arXiv subjects

A. K. Pan

Publications and source records attributed to A. K. Pan.

At least 55 records · Page 3Linked to original sources

arXiv2020

Interference experiment, anomalous weak value and Leggett-Garg test of macrorealism

Macrorealism is a classical world view asserting that the properties of macro-objects exist independently and irrespective of observation. One practical approach to test this view in quantum theory is to observe the quantum coherence for macro-object in an interference experiment. An elegant and conceptually appealing approach for testing the notion of macrorealism in quantum theory is through the violation of Leggett-Garg inequality. However, a conclusive Leggett-Garg test hinges on how the non-invasive measurability criteria is guaranteed in an experiment and remains a debated issue till date. In this work, we connect the practical and the conceptual approaches for testing the macrorealism through the weak value. We argue that whenever quantum effect is observed in an interference experiment there is an existence of anomalous weak value. Further, we demonstrate that whenever such weak value exists, one obtains the violation of a Leggett-Garg inequality in any interference experiment. Since the system itself serves as apparatus in a path-only interference experiment, one cannot salvage the macrorealism by abandoning the non-invasive measurability assumption. We provide a rigorous discussion about the assumptions involved in Leggett-Garg scenario and how our scheme fits into it. Further, using the quasiprobability approach we explain how non-invasive measurability condition is satisfied in our scheme.

quant-ph↗

arXiv2020

Device-independent certification of Hilbert space dimension using a family of Bell expressions

Dimension witness provides a device-independent certification of the minimal dimension required to reproduce the observed data without imposing assumptions on the functioning of the devices used to generate the experimental statistics. In this paper, we provide a family of Bell expressions where Alice and Bob perform $2^{n-1}$ and $n$ number of dichotomic measurements respectively which serve as the device-independent dimension witnesses of Hilbert space of $2^{m}$ dimensions with $m=1,2..2^{\lfloor n/2\rfloor}$. The family of Bell expressions considered here determines the success probability of a communication game known as $n$-bit parity-oblivious random access code. The parity obliviousness constraint is equivalent to preparation non-contextuality assumption in an ontological model of an operational theory. For any given $n\geq 3$, if such a constraint is imposed on the encoding scheme of the random-access code, then the local bound of the Bell expression reduces to the preparation non-contextual bound. We provide explicit examples for $n=4,5$ case to demonstrate that the relevant Bell expressions certify the qubit and two-qubit system, and for $n=6$ case, the relevant Bell expression certifies the qubit, two-qubit and three-qubit systems. We further demonstrate the sharing of quantum preparation contextuality by multiple Bobs sequentially to examine whether number of Bobs sharing the preparation contextuality is dependent on the dimension of the system. We provide explicit example of $n=5$ and $6$ to demonstrate that number of Bobs sequentially sharing the contextuality remains same for any of the $2^{m}$ dimensional systems.

quant-ph↗

arXiv2020

Quantum violation of variants of LGIs upto algebraic maximum for qubit system

In 1985, Leggett and Garg formulated a class of inequalities for testing the compatibility between macrorealism and quantum mechanics. In this paper, we point out that based on the same assumptions of macrorealism that are used in the derivation of Leggett-Garg inequalities (LGIs) , there is a scope of formulating another class of inequalities different from standard LGIs. By considering the three-time measurement scenario in a dichotomic system, we first propose an interesting variant of standard LGIs and show that its quantum violation is larger than the standard LGI. By extending this formulation to $n$-time measurement scenario, we found that the quantum violations of variants of LGIs for a \emph{qubit} system increase with $n$, and for a sufficiently large $n$ algebraic maximum can be reached. Further, we compare the quantum violations of our formulated LGIs with the standard LGIs and no-signaling in time formulation of macrorealism.

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arXiv2020

Swapping Intra-photon entanglement to Inter-photon entanglement using linear optical devices

We propose a curious protocol for swapping the intra-photon entanglement between path and polarization degrees of freedom of a single photon to inter-photon entanglement between two spatially separated photons which have never interacted. This is accomplished by using an experimental setup consisting of three suitable Mach-Zehnder interferometers along with number of beam splitters, polarization rotators and detectors. Using the same setup, we have also demonstrated an interesting quantum state transfer protocol, symmetric between Alice and Bob. Importantly, the Bell-basis discrimination is not required in both the swapping and state transfer protocols. Our proposal can be implemented using linear optical devices.

quant-ph↗

arXiv2020

Disembodiment of arbitrary number of properties in quantum Cheshire cat experiment

