arXiv subjects

Shiladitya Mal

Publications and source records attributed to Shiladitya Mal.

47 records · Page 3Linked to original sources

arXiv2018

Protecting temporal correlations of two-qubit states using quantum channels with memory

Quantum temporal correlations exhibited by violations of Leggett-Garg Inequality (LGI) and Temporal Steering Inequality (TSI) are in general found to be non-increasing under decoherence channels when probed on two-qubit pure entangled states. We study the action of decoherence channels, such as amplitude damping, phase-damping and depolarising channels when partial memory is introduced in a way such that two consecutive uses of the channels are time-correlated. We show that temporal correlations demonstrated by violations of the above temporal inequalities can be protected against decoherence using the effect of memory.

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arXiv2018

Steering a single system sequentially by multiple observers

Quantum mechanics puts a restriction on the number of observers who can simultaneously steer another observer's system, known as the monogamy of steering. In this work we find the limit of the number of observers (Bobs) who can steer another party's (Alice's) system invoking a scenario where half of an entangled pair is shared between a single Alice in one wing and several Bobs on the other wing, who act sequentially and independently of each other. When all the observers measure two dichotomic observables, we find that two Bobs can steer Alice's system going beyond the monogamy restriction. We further show that three Bobs can steer Alice's system considering a three-settings linear steering inequality, and then conjecture that at most $n$ Bobs can demonstrate steering of Alice's system when steering is probed through an $n$-settings linear steering inequality.

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arXiv2018

Witnessing entanglement sequentially: Maximally entangled states are not special

We investigate sharing of bipartite entanglement in a scenario where half of an entangled pair is possessed and projectively measured by one observer, called Alice, while the other half is subjected to measurements performed sequentially, independently, and unsharply, by multiple observers, called Bobs. We find that there is a limit on the number of observers in this entanglement distribution scenario. In particular, for a two-qubit maximally entangled initial shared state, no more than twelve Bobs can detect entanglement with a single Alice for arbitrary -- possibly unequal -- sharpness parameters of the measurements by the Bobs. Moreover, the number of Bobs remains unaltered for a finite range of near-maximal pure initial entanglement, a feature that also occurs in the case of equal sharpness parameters at the Bobs. Furthermore, we show that for non-maximally entangled shared pure states, the number of Bobs reduces with the amount of initial entanglement, providing a coarse-grained but operational measure of entanglement.

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arXiv2018

Testing local-realism and macro-realism under generalized dichotomic measurements

Generalised quantum measurements with two outcomes are fully characterised by two real parameters, dubbed as sharpness parameter and biasedness parameter and they can be linked with different aspects of the experimental setup. It is known that precision of measurements, characterised by the sharpness parameter of the measurements, reduces the possibility of probing quantum features like violation of local-realism (LR) or macro-realism (MR). Here we investigate the effect of biasedness together with sharpness of measurement and find a trade-off between those two parameters in the context of probing violation of LR and MR. Interestingly we also find the above mentioned trade-off is more robust in the later case.

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arXiv2017

Necessary and sufficient state condition for two-qubit steering using two measurement settings per party and monogamy of steering

We consider the Cavalcanti-Foster-Fuwa-Wiseman inequality~\cite{achsh} which is a necessary and sufficient steerability condition for two-qubit states with two measurement settings on each side. We derive the criterion which an arbitrary two-qubit state must satisfy in order to violate this inequality, and obtain its maximum attainable violation in quantum mechanics. The derived condition on the state parameters enables us to establish a tight monogamy relation for two-qubit steering.

