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Publications and source records attributed to Dipankar Home.

At least 37 records · Page 2Linked to original sources

arXiv2020

Comment on "Observing the "quantum Cheshire cat" effect with noninvasive weak measurement''

In a very recent work [arXiv:2004.07451], Kim et al claimed to have made the first genuine experimental observation of the Quantum Cheshire Cat effect. We dispute this claim on the ground that the setup employed is not adequate for making the weak measurements that define this interferometric effect. Half of the necessary weak values are not observed, and the other half is obtained indirectly by combining results measured with distinct setups.

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arXiv2019

Revisiting comparison between entanglement measures for two-qubit pure states

Given a non-maximally entangled state, an operationally significant question is to quantitatively assess as to what extent the state is away from the maximally entangled state, which is of importance in evaluating the efficacy of the state for its various uses as a resource. It is this question which is examined in this paper for two-qubit pure entangled states in terms of different entanglement measures like Negativity (N), Logarithmic Negativity (LN), and Entanglement of Formation (EOF). Although these entanglement measures are defined differently, to what extent they differ in quantitatively addressing the earlier mentioned question has remained uninvestigated. Theoretical estimate in this paper shows that an appropriately defined parameter characterizing the fractional deviation of any given entangled state from the maximally entangled state in terms of N is quite different from that computed in terms of EOF with their values differing up to ~ 15 % for states further away from the maximally entangled state. Similarly, the values of such fractional deviation parameters estimated using the entanglement measures LN and EOF, respectively, also strikingly differ among themselves with the maximum value of this difference being around 23 %. This analysis is complemented by illustration of these differences in terms of empirical results obtained from a suitably planned experimental study. Thus, such appreciable amount of quantitative non-equivalence between the entanglement measures in addressing the experimentally relevant question considered in the present paper highlights the requirement of an appropriate quantifier for such intent. We indicate directions of study that can be explored towards finding such a quantifier.

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arXiv2019

Persistence of quantum violation of macrorealism for large spins even under coarsening of measurement times

We investigate quantum violation of macrorealism for multilevel spin systems under the condition of coarsening of measurement times -- i.e., when measurement times have experimental indeterminacy. This is studied together with the effect of coarsening of measurement outcomes for which individual outcomes cannot be unambiguously discriminated. In our treatment, along with different measurement outcomes being clubbed together into two groups in order to model the coarsening of measurement outcomes, importantly, varying degrees of coarsening of measurement time intervals have also been considered. This then reveals that while for a given dimension, the magnitude of quantum violation of macrorealism decreases with the increasing degree of coarsening of measurement times, interestingly, this effect of coarsening of measurement times can be annulled by increasing the dimension of the spin system so that in the limit of large spin, the quantum violation of macrorealism continues to persist. Thus, the result obtained demonstrates that classicality for large spins does not emerge from quantum mechanics in spite of the coarsening of measurement times.

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arXiv2019

Pearson Correlation Coefficient as a measure for Certifying and Quantifying High Dimensional Entanglement

A scheme for characterizing entanglement using the statistical measure of correlation given by the Pearson correlation coefficient (PCC) was recently suggested that has remained unexplored beyond the qubit case. Towards the application of this scheme for the high dimensional states, a key step has been taken in a very recent work by experimentally determining PCC and analytically relating it to Negativity for quantifying entanglement of the empirically produced bipartite pure state of spatially correlated photonic qutrits. Motivated by this work, we present here a comprehensive study of the efficacy of such an entanglement characterizing scheme for a range of bipartite qutrit states by considering suitable combinations of PCCs based on a limited number of measurements. For this purpose, we investigate the issue of necessary and sufficient certification together with quantification of entanglement for the two-qutrit states comprising maximally entangled state mixed with white noise and coloured noise in two different forms respectively. Further, by considering these classes of states for d=4 and 5, extension of this PCC based approach for higher dimensions d is discussed.

