In this work, we introduce a special kind of quantum cloning machine called Hybrid quantum cloning machine. The introduced Hybrid quantum cloning machine or transformation is nothing but a combination of pre-existing quantum cloning transformations. In this sense it creates its own identity in the field of quantum cloners. Hybrid quantum cloning machine can be of two types: (i) State dependent and (ii) State independent or Universal. We study here the above two types of Hybrid quantum cloning machines. Later we will show that the state dependent hybrid quantum-cloning machine can be applied on only four input states. We will also find in this paper another asymmetric universal quantum cloning machine constructed from the combination of optimal universal B-H quantum cloning machine and universal anti-cloning machine. The fidelities of the two outputs are different and their values lie in the neighborhood of ${5/6} $
- Dec 29 2006 quant-ph arXiv:quant-ph/0612221v2In this work we have introduced two party games with respective winning conditions. One cannot win these games deterministically in the classical world if they are not allowed to communicate at any stage of the game. Interestingly we find out that in quantum world, these winning conditions can be achieved if the players share an entangled state. We also introduced a game which is impossible to win if the players are not allowed to communicate in classical world (both probabilistically and deterministically), yet there exists a perfect quantum strategy by following which, one can attain the winning condition of the game.
- Dec 15 2006 quant-ph arXiv:quant-ph/0612123v2It is a well known fact that a quantum state $|\psi(\theta,\phi)>$ are represented by a point on the Bloch sphere, characterized by two parameters $\theta$ and $\phi$. Here in this work, we find out another impossible operation in quantum information theory . We name this impossibility as 'Impossibility of partial swapping of quantum information '. By this we mean that if two unknown quantum states are given at the input port, there exists no physical process, consistent with the principles of quantum mechanics, by which we can partially swap either of the two parameters $\theta$ and $\phi$ between these two quantum states. In this work we provided the impossibility proofs for the qubits(i.e the quantum states taken from two dimensional Hilbert space) and this impossible operation can be shown to hold in higher dimension also.
- Oct 23 2006 quant-ph arXiv:quant-ph/0610171v1In this work we show that one cannot use non-local resources for probabilistic signalling even if one can delete a quantum state with the help of probabilistic quantum deletion machine. Here we find that probabilistic quantum deletion machine is not going to help us in identifying two statistical mixture at remote location. Also we derive the bound on deletion probability from no-signalling condition.
- Oct 23 2006 quant-ph arXiv:quant-ph/0610177v1The paper deals with the generalization of both Boltzmann entropy and distribution in the light of most-probable interpretation of statistical equilibrium. The statistical analysis of the generalized entropy and distribution leads to some new interesting results of significant physical importance.
- Aug 03 2006 quant-ph arXiv:quant-ph/0608023v1We know that we cannot split the information encoded in two non-orthogonal qubits into complementary parts deterministically. Here we show that each of the copies of the state randomly selected from a set of non orthogonal linearly independent states, splitting of quantum information can not be done even probabilistically. Here in this work we also show that under certain restricted conditions, we can probabilistically split the quantum information encoded in a qubit.
- May 23 2006 quant-ph arXiv:quant-ph/0605185v3In this work we investigate that whether one can construct single and two qubit gates for arbitrary quantum states from the principle of no signalling. We considered the problem for Pauli gates, Hadamard gate, C-Not gate.
- May 23 2006 quant-ph arXiv:quant-ph/0605186v3In this letter, we show the impossibility of the general operation introduced by Pati [3] using two different but consistent principles (i) no-signalling (ii) non increase of entanglement under LOCC.
- May 22 2006 quant-ph arXiv:quant-ph/0605173v1It is known that the stronger no-cloning theorem and the no-deleting theorem taken together provide the permanence property of quantum information. Also, it is known that the violation of the no-deletion theorem would imply signalling. Here, we show that the violation of the stronger no-cloning theorem could lead to signalling. Furthermore, we prove the stronger no-cloning theorem from the conservation of quantum information. These observations imply that the permanence property of quantum information is connected to the no-signalling and the conservation of quantum information.
- Feb 02 2006 quant-ph arXiv:quant-ph/0602016v3In this work, we show that 'splitting of quantum information' [6] is an impossible task from three different but consistent principles of unitarity of Quantum Mechanics, no-signalling condition and non increase of entanglement under Local Operation and Classical Communication.
- Jan 30 2006 quant-ph arXiv:quant-ph/0601181v2Suppose we are given an entangled pair and then one can ask how well we can produce two entangled pairs starting from a given entangled pair using only local operations. To give response of the above asked question, we study broadcasting of entanglement using state dependent quantum cloning machine as a local copier. We show that the length of the interval for probability-amplitude-squared for broadcasting of entanglement using state dependent cloner can be made larger than the length of the interval for probability-amplitude-squared for broadcasting entanglement using state independent cloner. Further we show that there exists local state dependent cloner which gives better quality copy (in terms of average fidelity) of an entangled pair than the local universal cloner.
- Nov 23 2005 quant-ph arXiv:quant-ph/0511211v1In this work we prescribe a more generalized quantum-deleting machine (input state dependent). The fidelity of deletion is dependent on some machine parameters such that on alteration of machine parameters we get back to standard deleting machines. We also carried out a various comparative study of various kinds of quantum deleting machines. We also plotted graphs, making a comparative study of fidelity of deletion of the deletion machines, obtained as particular cases on changing the machine parameters of our machine.
- Nov 18 2005 quant-ph arXiv:quant-ph/0511169v1The paper deals with the reformulation of quantum uncertainty relation involving position and momentum of a particle on the basis of the Kerridge measure of inaccuracy and the Fisher information.
- Nov 18 2005 quant-ph arXiv:quant-ph/0511171v1We have presented a new axiomatic derivation of Shannon Entropy for a discrete probability distribution on the basis of the postulates of additivity and concavity of the entropy function.We have then modified shannon entropy to take account of observational uncertainty.The modified entropy reduces, in the limiting case, to the form of Shannon differential entropy. As an application we have derived the expression for classical entropy of statistical mechanics from the quantized form of the entropy.
- Nov 17 2005 quant-ph arXiv:quant-ph/0511158v3This article discusses the important primitives of Superposition and Entanglement in Quantum Information Processing from physics point of view. System of spin-1/2 particles has been considered which presents itself as a logical and conceptual candidate to understand these concepts. The article is intended as a review of these important concepts and hopes to bring forth a conceptual framework in this regard.
- Oct 31 2005 quant-ph arXiv:quant-ph/0510221v6In this letter we establish the impossibility of existence of self replicating machine in the quantum world. We establish this result by three different but consistent approaches of linearity of quantum mechanics, no signalling condition and conservation of entanglement under local unitary operations.