Samir Kunkri

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.

Hardy's nonlocality argument as a witness for postquantum correlations

Recently, Gallego et.al. [Phys. Rev. Lett 107, 210403 (2011)] proved that any future information principle aiming at distinguishing between quantum and post-quantum correlation must be intrinsically multipartite in nature. We establish similar result by using device independent success probability of Hardys nonlocality argument for tripartite quantum system. We construct an example of a tri-partite Hardy correlation which is post-quantum but satisfies not only all bipartite information principle but also the GYNI inequality.

Optimal free will on one side in reproducing the singlet correlation

Bell’s theorem teaches us that there are quantum correlations that cannot be simulated by just shared randomness (local hidden variable). There are some recent results which simulate the singlet correlation by using either 1 bit or a binary (no-signaling) correlation which violates Bell’s inequality maximally. But there is one more possible way to simulate quantum correlation by relaxing the condition of independency of measurement on shared randomness. Recently, Hall showed that the statistics of a singlet state can be generated by sacrificing measurement independence where underlying distribution of hidden variables depends on measurement directions of both parties (Hall 2010 Phys. Rev. Lett. 105 250404). He also proved that for any model of singlet correlation, 86% measurement independence is optimal. In this paper, we show that 59% measurement independence is optimal for simulating the singlet correlation when the underlying distribution of hidden variables depends only on the measurements of one party. We also show that a distribution corresponding to this optimal lack of free will already exists in the literature which first appeared in the context of detection efficiency loophole (Gisin and Gisin 1999 Phys. Lett. A 323–7).

A complementary relation between classical bits and randomness in local part in the simulating singlet state

Recently, simulating the statistics of the singlet state with non-quantum resources has generated much interest. The singlet state statistics can be simulated by 1 bit of classical communication without using any further non-local correlation. But, interestingly, the singlet state statistics can also be simulated with no classical cost if a non-local box is used. In the first case, the output is completely deterministic whereas in the second case, outputs are completely random. We suggest a (possibly) signaling correlation resource which successfully simulates the singlet statistics, and subsequently leads to a complementary relation between the required classical bits and randomness in the local output involved in the simulation. Our result reproduces the above two models of simulation as extreme cases. We also discuss some important features in Leggetts non-local model and the model presented by Groblacher et al.

Locally accessible information and distillation of entanglement

A different type of complementarity relation is found between locally accessible information and final average entanglement for a given ensemble. It is also shown that in some well-known distillation protocols, this complementary relation is optimally satisfied. We discuss the interesting trade-off between locally accessible information and distillable entanglement for some states.

Nonlocality without inequality for spin-s systems

We critically review earlier works on Hardys nonlocality argument for two spin-s systems and show that solutions previously found in this regard were restricted due to imposition of some conditions which have no role in the argument of nonlocality. We provide a compact form of the nonlocality condition for two spin-s particles, and we also extend it to n number of spin-s particles. Finally we apply a more general kind of nonlocality argument, still without an inequality, to higher-spin systems.

Local simulation of singlet statistics for a restricted set of measurements

The essence of Bell’s theorem is that, in general, quantum statistics cannot be reproduced by a local hidden variable (LHV) model. This impossibility is strongly manifested when statistics collected by measuring certain local observables on a singlet state, violates the Bell inequality. In this work, we search for local POVMs with binary outcomes for which an LHV model can be constructed for a singlet state. We provide various subsets of observables for which an LHV model can be provided for singlet statistics.

Nonlocality without inequality for almost all two-qubit entangled states based on Cabello's nonlocality argument

Here we deal with a nonlocality argument proposed by Cabello, which is more general than Hardys nonlocality argument, but still maximally entangled states do not respond. However, for most of the other entangled states, maximum probability of success of this argument is more than that of the Hardys argument.

Local orthogonality provides a tight upper bound for Hardy's nonlocality

The amount of nonlocality in quantum theory is limited compared to that allowed in generalized no-signaling theory [Found. Phys. 24, 379 (1994)]. This feature, for example, gets manifested in the amount of Bell inequality violation as well as in the degree of success probability of Hardys (Cabellos) nonlocality argument. Physical principles like information causality and macroscopic locality have been proposed for analyzing restricted nonlocality in quantum mechanics---viz. explaining the Cirelson bound. However, these principles are not that much successful in explaining the maximum success probability of Hardys as well as Cabellos argument in quantum theory. Here we show that, a newly proposed physical principle namely Local Orthogonality does better by providing a tighter upper bound on the success probability for Hardys nonlocality. This bound is relatively closer to the corresponding quantum value compared to the bounds achieved from other principles.

Local randomness in Hardy's correlations: implications from the information causality principle

Study of non-local correlations in terms of Hardys argument has been quite popular in quantum mechanics. Hardys non-locality argument depends on some kind of asymmetry, but a two-qubit maximally entangled state, being symmetric, does not exhibit this kind of non-locality. Here we ask the following question: can this feature be explained by some principle outside quantum mechanics? The no-signaling condition does not provide a solution. But, interestingly, the information causality principle (Pawlowski et al 2009 Nature 461 1101) offers an explanation. It shows that any generalized probability theory which gives completely random results for local dichotomic observable, cannot provide Hardys non-local correlation if it is restricted by a necessary condition for respecting the information causality principle. In fact, the applied necessary condition imposes even more restrictions on the local randomness of measured observable. Still, there are some restrictions imposed by quantum mechanics that are not reproduced from the considered information causality condition.