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arXiv2019

Revealing the quantitative relation between simultaneous correlations in complementary bases and quantum steering for two-qubit Bell diagonal states

The present work is motivated by the question as to what aspect of correlation entailed by the two-qubit state serves as the appropriate quantitative resource for steering. To this end, considering Bell-diagonal states, suitable measures of simultaneous correlations in two and three complementary (mutually unbiased) bases are identified as the relevant resources for quantum steering. Quantitative relations between appropriate measures of quantum steering and the corresponding measures of simultaneous correlations in complementary bases are demonstrated which ensure that for two qubit steerable Bell-diagonal states, higher value of simultaneous correlations in mutually unbiased bases necessarily implies higher degree of quantum steering, both for two and three setting steering scenarios.

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arXiv2019

Remote State Preparation using Correlations beyond Discord

In recent years, exploring the possible use of separable states as resource for achieving quantum information processing(QIP) tasks has been gaining increasing significance. In this context, a particularly important demonstration has been that non-vanishing discord is the necessary condition for the separable states to be used as resource for remotely preparing any arbitrary pure target state [Nature Physics $8$, $666$ $(2012)$]. The present work stems from our observation that not only resource states with same discord can imply different efficiencies (in terms of average fidelity) of the remote state preparation (RSP) protocol, but also states with higher discord can imply lower RSP efficiency. This, therefore, necessitates identification of the relevant feature of quantum correlations which can appropriately quantify effectiveness of the resource state for the RSP protocol. To this end, for the two-qubit Bell-diagonal states, we show that an appropriate measure of simultaneous correlations in three mutually unbiased bases can serve to quantify usefulness of the resource for the RSP task using entangled as well as separable states, including non-discordant states as resource. In particular, it is revealed that zero-discord states having such non-vanishing measure can be useful for remotely preparing a subset of pure target states. Thus, this work shows that, using separable states, an effective resource for QIP tasks such as RSP can be provided by simultaneous correlations in mutually unbiased bases.

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arXiv2018

A tighter steering criterion using the Robertson-Schrodinger uncertainty relation

We consider quantum steering by non-Gaussian entangled states. The Reid steering criterion based on the Heisenberg uncertainty relation fails to detect steerability for many categories of such states. Here, we derive a tighter steering criterion using the Robertson-Schrödinger uncertainty relation. We show that our steering condition is able to detect steerability of several classes of non-Gaussian states such as entangled eigenstates of the two-dimensional harmonic oscillator, the photon subtracted squeezed vacuum state and the NOON state.

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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

Bipartite qutrit local realist inequalities and the robustness of their quantum mechanical violation

Distinct from the type of local realist inequality (known as the Collins-Gisin-Linden-Massar-Popescu or CGLMP inequality) usually used for bipartite qutrit systems, we formulate a new set of local realist inequalities for bipartite qutrits by generalizing Wigner's argument that was originally formulated for the bipartite qubit singlet state. This treatment assumes existence of the overall joint probability distributions in the underlying stochastic hidden variable space for the measurement outcomes pertaining to the relevant trichotomic observables, satisfying the locality condition and yielding the measurable marginal probabilities. Such generalized Wigner inequalities (GWI) do not reduce to Bell-CHSH type inequalities by clubbing any two outcomes, and are violated by quantum mechanics (QM) for both the bipartite qutrit isotropic and singlet states using trichotomic observables defined by six-port beam splitter as well as by the spin-$1$ component observables. The efficacy of GWI is then probed in these cases by comparing the QM violation of GWI with that obtained for the CGLMP inequality. This comparison is done by incorporating white noise in the singlet and isotropic qutrit states. It is found that for the six-port beam splitter observables, QM violation of GWI is more robust than that of the CGLMP inequality for singlet qutrit states, while for isotropic qutrit states, QM violation of the CGLMP inequality is more robust. On the other hand, for the spin-$1$ component observables, QM violation of GWI is more robust for both the type of states considered.