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arXiv2016

Quantum mechanical violation of macrorealism for large spin and its robustness against coarse-grained measurements

For multilevel spin systems, robustness of the quantum mechanical (QM) violation of macrorealism (MR) with respect to coarse grained measurements is investigated using three different necessary conditions of MR, namely, the Leggett-Garg inequality (LGI), Wigner's form of the Leggett-Garg inequality (WLGI) and the condition of no-signalling in time (NSIT). It is shown that for dichotomic sharp measurements, in the asymptotic limit of spin, the algebraic maxima of the QM violations of all these three necessary conditions of MR are attained. Importantly, the QM violations of all these persist in that limit even for \textit{arbitrary} unsharp measurements, i.e. for any non zero value of the sharpness parameter characterizing the degree of fuzziness of the relevant measurements. We also find that when different measurement outcomes are clubbed into two groups for the sake of dichotomising the outcomes, the asymmetry/symmetry in the number of outcomes in the two groups, signifying the degree of coarse graining of measurements, has a crucial role in discerning quantum violation of MR. The results clearly demonstrate that classicality does not emerges in the asymptotic limit of spin, whatever be the unsharpness and degree of coarse graining of the measurements.

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arXiv2016

Probing hierarchy of temporal correlation requires either generalised measurement or nonunitary evolution

Temporal steering and violation of the Leggett-Garg inequality are two different ways of probing the violation of macro-realistic assumptions in quantum mechanics. It is shown here that under unitary evolution and projective measurements the two types of temporal correlations lead to similar results. However, their inequivalence may be exhibited if either one of them is relaxed, i.e., by employing either generalized measurements, or noisy evolution, as we show here using relevant examples.

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arXiv2016

Sharing of Nonlocality of a single member of an Entangled Pair Is Not Possible by More Than Two Unbiased Observers on the other wing

We address the recently posed question as to whether the nonlocality of a single member of an entangled pair of spin $1/2$ particles can be shared among multiple observers on the other wing who act sequentially and independently of each other [1]. We first show that the optimality condition for the trade-off between information gain and disturbance in the context of weak or non-ideal measurements emerges naturally when one employs a one-parameter class of positive operator valued measures (POVMs). Using this formalism we then prove analytically that it is impossible to obtain violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality by more than two Bobs in one of the two wings using unbiased input settings with an Alice in the other wing.

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arXiv2015

Optimal violation of Leggett-Garg inequality for arbitrary spin and emergence of classicality through unsharp measurement

We consider temporal correlations of particles with arbitrary spin. We show that the Leggett-Garg inequality can be maximally violated irrespective of the value of spin, thus improving upon an earlier result by Kofler and Brukner [Phys. Rev. Lett. \textbf{99}, 180403 (2007)]. Our proof is accomplished through a suitable adoption of a measurement scheme which has previously been employed for studying the spatial correlation in a system with arbitrary spin. We next consider generalized or unsharp measurements as a method for coarse graining in a quantitative manner, and show that classicality emerges below a precise value of the sharpness parameter. Satisfaction of the Leggett-Garg inequality is shown to be a necessary and sufficient condition for macroscopic realism.

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arXiv2015

Wigner's form of the Leggett-Garg inequality, No-Signalling in Time, and Unsharp Measurements

Wigner's form of the local realist inequality is used to derive its temporal version for an oscillating two-level system involving two-time joint probabilities. Such an inequality may be regarded as a novel form of the Leggett-Garg inequality (LGI) constituting a necessary condition for macrorealism. The robustness of its quantum mechanical (QM) violation against unsharpness of measurement is investigated by using a suitable model of unsharp measurements. It is found that there exists a range of values of the sharpness parameter (characterizing precision of the relevant measurements) for which the usual LGI is satisfied by QM, but Wigner's form of the LGI (WLGI) is violated. This implies that for such unsharp measurements, the QM violation of macrorealism cannot be tested using the usual LGI, but can be tested using WLGI. In showing this, we take into account the general form of the usual LGI involving an arbitrary number of pairs of two-time correlation functions. Another recently proposed necessary condition for macrorealism, called `no-signalling in time', is also probed, showing that its QM violation persists for arbitrarily unsharp measurements.

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arXiv2014

Certifiable randomness from temporal correlations

Leggett-Garg inequalities (LGI) are constrains on certain combinations of temporal correlations obtained by measuring one and the same system at two different instants of time. The usual derivations of LGI assume \emph {macroscopic realism per se } and \emph {noninvasive measurability}. We derive these inequalities under a different set of assumptions, namely the assumptions of \emph{predictability} and \emph{no signaling in time}. As a novel implication of this derivation, we show that LGI can be used to certify randomness in a device independent way.

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