arXiv subjects

A. R. Usha Devi

Publications and source records attributed to A. R. Usha Devi.

At least 37 records · Page 2Linked to original sources

arXiv2017

N term pairwise correlation inequalities, steering and joint measurability

Chained correlation inequalities involving pairwise correlations of qubit observables in the equatorial plane are constructed based on the positivity of a sequence of moment matrices. When a jointly measurable set of fuzzy POVMs is employed in first measurement of every pair of sequential measurements, the chained pairwise correlations do not violate the classical bound imposed by the moment matrix positivity. We identify that incompatibility of measurements is only necessary, but not sufficient, in general, for the violation of the inequality. On the other hand, there exists a one-to-one equivalence between the degree of incompatibility (which quantifies the joint measurability) of the equatorial qubit observables and the optimal violation of a non-local steering inequality, proposed by Jones and Wiseman (Phys. Rev. A, 84, 012110 (2011)). To this end, we construct a local analogue of this steering inequality in a single qubit system and show that its violation is a mere reflection of measurement incompatibility of equatorial qubit POVMs, employed in first measurements in the sequential unsharp-sharp scheme.

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arXiv2017

Biseparability of noisy pseudopure, W and GHZ states using conditional quantum relative Tsallis entropy

We employ the conditional version of sandwiched Tsallis relative entropy to determine 1:N-1 separability range in the noisy one-parameter families of pseudopure and Werner-like N-qubit W, GHZ states. The range of the noisy parameter, for which the conditional sandwiched Tsallis relative entropy is positive, reveals perfect agreement with the necessary and sufficient criteria for the separability in the 1:N-1 partition of these one parameter noisy states.

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arXiv2015

Bipartite separability of one parameter families of states using conditional quantum relative Tsallis entropy

In any bipartition of a quantum state, it is proved that the negative values of the conditional version of sandwiched Tsallis relative entropy necessarily implies quantum entanglement. For any N, the separability ranges in the $1:N-1$ partition of symmetric one parameter families of noisy $N$-qubit W, GHZ, states are determined using the conditional quantum relative Tsallis entropy approach. The 1:N-1 separability range matches exactly with the range obtained through positive partial transpose criterion, for all N. The advantages of using non-commuting version of $q$-conditional relative Tsallis entropy is brought out through this and other one-parameter families of states.

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arXiv2015

Unsharp measurements and joint measurability

We give an overview of joint unsharp measurements of non-commuting observables using positive operator valued measures (POVMs). We exemplify the role played by joint measurability of POVMs in entropic uncertainty relation for Alice's pair of non-commuting observables in the presence of Bob's entangled quantum memory. We show that Bob should record the outcomes of incompatible (non-jointly measurable) POVMs in his quantum memory so as to beat the entropic uncertainty bound. In other words, in addition to the presence of entangled Alice-Bob state, implementing incompatible POVMs at Bob's end is necessary to beat the uncertainty bound and hence, predict the outcomes of non-commuting observables with improved precision. We also explore the implications of joint measurability to {\em validate} a moment matrix constructed from average pairwise correlations of three dichotomic non-commuting qubit observables. We prove that a classically acceptable moment matrix -- which ascertains the existence of a legitimate joint probability distribution for the outcomes of all the three dichotomic observables -- could be realized if and only if compatible POVMs are employed.

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arXiv2015

Joint Measurability and Temporal Steering

Quintino et. al. (Phys. Rev. Lett. 113, 160402 (2014)) and Uola et. al. (Phys. Rev. Lett. 113, 160403 (2014)) have recently established an intrinsic relation between non-joint measurability and Einstein-Podolsky- Rosen steering. They showed that a set of measurements is incompatible (i.e., not jointly measurable) if and only if it can be used for the demonstration of steering. In this paper, we prove the temporal analog of this result viz., a set of measurements are incompatible if and only if it exhibits temporal steering.

