arXiv subjects

Debasis Mondal

Publications and source records attributed to Debasis Mondal.

10 recordsLinked to original sources

arXiv2020

Self-testing of quantum states using symmetric local hidden state model

We introduce a symmetric local hidden state $(slhs)$ model in a scenario, where two spacially separated parties receive quantum states from an unknown source. We derive an inequality based on the model. A completely new form of nonlocality emerges from the resource theoretic point of view. The inequality singles out a larger set of quantum correlated states in the higher dimensional scenarios $(d> 2 $ X $2)$ than what is predicted by the existing $lhs$ model, opening a new front for the experimentalists to test the accuracy of the prediction. We propose an experiment to show the experimental violation of the inequality in the two qubit scenario and perform the experiment on the IBM quantum computer. However, the experimental method adopted for the two-qubit scenario does not naturally generalize in the higher dimensional scenarios and leaves the experimental verification of the claim open. We also show that the maximal violation of the inequality can be used to self-test the Bell state and measurement bases, leading to complete device-independence.

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arXiv2019

No nonlocal advantage of quantum coherence beyond quantum instrumentality

Recently, it was shown that quantum steerability is stronger than the bound set by the instrumental causal network. This implies, quantum instrumentality cannot simulate EPR-nonlocal correlations completely. In contrast, here we show that quantum instrumentality can indeed simulate EPR correlations completely and uniquely if viewed from the perspective of NAQC. Implication of our result is that the entire set of EPR-correlations can be explained by the LHS model in the instrumental causal background if viewed from the perspective of NAQC.

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arXiv2019

Authentication protocol based on collective quantum steering

It is well known that certain quantum correlations like quantum steering exhibit a monogamous relationship. In this paper, we exploit the asymmetric nature of quantum steering and show that there exist states which exhibit a polygamous correlation, known as collective correlation [He and Reid, Phys. Rev. Lett. 111, 250403 (2013)], where the state of one party, Alice, can be steered only by the joint effort of the other two parties, Bob and Charlie. As an example, we explicitly single out a particular set of $3$ qubit states which exhibit this polygamous relationship, known as collective steerability. We provide a recipe to identify the complete set of such states. We also provide a possible application of such states to an information theoretic task, termed as quantum key authentication (QKA) protocol. QKA can also be used in conjunction with other well known cryptography protocols to improve their security and we provide one such example with quantum private comparison (QPC).

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arXiv2018

Complementarity Relations Between Quantum Steering Criteria

Recently, a connection between quantum coherence and quantum steering was established and criteria for quantum steering or in other words, nonlocal advantage of quantum coherence (NAQC) were derived for two-qubit states. Here, we derive a set of complementarity relations between the steering or NAQC inequalities achieved by various criteria. We also extend the idea in the multi-partite scenario, specifically, in the three-qubit scenario, which can easily be generalized to the multi-partite scenario.

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arXiv2016

Non-Local Advantage of Quantum Coherence

A bipartite state is said to be steerable if and only if it does not have a single system description, i.e., the bipartite state cannot be explained by a local hidden state model. Several steering inequalities have been derived using different local uncertainty relations to verify the ability to control the state of one subsystem by the other party. Here, we derive complementarity relations between coherences measured on mutually unbiased bases using various coherence measures such as the $l_1$-norm, relative entropy and skew information. Using these relations, we derive conditions under which non-local advantage of quantum coherence can be achieved and the state is steerable. We show that not all steerable states can achieve such advantage.

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arXiv2016

Tighter Uncertainty and Reverse Uncertainty Relations

We prove a few novel state-dependent uncertainty relations for product as well the sum of variances of two incompatible observables. These uncertainty relations are shown to be tighter than the Roberson-Schrödinger uncertainty relation and other ones existing in the current literature. Also, we derive state dependent upper bound to the sum and the product of variances using the reverse Cauchy-Schwarz inequality and the Dunkl-Williams inequality. Our results suggest that not only we cannot prepare quantum states for which two incompatible observables can have sharp values, but also we have both, lower and upper limits on the variances of quantum mechanical observables at a fundamental level.

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arXiv2016

Quantum Speed Limit For Mixed States Using Experimentally Realizable Metric

The minimal time required for a system to evolve between two different states is an important notion for developing ultra-speed quantum computer and communication channel. Here, we introduce a new metric for non-degenerate density operator evolving along unitary orbit and show that this is experimentally realizable operation dependent metric on quantum state space. Using this metric, we obtain the geometric uncertainty relation that leads to a new quantum speed limit. Furthermore, we argue that this gives a tighter bound for the evolution time compared to any other bound. We also obtain a Levitin kind of bound for mixed states. We propose how to measure this new distance and speed limit in quantum interferometry. Finally, the lower bound for the evolution time of a quantum system is studied for any completely positive trace preserving map using this metric.

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arXiv2015

Quantum Coherence Sets The Quantum Speed Limit For Mixed States

We cast observable measure of quantum coherence or asymmetry as a resource to control the quantum speed limit (QSL) for unitary evolutions. For non-unitary evolutions, QSL depends on that of the state of the system and environment together. We show that the product of the time bound and the coherence (asymmetry) or the quantum part of the uncertainty behaves in a geometric way under partial elimination and classical mixing of states. These relations give a new insight to the quantum speed limit. We also show that our bound is experimentally measurable and is tighter than various existing bounds in the literature.

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arXiv2015

Steerability of Quantum Coherence in Accelerated Frame

The interplay between steering and quantum coherence is studied in a scenario, where two atoms move through an external massless scalar field. We show that just like entanglement, the steering induced coherence of the equilibrium state may increase or decrease with acceleration depending on the initial condition of the state. We also investigate the condition for coherence steerability - as opposed to simple state steerability. Interestingly, we find that the quantum coherence of the equilibrium state cannot be steered, even when the steering induced coherence is non-zero. We argue that under any condition, gravity prohibits the coherence steering of the equilibrium state.

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arXiv2015

Generalized Fubini-Study Metric and Fisher Information Metric

We provide an experimentally measurable local gauge $U(1)$ invariant Fubini-Study (FS) metric for mixed states. Like the FS metric for pure states, it also captures only the quantum part of the uncertainty in the evolution Hamiltonian. We show that this satisfies the quantum Cramer-Rao bound and thus arrive at a more general and measurable bound. Upon imposing the monotonicity condition, it reduces to the square-root derivative quantum Fisher Information. We show that on the Fisher information metric space dynamical phase is zero. A relation between square root derivative and logarithmic derivative is formulated such that both give the same Fisher information. We generalize the Fubini-Study metric for mixed states further and arrive at a set of Fubini-Study metric---called $α$ metric. This newly defined $α$ metric also satisfies the Cramer-Rao bound. Again by imposing the monotonicity condition on this metric, we derive the monotone $α$ metric. It reduces to the Fisher information metric for $α=1$.

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