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Amit Mukherjee

Publications and source records attributed to Amit Mukherjee.

43 records · Page 3Linked to original sources

Reciprocal ontological models show indeterminism of the order of quantum theory

The question whether indeterminism in quantum measurement outcomes is fundamental or is there a possibility of constructing a finer theory underlying quantum mechanics that allows no such indeterminism, has been debated for a long time. We show that within the class of ontological models due to Harrigan and Spekkens, those satisfying preparation-measurement reciprocity must allow indeterminism of the order of quantum theory. Our result implies that one can design quantum random number generator, for which it is impossible, even in principle, to construct a reciprocal deterministic model.

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Witnessing Genuine Mutipartite Non-locality

Genuine multipartite nonlocality is a salient feature of quantum systems, empowering the security of multi-party device independent cryptographic protocols. Given a correlation, characterizing and detecting genuineness have been subjected to recent studies. In this regard, we propose a Hardy-type argument which is able to detect genuine $n$-way nonlocality of arbitrary quantum systems. To understand the strength of this argument we also study the optimal success probability of the argument in a minimally constrained theory, namely the generalized no-signaling theory.

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All-versus-nothing violation of local realism from the Hardy paradox under no-signaling

Hardy's is one of the simplest arguments concerning non-locality. Recently Chen et. al. have proposed a more generalized Hardy-like argument and have shown that the probability of success increases with local system's dimension. Here we study the same in a minimally constrained theory, namely the generalized no-signaling theory(GNST). We find that not only the probability of success of this argument increases with local system dimension in GNST, it also takes a very simple functional form.

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Optimal quantum violation of Clauser-Horne-Shimony-Holt like steering inequality

We study a recently proposed Einstein-Podolsky-Rosen steering inequality [arXiv- 1412.8178 (2014)]. Analogous to Clauser-Horne-Shimony-Holt (CHSH) inequality for Bell nonlocality, in the simplest scenario, i.e., 2 parties, 2 measurements per party and 2 outcomes per measurement, this newly proposed inequality has been proved to be necessary and sufficient for steering. In this article, using an equivalence between measurement incompatibility (non joint measurability) and steering, we find the optimal violation amount of this inequality in quantum theory. Interestingly, the optimal violation amount matches with optimal quantum violation of CHSH inequality, i.e., Cirel'son quantity. We further study the optimal violation of this inequality for different bipartite quantum states. To our surprise we find that optimal violation amount is different for different $2$-qubit pure entangled states, which is not the case for all other existing steering inequalities.

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Ontological models, preparation contextuality and nonlocality

The ontological model framework for an operational theory has generated much interest in recent years. The debate concerning reality of quantum states has been made more precise in this framework. With the introduction of generalized notion of contextuality in this framework, it has been shown that completely mixed state of a qubit is \emph{preparation contextual}. Interestingly, this new idea of preparation contextuality has been used to demonstrate nonlocality of some $ψ$-epistemic models without any use of Bell's inequality. In particular, nonlocality of a non maximally $ψ$-epistemic model has been demonstrated from preparation contextuality of a maximally mixed qubit and Schrödinger's steerability of the maximally entangled state of two qubits [Phys. Rev. Lett {\bf 110}, 120401 (2013)]. In this paper, we, show that any mixed state is preparation contextual. We, then, show that nonlocality of any bipartite pure entangled state, with Schmidt rank two, follows from preparation contextuality and steerability provided we impose certain condition on the epistemicity of the underlying ontological model. More interestingly, if the pure entangled state is of Schmidt rank greater than two, its nonlocality follows without any further condition on the epistemicity. Thus our result establishes a stronger connection between nonlocality and preparation contextuality by revealing nonlocality of any bipartite pure entangled states without any use of Bell-type inequality.

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Local deterministic simulation of equatorial Von Neumann measurements on tripartite GHZ state

Experimental free-will or measurement independence is one of the crucial assumptions in derivation of any nonlocal theorem. Any nonlocal correlation obtained in quantum world can have a local deterministic explanation if there is no experimental free-will in choosing the measurement settings. Recently, in [Phys. Rev. Lett. {\bf105}, 250404 (2010)] it has been shown that to obtain a local deterministic description for singlet state correlation one does not need to give up measurement independence completely, but a partial measurement dependence suffices. In three party scenario considering GHZ correlation one can exhibit absolute contradiction between quantum theory and local realism. In this paper we show that such correlation also has local deterministic description if measurement independence is given up, even if not completely. We provide a local deterministic model for equatorial Von Neumann measurements on tripartite GHZ state by sacrificing measurement independence partially.

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Device independent Schmidt rank witness by using Hardy paradox

Schmidt rank of bipartite pure state serves as a testimony of entanglement. It is a monotone under local operation + classical communications (LOCC) and puts restrictions in LOCC convertibility of quantum states. Identifying the Schmidt rank of an unknown quantum state therefore seek importance from information theoretic perspective. In this work it is shown that a modified version of Hardy's argument, which reveals the contradiction of quantum theory with local realism, turns out to be useful for inspecting the minimal Schmidt rank of the unknown state and hence also the minimal dimension of the system. Use of Hardy's test in such task provides a practical advantage: the Schmidt rank can be determined without knowing the detailed functioning of the experimental devices i.e., Hardy's test suffices to be a device independent Schmidt rank witness.

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