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arXiv2014

Joint measurability, steering and entropic uncertainty

The notion of incompatibility of measurements in quantum theory is in stark contrast with the corresponding classical perspective, where all physical observables are jointly measurable. It is of interest to examine if the results of two or more measurements in the quantum scenario can be perceived from a classical point of view or they still exhibit non-classical features. Clearly, commuting observables can be measured jointly using projective measurements and their statistical outcomes can be discerned classically. However, such simple minded association of compatibility of measurements with commutativity turns out to be limited in an extended framework, where the usual notion of sharp projective valued measurements of self adjoint observables gets broadened to include unsharp measurements of generalized observables constituting positive operator valued measures (POVM). There is a surge of research activity recently towards gaining new physical insights on the emergence of classical behavior via joint measurability of unsharp observables. Here, we explore the entropic uncertainty relation for a pair of discrete observables (of Alice's system) when an entangled quantum memory of Bob is restricted to record outcomes of jointly measurable POVMs only. Within the joint measurability regime, the sum of entropies associated with Alice's measurement outcomes - conditioned by the results registered at Bob's end - are constrained to obey an entropic steering inequality. In this case, Bob's non-steerability reflects itself as his inability in predicting the outcomes of Alice's pair of non-commuting observables with better precision, even when they share an entangled state. As a further consequence, the quantum advantage envisaged for the construction of security proofs in key distribution is lost, when Bob's measurements are restricted to the joint measurability regime.

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arXiv2014

What does monogamy in higher powers of a correlation measure mean?

We examine here the proposition that all multiparty quantum states can be made monogamous by considering positive integral powers of any quantum correlation measure. With Rajagopal-Rendell quantum deficit as the measure of quantum correlations for symmetric 3-qubit pure states, we illustrate that monogamy inequality is satisfied for higher powers of quantum deficit. We discuss the drawbacks of this inequality in quantification of correlations in the state. We also prove a monogamy inequality in higher powers of classical mutual information and bring out the fact that such inequality need not necessarily imply restricted shareability of correlations. We thus disprove the utility of higher powers of any correlation measure in establishing monogamous nature in multiparty quantum states.

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arXiv2014

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

Quantum mechanical wave-particle duality is quantified in terms of a trade-off relation between the fringe visibility and the which-way distinguishability in an interference experiment. This relation is recently generalized by Banaszek et. al., (Nature Communications 4, 2594, 2013) when the particle is equipped with an internal degree of freedom such as spin. Here, we extend the visibility-distinguishability trade-off relation to quantum interference of a particle possessing an internal degree of freedom, when the which-way detector state is entangled with an ancillary system. We introduce an extended which-way distinguishability and the associated extended fringe visibility satisfying the duality inequality in this scenario. We illustrate, with the help of three specific examples, that while the which-way information inferred solely from the detector state (without ancilla) vanishes, the extended distinguishability retrievable via measurements on the detector-ancilla entangled state is non-zero. Furthermore, in all the three examples, the extended visibility and the generalized visibility (which was introduced by Banaszek et. al., Nature Communications 4, 2594, 2013)) match identically with each other.

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arXiv2014

From the sandwiched quantum relative Tsallis entropy to its conditional form: Separability criterion beyond local and global spectra

The quantum relative Renyi entropy of two density matrices was recently extended when the two do not commute, from which a conditional entropy is identified. This is here extended to the corresponding Tsallis relative entropy and to its conditional form. This new expression of Tsallis conditional entropy is shown to witness entanglement beyond the method based on global and local spectra of composite quantum states. When the reduced density matrix happens to be a maximally mixed state, this conditional entropy coincides with the expression in terms of Tsallis entropies derived earlier by Abe and Rajagopal (Physica A 289, 157 (2001)). Separability range in one parameter family of W and GHZ states with 3 and 4 qubits is explored here and it is shown that the results inferred from negative Tsallis conditional entropy matches with that obtained through Peres partial transpose criteria for one-parameter family of W states, in one of its partitions. The criteria is shown to be non-spectral through its usefulness in identifying entanglement in isospectral density matrices.

