# Top arXiv papers

• Apr 24 2014 quant-ph cs.IT math.IT
The Polyanskiy-Verdú paradigm provides an elegant way of using generalized-divergences to obtain strong converses and thus far has remained confined to protocols involving channels (classical or quantum). In this paper, drawing inspirations from it, we provide strong converses for protocols involving LOCC (local operations and classical communication). The key quantity that we work with is the Rényi relative entropy of entanglement. We provide a strong converse for the quantum state merging protocol that gives an exponential decay of the fidelity of the protocol for rates below the optimum with the number of copies of the state and are provided both for entanglement rate with LOCC as well as for classical communication with one-way LOCC. As an aside, the developments also yield short strong converses for the entanglement-concentration of pure states and the Schumacher compression.
• Apr 24 2014 quant-ph
We introduce the strong security of quantum ramp secret sharing by translating the corresponding notion of classical ramp secret sharing. Then we propose an explicit construction of quantum ramp secret sharing scheme with strong security. The sizes of a secret and shares are the same as those of the conventional quantum ramp secret sharing scheme by Ogawa et al.
• We introduce a new class of continuous matrix product (CMP) states and establish the stochastic master equations (quantum filters) for an arbitrary quantum system probed by a bosonic input field in this class of states. We show that this class of CMP states arise naturally as outputs of a Markovian model, and that input fields in these states lead to master and filtering (quantum trajectory) equations which are matrix-valued. Furthermore, it is shown that this class of continuous matrix product states include the (continuous-mode) single photon and time-ordered multi-photon states.
• Quantum networks play an important role in the implementation of quantum computing, communication and metrology. Circuit quantum electrodynamics (QED), consisting of superconducting artificial atoms coupled to on-chip resonators, provides a prime candidate to implement these networks due to their controllability and scalability. Furthermore, recent advances have also pushed the technology to the ultrastrong coupling (USC) regime of light-matter interaction, where the qubit-cavity coupling strength reaches a considerable fraction of the cavity frequency. Here, we propose the implementation of a scalable quantum random-access memory (QRAM) architecture based on a circuit QED network, whose edges operate in the USC regime. In particular, we study the storage and retrieval of quantum information in a parity-protected quantum memory and propose quantum interconnects in experimentally feasible schemes. Our proposal may pave the way for novel quantum memory applications ranging from entangled-state cryptography, teleportation, purification, fault-tolerant quantum computation, to quantum simulations.
• Apr 24 2014 hep-th gr-qc
We prove the generalized Covariant Entropy Bound, $\Delta S\leq (A-A')/4G\hbar$, for light-sheets with initial area $A$ and final area $A'$. The entropy $\Delta S$ is defined as a difference of von Neumann entropies of an arbitrary state and the vacuum, with both states restricted to the light-sheet under consideration. The proof applies to free fields, in the limit where gravitational backreaction is small. We do not assume the null energy condition. In regions where it is violated, we find that the bound is protected by the defining property of light-sheets: that their null generators are nowhere expanding.
• In analogy to transistors in classical electronic circuits, a quantum optical switch is an important element of quantum circuits and quantum networks. Operated at the fundamental limit where a single quantum of light or matter controls another field or material system, it may enable fascinating applications such as long-distance quantum communication, distributed quantum information processing and metrology, and the exploration of novel quantum states of matter. Here, by strongly coupling a photon to a single atom trapped in the near field of a nanoscale photonic crystal cavity, we realize a system where a single atom switches the phase of a photon, and a single photon modifies the atom's phase. We experimentally demonstrate an atom-induced optical phase shift that is nonlinear at the two-photon level, a photon number router that separates individual photons and photon pairs into different output modes, and a single-photon switch where a single "gate" photon controls the propagation of a subsequent probe field. These techniques pave the way towards integrated quantum nanophotonic networks involving multiple atomic nodes connected by guided light.
• Apr 24 2014 cs.CG cs.DM cs.DS
We show that any $y$-monotone poly-line drawing can be straightened out while maintaining $y$-coordinates and height. The width may increase much, but we also show that on some graphs exponential width is required if we do not want to increase the height. Likewise $y$-monotonicity is required: there are poly-line drawings (not $y$-monotone) that cannot be straightened out while maintaining the height. We give some applications of our result.
• Apr 24 2014 math.GT
In view of the self-linking invariant, the number $|K|$ of framed knots in $S^3$ with given underlying knot $K$ is infinite. In fact, the second author previously defined affine self-linking invariants and used them to show that $|K|$ is infinite for every knot in an orientable manifold unless the manifold contains a connected sum factor of $S^1\times S^2$; the knot $K$ need not be zero-homologous and the manifold is not required to be compact. We show that when $M$ is orientable, the number $|K|$ is infinite unless $K$ intersects a non-separating sphere at exactly one point, in which case $|K|=2$; the existence of a non-separating sphere implies that $M$ contains a connected sum factor of $S^1\times S^2$. For knots in nonorientable manifolds we show that if $|K|$ is finite, then $K$ is disorienting, or there is an isotopy from the knot to itself which changes the orientation of its normal bundle, or it intersects some embedded $S^2$ or $\mathbb R P^2$ at exactly one point, or it intersects some embedded $S^2$ at exactly two points in such a way that a closed curve consisting of an arc in $K$ between the intersection points and an arc in $S^2$ is disorienting.