The quantum Cheshire cat is an effect demonstrated within the framework of weak measurement aided with post-selection scenario where the property (say, grin) of a quantum particle (the cat) can be found in a spatially separated location from its position. In this work, we first propose interesting variants of quantum Cheshire cat where disembodiment of two different properties of a `cat' is demonstrated, so that, the \emph{grin} and the \emph{meowing} of it can be found in two different paths on an interferometer while the cat is in another path. We further extend this proposal for three-qutrit and $d$-qudit systems of a single particle. We provide sketches of the experimental proposals for testing our scheme by using the path, spin and energy degrees of freedoms of a single neutron and the path, polarization and orbital angular momentum of a single photon.

quant-ph↗

arXiv2020

Semi-device independent randomness certification using Mermin's proof of Kochen-Specker contextuality

Randomness is a potential resource for cryptography, simulations and algorithms. Non-local correlations violating Bell's inequality certify the generation of bit strings whose randomness is guaranteed in a device-independent manner. We provide interesting semi-device independent randomness certification protocols by Kochen-Specker (KS) contextuality. For this, we first cast the Mermin's magic-square proof of KS contextuality for two-qubit system as a semi-device independent communication game in prepare-measure scenario. This provides a semi-device independent certification of two-bit of randomness. Further, by using Mermin's magic-star proof of KS theorem involving three-qubit system, we certify three-bit of randomness. We conjecture that our proposals can be extended to certify any arbitrary bit of randomness through a suitable KS proof of contextuality valid for higher dimensional system.

quant-ph↗

arXiv2020

Two definitions of maximally $ψ$-epistemic ontological model and preparation non-contextuality

An ontological model is termed as maximally $ψ$-epistemic if the overlap between any two quantum states is fully accounted for by the overlap of their respective probability distributions of ontic states. However, in literature, there exists the two different mathematical definitions (termed here as 1M$ψ$E and 2M$ψ$E) that capture the equivalent notion of maximal $ψ$-epistemicity. In this work, we provide three theorems to critically examine the connections between preparation non-contextuality and the aforementioned two definitions of maximal $ψ$- epistemicity. In Theorem-1, we provide a simple and direct argument of an existing proof to demonstrate that the mixed state preparation non-contextuality implies the first definition of maximal $ψ$-epistemicity. In Theorem-2, we prove that the second definition of maximal $ψ$-epistemicity implies pure-state preparation non-contextuality. If both the definitions capture the equivalent notion of maximal $ψ$-epistemicity then from the aforementioned two theorems one infers that the mixed-state preparation non-contextuality implies pure-state preparation non-contextuality. But, in Theorem-3, we demonstrate that the mixed-state preparation non-contextuality in an ontological model implies pure-state contextuality and vice-versa. This leads one to conclude that 1M$ψ$E and 2M$ψ$E capture inequivalent notion of maximal $ψ$-epistemicity. The implications of our results and their connections to other no-go theorems are discussed.

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arXiv2020

Probing inequivalent forms of Legget-Garg inequality in subatomic systems

We study various formulations of Leggett-Garg inequality (LGI), specifically, the Wigner and Clauser-Horne forms of LGI, in the context of subatomic systems, in particular, three flavor neutrino as well as meson systems. The optimal forms of various LGIs for either neutrinos or mesons are seen to depend on measurement settings. For the neutrinos, some of these inequalities can be written completely in terms of experimentally measurable probabilities. Hence, the Wigner and Clauser-Horne forms of LGI are found to be more suitable as compared to the standard LGI from the experimental point of view for the neutrino system. Further, these inequalities exhibit maximum quantum violation around the energies roughly corresponding to the maximum neutrino flux. The Leggett-Garg type inequality is seen to be more suited for the meson dynamics. The meson system being inherently a decaying system, allows one to see the effect of decoherence on the extent of violation of various inequalities. Decoherence is observed to reduce the degree of violation, and hence the nonclassical nature of the system.

hep-ph↗

arXiv2019

Revealing universal quantum contextuality through communication games

A theory is universal contextual if its prediction cannot be reproduced by an ontological model satisfying both preparation and measurement noncontextuality assumptions. In this report, we first generalize the logical proofs of quantum preparation and measurement contextuality for qubit system for any odd number of preparations and measurements. Based on the logical proof, we derive testable universally non-contextual inequalities violated by quantum theory. We then propose a class of two-party communication games and show that the average success probability of winning such games is solely linked to suitable Bell expression whose local bound is greater than universal non-contextual bound. Thus, for a given state, even if quantum theory does not exhibit non-locality, it may still reveal non-classicality by violating the universal non-contextual bound. Further, we consider a different communication game to demonstrate that for a given choices of observables in quantum theory, even if there is no logical proof of preparation and measurement contextuality exist, the universal quantum contextuality can be revealed through that communication game. Such a game thus test a weaker form of universal non-contextuality with minimal assumption.