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arXiv2013

Entropic uncertainty assisted by temporal memory

The uncertainty principle brings out intrinsic quantum bounds on the precision of measuring non-commuting observables. Statistical outcomes in the measurement of incompatible observables reveal a trade-off on the sum of corresponding entropies. Massen-Uffink entropic uncertainty relation (Phys. Rev. Lett. 60, 1103 (1988)) constrains the sum of entropies associated with incompatible measurements. The entropic uncertainty principle in the presence of quantum memory (Nature Phys. 6, 659 (2010)) brought about a fascinating twist by showing that quantum side information, enabled due to entanglement, helps in beating the uncertainty of non-commuting observables. Here we explore the interplay between temporal correlations and uncertainty. We show that with the assistance of a prior quantum temporal information achieved by sequential observations on the same quantum system at different times, the uncertainty bound on entropies gets reduced.

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arXiv2013

Inversion of moments to retrieve joint probabilities in quantum sequential measurements

A sequence of moments encode the corresponding probability distribution. Probing if quantum joint probability distribution can be retrieved from the associated set of moments -- realized in the sequential measurement of a dichotomic observable at different time intervals -- reveals a negative answer i.e., the joint probabilities of sequential measurements do not agree with the ones obtained by inverting the moments. This is indeed a reflection of the non-existence of a bonafide grand joint probability distribution, consistent with all the physical marginal probability distributions. Here we explicitly demonstrate that given the set of moments, it is not possible to retrieve the three-time quantum joint probability distribution resulting from quantum sequential measurement of a single qubit dichotomic observable at three different times. Experimental results using a nuclear magnetic resonance (NMR) system are reported here to corroborate these theoretical observations viz., the incompatibility of the three-time joint probabilties with those extracted from the moment sequence.

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arXiv2013

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-$s$ particles sharing a state of zero total spin. This brings forth the violation of the entropic Leggett-Garg inequality by a rotating quantum spin-$s$ system in similar manner as does the entropic Bell inequality (Phys. Rev. Lett. 61, 662 (1988)) by a pair of spin-$s$ particles forming a composite spin singlet state.

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arXiv2013

Quantum reading of digital memory with non-Gaussian entangled light

It has been shown recently (Phys. Rev. Lett. 106, 090504 (2011)) that entangled light with Einstein-Podolsky-Rosen (EPR) correlations retrieves information from digital memory better than any classical light. In identifying this, a model of digital memory with each cell consisting of reflecting medium with two reflectivities (each memory cell encoding the binary numbers 0 or 1) is employed. The readout of binary memory essentially corresponds to discrimination of two Bosonic attenuator channels characterized by different reflectivities. The model requires an entire mathematical paraphernalia of continuous variable Gaussian setting for its analysis, when arbitrary values of reflectivities are considered. Here we restrict to a basic quantum read-out mechanism with non-Gaussian entangled states of light, with the binary channels to be discriminated being ideal memory characterized by reflectivity one i.e., an identity channel and thermal noise channel, where the signal light illuminating the memory location gets completely lost (zero reflectivity) and only a white thermal noise hitting the upper side of the memory reaches the decoder. We compare the quantum reading efficiency of entangled light with any classical source of light in this model. We show that entangled transmitters offer better reading performance than any classical transmitters of light in the regime of low signal intensity.