• We present a theory of magnetotransport through an electronic orbital, where the electron spin interacts with a (sufficiently) large external spin via an exchange interaction. Using a semiclassical approximation, we derive a set of equations of motions for the electron density matrix and the mean value of the external spin that turns out to be highly non-linear. The dissipation via the electronic leads are implemented in terms of a quantum master equation that is combined with the non-linear terms of the spin-spin interaction. With an anisotropic exchange coupling a variety of dynamics is generated, such as self-sustained oscillations with parametric resonances or even chaotic behavior. Within our theory we can integrate a Maxwell demon-like closed-loop feedback scheme, that is capable of transporting particles against an applied bias voltage and that can be used to implement a spin filter to generate spin-dependent oscillating currents of opposite directions.
• Quantum discord is a function of density-matrix elements (and through them, e.~g., of temperature, applied fields, time, and so forth). The domain of such a function in the case of two-qubit system with X or centrosymmetric (CS) density matrix can consist at most of three subdomains: two ones, where the quantum discord is expressed in closed analytical forms (Q_0 and Q_\pi/2), and an intermediate subdomain in which for determining the quantum discord Q_\theta it is required to solve numerically a one-dimensional minimization problem to find the optimal measurement angle \theta∈(0,\pi/2). Exact equations for determining the boundaries between these subdomains are obtained and solved for a number of models. The Q_\theta subdomains are discovered in the anisotropic spin dimers in external field. On the other hand, coinciding boundaries and therefore sudden transitions between optimal measurement angles \theta=\pi/2 and \theta=0 are observed in dynamics of spin currying particles in closed nanopore and also in phase flip channels. In latter cases the solutions are entirely analytical.
• Apr 24 2014 cs.IT math.IT
Spatially-coupled LDPC codes are known to have excellent asymptotic properties. Much less is known regarding their finite-length performance. We propose a scaling law to predict the error probability of finite-length spatially coupled ensembles when transmission takes place over the binary erasure channel. We discuss how the parameters of the scaling law are connected to fundamental quantities appearing in the asymptotic analysis of these ensembles and we verify that the predictions of the scaling law fit well to the data derived from simulations over a wide range of parameters. The ultimate goal of this line of research is to develop analytic tools for the design of good finite-length error correcting codes.
• Apr 24 2014 cs.IT cs.CR math.IT
We consider information theoretic secret key agreement and secure function computation by multiple parties observing correlated data, with access to an interactive public communication channel. Our main result is an upper bound on the secret key length, which is derived using a reduction of binary hypothesis testing to multiparty secret key agreement. Building on this basic result, we derive new converses for multiparty secret key agreement. Furthermore, we derive converse results for the oblivious transfer problem and the bit commitment problem by relating them to secret key agreement. Finally, we derive a necessary condition for the feasibility of secure computing by trusted parties that seek to compute a function of their collective data, using interactive public communication that by itself does not give away the value of the function. In many cases, we strengthen and improve upon previously known converse bounds. Our results are single-shot and do not assume that the observations are independent and identically distributed. For the case when the observations are indeed independent and identically distributed, we derive strong versions of previously known converses.
• Apr 24 2014 math.OC cs.AI
Multi-stage optimization under uncertainty techniques can be used to solve long-term management problems. Although many optimization modeling language extensions as well as computational environments have been proposed, the acceptance of this technique is generally low, due to the inherent complexity of the modeling and solution process. In this paper a simplification to annotate multi-stage decision problems under uncertainty is presented - this simplification contrasts with the common approach to create an extension on top of an existing optimization modeling language. This leads to the definition of meta models, which can be instanced in various programming languages. An example using the statistical computing language R is shown.
• Apr 24 2014 quant-ph
It has been shown in earlier works that the vertices of Platonic solids are good measurement choices for tests of EPR-steering using isotropically entangled pairs of qubits. Such measurements are regularly spaced, and measurement diversity is a good feature for making EPR-steering inequalities easier to violate in the presence of experimental imperfections. However, such measurements are provably suboptimal. Here, we develop a method for devising optimal strategies for tests of EPR-steering, in the sense of being most robust to mixture and inefficiency (while still closing the detection loophole of course), for a given number $n$ of measurement settings. We allow for arbitrary measurement directions, and arbitrary weightings of the outcomes in the EPR-steering inequality. This is a difficult optimization problem for large $n$, so we also consider more practical ways of constructing near-optimal EPR-steering inequalities in this limit.