quant-ph↗

arXiv2019

Macrorealistic inequalities stronger than the standard Leggett-Garg inequalities

In two-party, two-input and two-output measurement scenario only relevant Bell's inequality is the Clauser-Horne-Shimony-Holt (CHSH) form. They also provide the necessary and sufficient conditions for local realism. Any other form, such as, Clauser-Horne and Wigner forms reduce to the CHSH one. Standard Leggett-Garg inequalities are often considered to be the temporal analog of CHSH inequalities. But, they do not provide the necessary and sufficient conditions for macrorealism. There is thus scope of formulating new macrorealist inequalities different and stronger than the standard Leggett-Garg inequalities for testing compatibility between the macrorealism and quantum theory. In this paper, we propose three different classes of macrorealistic inequalities in three-time scenario; (i) The ones equivalent to standard Leggett-Garg inequalities in both macrorealist model and in quantum theory. (ii) A class of inequalities which are equivalent to the standard ones in macrorealist model but inequivalent and stronger in quantum theory (iii) Another class of inequalities which are inquivalent to the all formulations of Leggett-Garg inequalities both in macrorealist model and in quantum theory. This class of macrorealist inequalities reveals the incompatibility between macrorealism and quantum theory for specific cases even when any other formulation of Leggett-Garg inequalities fail to do so. We extend the formulations of the class (ii) inequalities to the four-time and two-time measurement scenario. Further, we provide a brief discussion about the alternate formulation of macrorealism which was derived based on the no-signaling in time conditions.

quant-ph↗

arXiv2019

Sharing non-locality and non-trivial preparation contextuality using same family of Bell expressions

In [Phys. Rev. Lett. 114, 250401 (2015)] the sharing of non-locality by multiple observers was demonstrated through the quantum violation of Clauser-Horne-Shimony-Halt inequality. In this paper we provide a scheme for sharing of non-locality and non-trivial preparation contextuality sequentially through the quantum violation of a family of Bell's inequalities where Alice and Bob perform $2^{n-1}$ and $n$ numbers of measurements of dichotomic observables respectively. For this, we consider that Alice always performs projective measurement and multiple Bobs sequentially perform unsharp measurement. We show that when Bob's choices of measurement settings are unbiased, maximum two Bobs can sequentially share the non-locality through the violation of our inequalities. Further, we show that the local bound of the aforementioned family of inequalities gets reduced if non-trivial preparation non-contextuality assumptions are further imposed. Then there is a chance to share the non-trivial preparation contextuality for more number of Bobs than that of non-locality. We demonstrate that the non-trivial preparation contextuality can be sequentially shared by arbitrary numbers of Bob for unbiased choices of his measurement settings.

quant-ph↗

arXiv2018

CHSH inequalities with appropriate response function for POVM and their quantum violation

In the derivation of local bound of a Bell's inequality, the response functions corresponding to the different outcomes of measurements are fixed by the relevant hidden variables irrespective of the fact if the measurement is unsharp. In the context of a recent result by Spekkens that tells even in an ontological model the unsharp observable cannot be assigned a deterministic response function, we derive a modified local bound of CHSH inequality in unsharp measurement scenario. We consider response function for a given POVM which is determined by the response functions of the relevant projectors appearing in its spectral representation. In this scenario, the local bound of CHSH inequality is found to be dependent on the unsharpness parameter. This then enables us to show that the quantum violation of CHSH inequality for unbiased spin-POVMs occurs whenever there is violation for their sharp counterpart. For the case of biased POVMs, it is shown that the quantum violation of CHSH inequality can be obtained for ranges of sharpness parameter for which no violation obtained using standard local bound of CHSH inequality.

quant-ph↗

arXiv2018

Quantum contextuality for a three-level system sans realist model

Recently, an interesting form of non-classical effect which can be considered as a form of contextuality within quantum mechanics, has been demonstrated for a four-level system by discriminating the different routes that are taken for measuring a single observable. In this paper, we provide a simpler version of that proof for a single qutrit, which is also within the formalism of quantum mechanics and without recourse to any realist hidden variable model. The degeneracy of the eigenvalues and the L$\ddot{u}$der projection rule play important role in our proof.

