results for au:Dogra_S in:quant-ph

- Mar 20 2017 quant-ph arXiv:1703.06102v1We use the Majorana geometrical representation for a qutrit, where a pair of points on a unit sphere represents its quantum states. A canonical form for qutrit states is presented, where every qutrit state can be obtained from a one-parameter family of states via $SO(3)$ action. The notion of spin-1 magnetization which is invariant under $SO(3)$, is discussed and geometrically interpreted on the Majorana sphere. We study the dynamics of the pair of points representing a qutrit state under various useful quantum operations and connect them to different NMR operations. In our scheme, the rigid rotation of this pair of points under $SO(3)$ corresponds to non-selective pulses in NMR, while transition-selective NMR pulses are generated by the eight generators of $SU(3)$ and typically lead to the movement of only one point at a time on the Majorana sphere. Using the Majorana picture, we also describe the action of several quantum gates and the insights gained, are used to perform experiments on a spin-1 system (the NMR qutrit) oriented in a liquid crystalline environment. Finally, using the Gell Mann matrix picture we describe and experimentally implement a scheme for complete qutrit state tomography.
- Feb 09 2017 quant-ph arXiv:1702.02418v1The principle of superposition is an intriguing feature of Quantum Mechanics, which is regularly exploited at various instances. A recent work [PRL \textbf116, 110403 (2016)] shows that the fundamentals of Quantum Mechanics restrict the superposition of two arbitrary pure states of a quantum system, even though it is possible to superpose two quantum states with partial prior knowledge. The prior knowledge imposes geometrical constraints on the choice of input pure states. We discuss an experimentally feasible protocol to superpose multiple pure states of a $d$ dimensional quantum system and carry out an explicit experimental realization to superpose two single-qubit pure states on a two-qubit NMR quantum information processor.
- Nov 03 2015 quant-ph arXiv:1511.00241v1We experimentally test quantum contextuality of a single qutrit using NMR. The contextuality inequalities based on nine observables developed by Kurzynski et. al. are first reformulated in terms of traceless observables which can be measured in an NMR experiment. These inequalities reveal the contextuality of almost all single-qutrit states. We demonstrate the violation of the inequality on four different initial states of a spin-1 deuterium nucleus oriented in a liquid crystal matrix, and follow the violation as the states evolve in time. We also describe and experimentally perform a single-shot test of contextuality for a subclass of qutrit states whose density matrix is diagonal in the energy basis.
- Apr 21 2015 quant-ph arXiv:1504.04856v1We experimentally construct a novel three-qubit entangled W-superposition ($\rm W \bar{\rm W}$) state on an NMR quantum information processor. We give a measurement-based filtration protocol for the invertible local operation (ILO) that converts the $\rm W \bar{\rm W}$ state to the GHZ state, using a register of three ancilla qubits. Further we implement an experimental protocol to reconstruct full information about the three-party $\rm W \bar{\rm W}$ state using only two-party reduced density matrices. An intriguing fact unearthed recently is that the $\rm W \bar{\rm W}$ state which is equivalent to the GHZ state under ILO, is in fact reconstructible from its two-party reduced density matrices, unlike the GHZ state. We hence demonstrate that although the $\rm W \bar{\rm W}$ state is interconvertible with the GHZ state, it stores entanglement very differently.
- Mar 24 2015 quant-ph arXiv:1503.06624v1The quantum Fourier transform (QFT) is a key ingredient of several quantum algorithms and a qudit-specific implementation of the QFT is hence an important step toward the realization of qudit-based quantum computers. This work develops a circuit decomposition of the QFT for hybrid qudits based on generalized Hadamard and generalized controlled-phase gates, which can be implemented using selective rotations in NMR. We experimentally implement the hybrid qudit QFT on an NMR quantum emulator, which uses four qubits to emulate a single qutrit coupled to two qubits.
- Jul 15 2014 quant-ph arXiv:1407.3448v2We experimentally explore the state space of three qubits on an NMR quantum information processor. We construct a scheme to experimentally realize a canonical form for general three-qubit states up to single-qubit unitaries. This form involves a non-trivial combination of GHZ and W-type maximally entangled states of three qubits. The general circuit that we have constructed for the generic state reduces to those for GHZ and W states as special cases. The experimental construction of a generic state is carried out for a nontrivial set of parameters and the good fidelity of preparation is confirmed by complete state tomography. The GHZ and W-states are constructed as special cases of the general experimental scheme. Further, we experimentally demonstrate a curious fact about three-qubit states, where for almost all pure states, the two-qubit reduced states can be used to reconstruct the full three-qubit state. For the case of a generic state and for the W-state, we demonstrate this method of reconstruction by comparing it with the directly tomographed three-qubit state.
- Jun 20 2014 quant-ph arXiv:1406.5026v1We present the NMR implementation of a recently proposed quantum algorithm to find the parity of a permutation. In the usual qubit model of quantum computation, speedup requires the presence of entanglement and thus cannot be achieved by a single qubit. On the other hand, a qutrit is qualitatively more quantum than a qubit because of the existence of quantum contextuality and a single qutrit can be used for computing. We use the deuterium nucleus oriented in a liquid crystal as the experimental qutrit. This is the first experimental exploitation of a single qutrit to carry out a computational task.