Somshubhro Bandyopadhyay

Teleportation and secret sharing with pure entangled states

We present two optimal methods of teleporting an unknown qubit using any pure entangled state. We also discuss how such methods can also have successful application in quantum secret sharing with pure multipartite entangled states.

Bell's inequality for a single spin-1/2 particle and quantum contextuality

Abstract We argue that for a single particle Bells inequality is a consequence of noncontextuality and is incompatible with statistical predictions of quantum mechanics. Thus noncontextual models can be empirically falsified, independent of locality condition. For this an appropriate entanglement between disjoint Hilbert spaces pertaining to translational and spin degrees of freedom of a single spin-1/2 particle is invoked.

Entanglement observables and witnesses for interacting quantum spin systems

We discuss the detection of entanglement in interacting quantum spin systems. First, thermodynamic Hamiltonian-based witnesses are computed for a general class of one-dimensional spin-1/2 models. Second, we introduce optimal bipartite entanglement observables. We show that a bipartite entanglement measure can generally be associated with a set of independent two-body spin observables whose expectation values can be used to witness entanglement. The number of necessary observables is ruled by the symmetries of the model. Illustrative examples are presented.

LOCC distinguishability of unilaterally transformable quantum states

We consider the question of perfect local distinguishability of mutually orthogonal bipartite quantum states, with the property that every state can be specified by a unitary operator acting on the local Hilbert space of Bob. We show that if the states can be exactly discriminated by one-way local operations and classical communication (LOCC) where Alice goes first, then the unitary operators can also be perfectly distinguished by an orthogonal measurement on Bobs Hilbert space. We give examples of sets of N ≤ d maximally entangled states in d⊗d for d = 4,5,6 that are not perfectly distinguishable by one-way LOCC. Interestingly, for d = 5,6, our examples consist of four and five states, respectively. We conjecture that these states cannot be perfectly discriminated by two-way LOCC.

Conclusive exclusion of quantum states

In the task of quantum state exclusion, we consider a quantum system prepared in a state chosen from a known set. The aim is to perform a measurement on the system which can conclusively rule that a subset of the possible preparation procedures cannot have taken place. We ask what conditions the set of states must obey in order for this to be possible and how well we can complete the task when it is not. The task of quantum state discrimination forms a subclass of this set of problems. Within this paper, we formulate the general problem as a semidefinite program (SDP), enabling us to derive sufficient and necessary conditions for a measurement to be optimal. Furthermore, we obtain a necessary condition on the set of states for exclusion to be achievable with certainty, and we give a construction for a lower bound on the probability of error. This task of conclusively excluding states has gained importance in the context of the foundations of quantum mechanics due to a result from Pusey, Barrett, and Rudolph (PBR). Motivated by this, we use our SDP to derive a bound on how well a class of hidden variable models can perform at a particular task, proving an analog of Tsirelsons bound for the PBR experiment and the optimality of a measurement given by PBR in the process. We also introduce variations of conclusive exclusion, including unambiguous state exclusion, and state exclusion with worst-case error.

Entangling capacities of noisy two-qubit Hamiltonians

We study the limits imposed by intrinsic fluctuations in system-control parameters on the ability of two-qubit (exchange) Hamiltonians to generate entanglement, starting from arbitrary initial states. We find three classes for Gaussian and Laplacian fluctuations. For the Ising and XYZ models there are qualitatively distinct, sharp entanglement-generation transitions, while the class of Heisenberg, XY, and XXZ Hamiltonians is capable of generating entanglement for any finite noise level. Our findings imply that exchange Hamiltonians are surprisingly robust in their ability to generate entanglement in the presence of noise, thus potentially reducing the need for quantum error correction.

Origin of noisy states whose teleportation fidelity can be enhanced through dissipation

Recently, Badziag et al. [Phys. Rev. A 62, 012311 (2000)] obtained a class of noisy states whose teleportation fidelity can be enhanced by subjecting one of the qubits to dissipative interaction with the environment via an amplitude damping channel (ADC). We show that such noisy states result while sharing the states

Non-full rank bound entangled states satisfying the range criterion

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Limitations on Separable Measurements by Convex Optimization

across the ADC. We also show that under similar dissipative interactions, different Bell states give rise to noisy entangled states that are qualitatively very different from each other in the sense that only the noisy entangled states constructed from the Bell states

Entanglement cost of nonlocal measurements

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