Guruprasad Kar

Distinguishability of Bell states.

More than two multipartite orthogonal states cannot always be discriminated if only local operations and classical communication (LOCC) are allowed. We show that four Bell states cannot be discriminated by LOCC, even probabilistically, using the separability properties of a four-party unlockable bound entangled state. Using an existing inequality among the measures of entanglement, we show that any three Bell states cannot be discriminated with certainty by LOCC. Exploiting the inequality, we calculate the distillable entanglement of a certain class of 4 multiply sign in circle 4 mixed 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.

Distinguishability of maximally entangled states

In 2x2, more than two orthogonal Bell states with a single copy can never be discriminated with certainty if only local operations and classical communication (LOCC) are allowed. We show here that more than d numbers of pairwise orthogonal maximally entangled states in dxd, which are in canonical form, used by Bennett et al. [Phys. Rev. Lett. 70, 1895 (1993)], can never be discriminated with certainty by LOCC, when single copies of the states are provided. Interestingly we show here that all orthogonal maximally entangled states, which are in canonical form, can be discriminated with certainty by LOCC if and only if two copies of each of the states are provided. We provide here a conjecture regarding the highly nontrivial problem of local distinguishability of any d or fewer numbers of pairwise orthogonal maximally entangled states in dxd (in the single copy case)

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.

Degree of complementarity determines the nonlocality in quantum mechanics

Complementarity principle is one of the central concepts in quantum mechanics which restricts joint measurement for certain observables. Of course, later development shows that joint measurement could be possible for such observables with the introduction of a certain degree of unsharpness or fuzziness in the measurement. In this paper, we show that the optimal degree of unsharpness, which guarantees the joint measurement of all possible pairs of dichotomic observables, determines the degree of nonlocality in quantum mechanics as well as in more general no-signaling theories.

Local indistinguishability of orthogonal pure states by using a bound on distillable entanglement

We show that the four states a‖00>+b‖11>, b‖00>-a‖11>, c‖01>+d‖10>, and d‖01>-c‖10>cannot be discriminated with certainty if only local operations and classical communication (LOCC) are allowed and if only a single copy is provided, except in the case when they are simply ‖00>, ‖11>, ‖01>, and ‖10> (in which case they are trivially distinguishable with LOCC). We go on to show that there exists a continuous range of values of a, b, c, and d such that even three states among the above four are not locally distinguishable, if only a single copy is provided. The proof follows from the fact that logarithmic negativity is an upper bound of distillable entanglement.

Optimal cloning and no signaling

Abstract It is shown that the no signaling constraint generates the whole class of 1 → 2 optimal quantum cloning machines of single qubits

Local cloning of Bell states and distillable entanglement

The necessary and sufficient amount of entanglement required for cloning of orthogonal Bell states by local operation and classical communication is derived, and using this result we provide here some additional examples of reversible as well as irreversible states.

No-flipping as a consequence of no-signalling and non-increase of entanglement under LOCC

Abstract Non-existence of universal flipper for arbitrary quantum states is a fundamental constraint on the allowed operations performed on physical systems. The largest set of qubits that can be flipped by a single machine is a great circle of the Bloch-sphere. In this Letter, we show the impossibility of universal exact-flipping operation, first by using the fact that no faster than light communication is possible and then by using the principle of “non-increase of entanglement under LOCC”. Interestingly, in both the cases, there is no violation of the two principles if and only if the set of states to be flipped, form a great circle.

Unsharp spin-12 observables and CHSH inequalities

Abstract A quantitative study of the unsharpness needed for unsharp spin - 1 2 observables to satisfy the Bell/CHSH inequalities shows that the result obtained by Busch has to be corrected due to unexpected correlations. It is also demonstrated that the original Bell inequality is inappropriate for unsharp spin observables.