quant-ph↗

arXiv2018

Faithful Pointer for qubit measurement

In the context of von Neumann projective measurement scenario for a qubit system, it is widely believed that the mutual orthogonality between the post-interaction pointer states is the sufficient condition for achieving the ideal measurement situation. However, for experimentally verifying the observable probabilities, the real space distinction between the pointer distributions corresponding to post-interaction pointer states play crucial role. It is implicitly assumed that mutual orthogonality ensures the support between the post-interaction pointer distributions to be disjoint. We point out that mutual orthogonality (formal idealness) does \emph{not} necessarily imply the real space distinguishability (operational idealness), but converse is true. In fact, for the commonly referred Gaussian wavefunction, it is possible to obtain a measurement situation which is formally ideal but fully nonideal operationally. In this paper, we derive a class of pointer states, that we call faithful pointers, for which the degree of formal (non)idealness is equal to the operational (non)idealness. In other words, for the faithful pointers, if a measurement situation is formally ideal then it is operationally ideal and vice versa.

quant-ph↗

arXiv2018

Optimal quantum preparation contextuality in $n$-bit parity-oblivious multiplexing task

In [ PRL, 102, 010401 (2009)], Spekkens et al., have shown that quantum preparation contextuality can power the parity-oblivious multiplexing (POM) task. The bound on the optimal success probability of $n$-bit POM task performed with the classical resources was shown to be the \textit{same} as in a preparation non-contextual theory. This non-contextual bound is violated if the task is performed with quantum resources. While in $2$-bit POM task the optimal quantum success probability is achieved, in 3-bit case optimality was left as an open question. In this paper, we show that the quantum success probability of a $n$-bit POM task is solely dependent on a suitable $2^{n-1}\times n$ Bell's inequality and optimal violation of it optimizes the success probability of the said POM task. Further, we discuss how the degree of quantum preparation contextuality restricts the amount of quantum violations of Bell's inequalities, and consequently the success probability of a POM task.

quant-ph↗

arXiv2018

On the violation of L$\ddot{u}$ders bound of macrorealist and noncontextual inequalities

In a recent Letter [PRL, 113, 050401 (2014)], it is shown that the quantum violation of a three-time Leggett-Garg inequality (LGI) for a dichotomic qutrit system can exceed the L$\ddot{u}$ders bound. This is obtained by using a degeneracy breaking projective measurement rule which the authors termed as von Neumann rule. Such violation can even approach the algebraic maximum in the asymptotic limit of system size. In this paper, we question the implication of such violation of L$\ddot{u}$ders bound and its conceptual relevance in LG scenario. We note an important fact that the basis for implementing the proposed von Neumann rule for a degenerate observable is non-unique and show that the violation of L$\ddot{u}$ders bound is crucially dependent on the choice of basis. Further, we demonstrate the violation of L$\ddot{u}$ders bound of the simplest non-contextual inequality (NCI) which is in contrast to the reasoning provided in the aforementioned Letter. This result further raises the doubts regarding the validity of the proposed rule as a viable projective measurement. We discuss the relevance of such results with respect to the usual quantum violation of LGI and NCI.

quant-ph↗

arXiv2018

Sub-Planck structure in a mixed state

The persistence of sub-Planck structure in phase space with loss of coherence is demonstrated in a mixed state, which comprises two terms in the density matrix. Its utility in carrying out Heisenberg-limited measurement and quantum parameter estimation have been shown. It is also shown that the mixed state performs equally well as the compass state for carrying out precision measurements. The advantage of using mixed state relies on the fact that such a state can be easier to prepare and may appear from pure states after partial loss of coherence. We explicate the effect of environment on these sub-Planck structures in the mixed state and estimates the time scale of complete decoherence.

quant-ph↗

arXiv2017

Probing various formulations of macrorealism for unsharp quantum measurements

Standard Leggett and Garg inequalities (SLGIs) were formulated for testing the incompatibility between the classical worldview of macrorealism and quantum mechanics. In recent times, various other formulations, such as Wigner form of LGIs (WLGIs), entropic LGIs (ELGIs) and the no-signaling in time (NSIT) condition have also been proposed. It is also recently argued that no set of SLGIs can provide the necessary and sufficient conditions for macrorealism but a suitable conjunction of NSIT conditions provides the same. In this paper, we first provide a comparative study of the various formulations of LGIs for testing macrorealism pertaining to the two different unsharp measurements. While the violations of WLGIs are more robust than SLGIs and ELGIs for spin-POVMs, here we demonstrate that for the case of biased POVMs, the quantum violations of both SLGIs and ELGIs provide the same robustness as WLGIs. Importantly, the violations of all formulations of LGIs can be achieved for \textit{any non-zero value} of unsharpness parameter. We have also studied the connection between LGIs and NSIT conditions. Further, we investigate the role of the joint measurability of the POVMs in the violation of LGIs and found that there is no generic connection.

quant-ph↗