H. S. Karthik

Macrorealism from entropic Leggett-Garg inequalities

We formulate entropic Leggett-Garg inequalities, which place constraints on the statistical outcomes of temporal correlations of observables. The information theoretic inequalities are satisfied if macrorealism holds. We show that the quantum statistics underlying correlations between time-separated spin component of a quantum rotor mimics that of spin correlations in two spatially separated spin-

The uncertainty product of position and momentum in classical dynamics

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Joint measurability, steering, and entropic uncertainty

particles sharing a state of zero total spin. This brings forth the violation of the entropic Leggett-Garg inequality by a rotating quantum spin-

Inversion of moments to retrieve joint probabilities in quantum sequential measurements

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N-term pairwise-correlation inequalities, steering, and joint measurability

system in a similar manner as does the entropic Bell inequality [S. L. Braunstein and C. M. Caves, Phys. Rev. Lett. 61, 662 (1988)] by a pair of spin-

Quantum which-way information and fringe visibility when the detector is entangled with an ancilla

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Equivalence of classicality and separability based on P phase---space representation of symmetric multiqubit states

particles forming a composite spin singlet state.

Joint measurability and temporal steering

It is generally believed that the classical regime emerges as a limiting case of quantum theory. Exploring such quantum-classical correspondences provides a deeper understanding of foundational aspects and has attracted a great deal of attention since the early days of quantum theory. It has been proposed that since a quantum mechanical wave function describes an intrinsic statistical behavior, its classical limit must correspond to a classical ensemble—not to an individual particle. This idea leads us to ask how the uncertainty product of canonical observables in the quantum realm compares with the corresponding dispersions in the classical realm. In this paper, we explore parallels between the uncertainty product of position and momentum in stationary states of quantum systems and the corresponding fluctuations of these observables in the associated classical ensemble. We confine ourselves to one-dimensional conservative systems and show, with the help of suitably defined dimensionless physical quantiti...It is generally believed that classical regime emerges as a limiting case of quantum theory. Exploring such quantum-classical correspondences in a more transparent manner is central to the deeper understanding of foundational aspects and has attracted a great deal of attention – starting from the early days of quantum theory. While it is often highlighted that quantum to classical transition occurs in the limit ~ → 0, several objections have been raised about its suitability in some physical contexts. Ehrenfest’s theorem is another widely discussed classical limit – however, its inadequacy has also been pointed out in specific examples. It has been proposed that since a quantum mechanical wave function inherits an intrinsic statistical behavior, its classical limit must correspond to a classical ensemble – not an individual particle. This opens up the question “how would uncertainty relations of canonical observables compare themselves in quantum and classical realms?” In this paper we explore parallels between uncertainty relations in stationary states of quantum systems and that in the corresponding classical ensemble. We confine ourselves to one dimensional conservative systems and show, with the help of suitably defined dimensionless physical quantities, that first and second moments of the canonical observables match with each other in classical and quantum descriptions – resulting in an identical structure for uncertainty relations in both the realms.

Entropic uncertainty assisted by temporal memory

There has been a surge of research activity recently on the role of joint measurability of unsharp observables in nonlocal features, viz., violation of Bell inequality and EPR steering. Here, we investigate the entropic uncertainty relation for a pair of noncommuting observables (of Alices system) when an entangled quantum memory of Bob is restricted to record outcomes of jointly measurable positive operator valued measures. We show that with this imposed constraint of joint measurability at Bobs end, the entropic uncertainties associated with Alices measurement outcomes - conditioned by the results registered at Bobs end - obey an entropic steering inequality. Thus, Bobs nonsteerability is intrinsically linked to his inability to predict the outcomes of Alices pair of noncommuting observables with better precision, even when they share an entangled state. As a further consequence, we prove that in the joint measurability regime, the quantum advantage envisaged for the construction of security proofs in quantum key distribution is lost. © 2015 American Physical Society.

Conditional entropic uncertainty and quantum correlations

A sequence of moments obtained from statistical trials encodes a classical probability distribution. However, it is well known that an incompatible set of moments arises in the quantum scenario, when correlation outcomes associated with measurements on spatially separated entangled states are considered. This feature, viz., the incompatibility of moments with a joint probability distribution, is reflected in the violation of Bell inequalities. Here, we focus on sequential measurements on a single quantum system and investigate if moments and joint probabilities are compatible with each other. By considering sequential measurement of a dichotomic dynamical observable at three different time intervals, we explicitly demonstrate that the moments and the probabilities are inconsistent with each other. Experimental results using a nuclear magnetic resonance system are reported here to corroborate these theoretical observations, viz., the incompatibility of the three-time joint probabilities with those extracted from the moment sequence when sequential measurements on a single-qubit system are considered.