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arXiv2012

Non-Markovianity and Clauser-Horne-Shimony-Holt (CHSH)-Bell inequality violation in quantum dissipative systems

We examine the non-Markovian dynamics in a multipartite system of two initially correlated atomic qubits, each located in a single-mode leaky cavity and interacting with its own bosonic reservoir. We show the dominance of non-Markovian features, as quantified by the difference in fidelity of the evolved system with its density matrix at an earlier time, in three specific two-qubit partitions associated with the cavity-cavity and atom-reservoir density matrices within the same subsystem, and the cavity-reservoir reduced matrix across the two subsystems. The non-Markovianity in the cavity-cavity subsystem is seen to be optimized in the vicinity of the exceptional point. The CHSH-Bell inequality computed for various two-qubit partitions show that high non-locality present in a specific subsystem appears in conjunction with enhanced non-Markovian dynamics in adjacent subsystems. This is in contrast to the matching existence of non-locality and quantum correlations in regions spanned by time t and the cavity decay rate for select partitions. We discuss the applicability of these results to photosynthetic systems.

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arXiv2012

Quantum discord and classical correlation can tighten the uncertainty principle in the presence of quantum memory

Uncertainty relations capture the essence of the inevitable randomness associated with the outcomes of two incompatible quantum measurements. Recently, Berta et al. have shown that the lower bound on the uncertainties of the measurement outcomes depends on the correlations between the observed system and an observer who possesses a quantum memory. If the system is maximally entangled with its memory, the outcomes of two incompatible measurements made on the system can be predicted precisely. Here, we obtain a new uncertainty relation that tightens the lower bound of Berta et al., by incorporating an additional term that depends on the quantum discord and the classical correlations of the joint state of the observed system and the quantum memory. We discuss several examples of states for which our new lower bound is tighter than the bound of Berta et al. On the application side, we discuss the relevance of our new inequality for the security of quantum key distribution and show that it can be used to provide bounds on the distillable common randomness and the entanglement of formation of bipartite quantum states.

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arXiv2012

Interplay of quantum stochastic and dynamical maps to discern Markovian and non-Markovian transitions

It is known that the dynamical evolution of a system, from an initial tensor product state of system and environment, to any two later times, t1,t2 (t2>t1), are both completely positive (CP) but in the intermediate times between t1 and t2 it need not be CP. This reveals the key to the Markov (if CP) and nonMarkov (if it is not CP) avataras of the intermediate dynamics. This is brought out here in terms of the quantum stochastic map A and the associated dynamical map B -- without resorting to master equation approaches. We investigate these features with four examples which have entirely different physical origins (i) a two qubit Werner state map with time dependent noise parameter (ii) Phenomenological model of a recent optical experiment (Nature Physics, 7, 931 (2011)) on the open system evolution of photon polarization. (iii) Hamiltonian dynamics of a qubit coupled to a bath of $N$ qubits and (iv) two qubit unitary dynamics of Jordan et. al. (Phys. Rev. A 70, 052110 (2004)) with initial product states of qubits. In all these models, it is shown that the positivity/negativity of the eigenvalues of intermediate time dynamical B map determines the Markov/non-Markov nature of the dynamics.

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arXiv2011

Monogamy of quantum correlations in three qubit pure states using Rajagopal-Rendell (RR) quantum deficit

The limitation on the shareability of quantum entanglement over several parties, the so-called monogamy of entanglement, is an issue that has caught considerable attention of quantum informa- tion community over the last decade. A natural question of interest in this connection is whether monogamy of correlations is true for correlations other than entanglement. This issue is examined here by choosing quantum deficit, proposed by Rajagopal and Rendell, an operational measure of correlations. In addition to establishing the polygamous nature of the class of three qubit sym- metric pure states characterized by two distinct Majorana spinors (to which the W states belong), those with three distinct Majorana spinors (to which GHZ states belong) are shown to either obey or violate monogamy relations. While the generalized W states can be mono/polygamous, the generalized GHZ states exhibit monogamy with respect to quantum deficit. The issue of us- ing monogamy conditions based on quantum deficit to witness the states belonging to SLOCC inequivalent classes is discussed in the light of these results.

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arXiv2011

Uncertainty relations in the realm of classical dynamics

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 hbar tending to zero, 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.

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