• Apr 24 2014 cs.GT
• Apr 24 2014 astro-ph.SR
• Apr 24 2014 physics.optics quant-ph
• Apr 24 2014 math.PR math-ph math.MP
• Apr 24 2014 astro-ph.SR
• Apr 24 2014 math.DG math.QA
• Apr 24 2014 nucl-th nucl-ex
• Apr 24 2014 math.OA
• Apr 24 2014 math.NA
• Apr 24 2014 hep-lat
• Apr 24 2014 cs.AR
• Apr 24 2014 math.OC
• Apr 24 2014 cs.IT math.IT
• Apr 24 2014 hep-th
• Apr 24 2014 astro-ph.SR
• Apr 24 2014 cond-mat.mtrl-sci
• Apr 24 2014 astro-ph.SR
• Apr 24 2014 cond-mat.mtrl-sci
• Apr 24 2014 cond-mat.str-el
• Apr 24 2014 astro-ph.GA astro-ph.HE
• Apr 24 2014 hep-ph astro-ph.HE
• Apr 24 2014 cs.ET
• Apr 24 2014 astro-ph.CO hep-ph
• Apr 24 2014 math.AP
• Apr 24 2014 q-bio.PE
• Apr 24 2014 quant-ph hep-th
• Apr 24 2014 nucl-th hep-ph
• Apr 24 2014 physics.flu-dyn
• Apr 24 2014 astro-ph.IM
• Apr 24 2014 cs.SI cs.CY physics.soc-ph
• Apr 24 2014 math.AP math-ph math.MP
• Apr 24 2014 stat.ML cs.LG
• Apr 24 2014 astro-ph.SR
• Apr 24 2014 cs.SY
• Apr 24 2014 math.DS math.SG
• Apr 24 2014 math.HO
• Apr 24 2014 math.KT
• Apr 24 2014 math.PR math-ph math.MP
• Apr 24 2014 cs.GT
• Apr 24 2014 astro-ph.SR
• Apr 24 2014 hep-ph hep-lat
• Apr 24 2014 cs.IT math.IT
• Apr 24 2014 quant-ph math.LO
• Apr 24 2014 math.CO math.PR
• Apr 24 2014 math.ST stat.TH
• Apr 24 2014 math.GT math.DS
• Apr 24 2014 hep-ph hep-th

Piotr Migdał 6 days ago
A podcast summarizing this paper, by Geoff Engelstein: [The Dice Tower # 351 - Dealing with the Mockers (43:55 - 50:36)](http://dicetower.coolstuffinc.com/tdt-351-dealing-with-the-mockers), and [an alternative link on the BoardGameGeek](http://boardgamegeek.com/boardgamepodcastepisode/117163/tdt-351 ...(continued)
Matt Hastings 16 days ago
Glad the coarse-graining is clear now. Regarding separating out a qubit, my claim is not just that if sites 1,N are in a pure state one can separate out a qubit. I also claim that even if sites 1,N are in a mixed state of the form $\sum_{\text{correctable errors} E_1 \text{and} E_2} p(E_1,E_2) E_1 ...(continued) Ari Mizel 16 days ago Thanks for clearing things up about the definition of coarse-graining; I guess I thought the name suggested some kind of real-space renormalization. About separating out a qubit: I wrote that one expects "the result to be close to a mixed state like$∑_{\text{correctable errors } E_1 \text{ and } ...(continued)
Matt Hastings 17 days ago
Hi Ari, let me reply to your second point first, since I think there may be a misunderstanding about "coarse-graining". If we mistakenly treated the polylog chains as a single spin-1/2 chain, this would give an incorrect result, but I certainly did not suggest doing anything like that. Instead,if ...(continued)
Ari Mizel 17 days ago
Matt, I still take issue with the coarse-graining approach. 1) You wrote "When we say "close to maximal entanglement", we mean we can separate out a qubit from coarse-grained spin 1 and a qubit from coarse-grained spin N (let me stick to my notation) and those two qubits are close to maximally enta ...(continued)
Matt Hastings 20 days ago
One can indeed always ask this coarse-graining question, and one important issue is how strong the resulting interactions are. The coarse-graining itself is definitely well-defined, the question is whether one correctly treats the resulting 1d system. In this case, there is a variational argument ...(continued)
Ari Mizel 20 days ago
You raise an interesting question. It can perhaps be simplified slightly by imagining a quantum circuit that initializes 2 qubits to |0>, generates an EPR pair between qubits 1 and 2, then applies N-1 identity gates to qubit 2. The circuit can be turned into a fault-tolerant version of itself, and ...(continued)
Matt Hastings 21 days ago
I am curious about the following setting. Consider a quantum circuit that initializes N qubits to |0>, then generates an EPR pair in qubits 1 and 2, and then applies SWAPs to move the qubit from 2 to 3 to 4 to ... to N, leaving ultimately an EPR pair between 1 and N. This can be turned into some f ...(continued)
Jarrod McClean 22 days ago
Ryan is exactly correct. The method would work with any of the clock constructions, however we decided that the machinery they developed to make sure it was implementable in qubits was unnecessary overhead for a classical implementation, where having a qudit with large d does not present a great ch ...(continued)
Ari Mizel 22 days ago
Thanks for the remark, Steve. I do not have additional numerics, but I don't think that the translational invariance plays an important role in the spin-wave form of the excitations. I think that the local excitations approximately satisfy a tight-binding Hamiltonian with hopping between adjacent ...(continued)