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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

Nonlocality in Remote State Preparation vis-a-vis Teleportation

The hitherto unexplored nonlocality of quantum correlations in the information transfer protocol of remote state preparation (RSP) is investigated in terms of a unified nonlocality argument formulated for teleportation as well as for two distinct RSP schemes. The argument differs only in the respective types of local measurements used in each scenario. One of the RSP schemes uses single particle projective measurements, while the other uses joint Bell-basis measurements. Interestingly, the quantum mechanical violations of the Bell-CHSH type inequalities formulated for each of the RSP setups, while being equal to each other, also turn out to be equal to that of the corresponding Bell-CHSH type local realist inequality for teleportation, using the common resource of non-maximally entangled state. This reveals that for such a resource state, the maximum amount of extractable nonlocality of correlations involved in the transfer of information is the same for the standard teleportation protocol and the two RSP schemes considered here, thereby implying that the essential difference between teleportation and remote state preparation lies in the amount of classical information required to be exchanged between parties, and not in the nonlocality of underlying correlations.

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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

Manifestation of pointer state correlations in complex weak values of quantum observables

In the weak measurement (WM) scenario involving weak interaction and postselection by projective measurement, the empirical significance of weak values is manifested in terms of shifts in the measurement pointer's mean position and mean momentum. In this context, a general quantitative treatment is presented in this paper by taking into account the hitherto unexplored effect of correlations among the pointer degrees of freedom which pertain to an arbitrary multidimensional preselected pointer state. This leads to an extension of the earlier results, showing that, for complex weak values, the correlations among different pointer degrees of freedom can crucially affect the way the imaginary parts of the weak values are related to the observed shifts of the mean pointer position and momentum. The particular relevance of this analysis is discussed in the case of sequential weak interactions, followed by a postselection (called sequential WM) which, in the special case, reduces to the usual WM scheme involving a single weak interaction and postseletion, modified by the effect of pointer state correlations.

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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

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

Multipartite Bell-type Inequality by Generalizing Wigner's Argument

Wigner's argument inferring Bell-type inequality for the EPR-Bohm entangled state is generalized here for any N-partite state. This is based on assuming for the relevant dichotomic observables the existence of the overall joint probability distributions, satisfying the locality condition, that would yield the measurable marginal probabilities. For any N, such Generalized Wigner's Inequality (GWI) is violated by quantum mechanics for all pure entangled states. The efficacy of GWI is probed, comparing with the Seevinck-Svetlichny multipartite Bell-type inequality, by calculating threshold visibilities for the quadripartite GHZ, Cluster andWstates that determine their respective robustness with respect to the quantum mechanical violation of GWI in the presence of white noise.

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arXiv2014

Unification of Bell, Leggett-Garg and Kochen-Specker inequalities: A hybrid spatio-temporal inequality

The Bell-type (spatial), Kochen-Specker (contextuality) or Leggett-Garg (temporal) inequalities are based on classically plausible but otherwise quite distinct assumptions. For any of these inequalities, satisfaction is equivalent to a joint probability distribution for all observables in the experiment. This implies a joint distribution for all pairs of observables, and is indifferent to whether or not they commute in the theory. This indifference underpins a unification of the above inequalities into a general framework of correlation inequalities. When the physical scenario is such that the correlated pairs are all compatible, the resulting correlation is non-signaling, which may be local or multi-particle, corresponding to contextuality or Bell-type inequalities. If the pairs are incompatible, the resulting correlation corresponds to Leggett-Garg (LG) inequalities. That quantum mechanics (QM) violates all these inequalities suggests a close connection between the local, spatial and temporal properties of the theory. As a concrete manifestation of the unification, we extend the method due to Roy and Singh (J. Phys. A, 11, L167 (1978)) to derive and study a new class of hybrid spatio-temporal inequalities, where the correlated pairs in the experiment are both compatible or incompatible. The implications for cryptography and monogamy inequalities of the unification are briefly touched upon.

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arXiv2013

Larmor precession reexamined: Testable correction and its ramifications

For a spin-polarized plane wave passing through a spin-rotator containing uniform magnetic field, we provide a detailed analysis for solving the appropriate Schrödinger equation. A modified expression for spin precession is obtained which reduces to the standard Larmor precession relation when kinetic energy is very large compared to the spin-magnetic field interaction. We show that there are experimentally verifiable regimes of departure from the standard Larmor precession formula. The treatment is then extended to the case of a spin-polarized wave packet passing through a uniform magnetic field. The results based on the standard expression for Larmor precession and that obtained from the modified formula are compared in various regimes of the experimental parameters.

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