arXiv subjects

Arun Kumar Pati

Publications and source records attributed to Arun Kumar Pati.

At least 37 records · Page 2Linked to original sources

arXiv2022

Quantum Speed Limits for Observables

In the Schr{ö}dinger picture, the state of a quantum system evolves in time and the quantum speed limit describes how fast the state of a quantum system evolves from an initial state to a final state. However, in the Heisenberg picture the observable evolves in time instead of the state vector. Therefore, it is natural to ask how fast an observable evolves in time. This can impose a fundamental bound on the evolution time of the expectation value of quantum mechanical observables. We obtain the quantum speed limit time-bound for observable for closed systems, open quantum systems and arbitrary dynamics. Furthermore, we discuss various applications of these bounds. Our results can have several applications ranging from setting the speed limit for operator growth, correlation growth, quantum thermal machines, quantum control and many body physics.

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arXiv2022

Entanglement Meter: Estimation of entanglement with single copy in Interferometer

Efficient certification and quantification of high dimensional entanglement of composite systems are challenging both theoretically as well as experimentally. Here, we demonstrate that several entanglement detection methods can be implemented efficiently in a Mach-Zehnder Interferometric set-up. In particular, we demonstrate how to measure the linear entropy and the negativity of bipartite systems from the visibility of Mach-Zehnder interferometer using single copy of the input state. Our result shows that for any two qubit pure bipartite state, the interference visibility is a direct measure of entanglement. We also propose how to measure the mutual predictability experimentally from the intensity patterns of the interferometric set-up without having to resort to local measurements of mutually unbiased bases. Furthermore, we show that the entanglement witness operator can be measured in a interference setup and the phase shift is sensitive to the separable or entangled nature of the state. Our proposals bring out the power of Interferometric set-up in entanglement detection of pure and several mixed states which paves the way towards design of entanglement meter.

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arXiv2022

Stronger Quantum Speed Limit

The quantum speed limit provides fundamental bound on how fast a quantum system can evolve between the initial and the final states. For the unitary evolution, the celebrated Mandelstam-Tamm (MT) bound has been widely studied for various systems. Here, we prove a stronger quantum speed limit (SQSL) for all quantum systems undergoing arbitrary unitary evolution and show that the MT bound is a special case of the stronger quantum speed limit. We apply our result for single system as well as for composite systems in separable and entangled states and show that the new bound is indeed tight. The stronger quantum speed limit will have wide range of applications in quantum control, quantum computing and quantum information processing.

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arXiv2022

Capacity of Entanglement for Non-local Hamiltonian

The notion of capacity of entanglement is the quantum information theoretic counterpart of the heat capacity which is defined as the second cumulant of the entanglement spectrum. Given any bipartite pure state, we can define the capacity of entanglement as the variance of the modular Hamiltonian in the reduced state of any of the subsystems. Here, we study the dynamics of this quantity under non-local Hamiltonian. Specifically, we address the question: Given an arbitrary non-local Hamiltonian what is the capacity of entanglement that the system can possess? As an useful application, we show that the quantum speed limit for creating the entanglement is not only governed by the fluctuation in the non-local Hamiltonian, but also depends inversely on the time average of square root of the capacity of entanglement. Furthermore, we discuss this quantity for a general self-inverse Hamiltonian and provide a bound on the rate of the capacity of entanglement. Towards the end, we generalise the capacity of entanglement for bipartite mixed states based on the relative entropy of entanglement and show that the above definition reduces to the capacity of entanglement for pure bipartite states. Our results can have several applications in diverse areas of physics.

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arXiv2022

Information Bleaching, No-Hiding Theorem and Indefinite Causal Order

The information bleaching refers to any physical process that removes quantum information from the initial state of the physical system. The no-hiding theorem proves that if information is lost from the initial system, then it cannot remain in the bipartite quantum correlation and must be found in the remainder of the Hilbert space. We show that when hiding map acts on the input state in the presence of indefinite causal order, then it is possible to hide quantum information in the correlation. One may ask, does it then violate the no-hiding theorem? We analyse this question and argue that in the extended Hilbert space, it will still respect the no-hiding theorem. We also discuss how to mask quantum information using superposition of two hiding maps. Our results can have interesting implications in preserving the fidelity of information, preservation of quantum coherence and work extraction in the presence of two hiding maps with indefinite causal order. Furthermore, we apply the hiding maps in the presence of indefinite causal order on half of an entangled pair and show that entanglement cannot be preserved. Finally, we discuss that even though quantum entanglement is destroyed, the entanglement fidelity under indefinite causal order is non-zero and can approach close to one.

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arXiv2022

Estimating quantum coherence by noncommutativity of any observable and its incoherent part

We establish a lower bound on the quantum coherence of an arbitrary quantum state in arbitrary dimension, using a noncommutativity estimator of an arbitrary observable of sub-unit norm, where the estimator is the commutator of the observable and its incoherent or classical part. The relation provides a direct method of obtaining an estimate of the quantum coherence of an arbitrary quantum state, without resorting to quantum state tomography or the existing witness operators.

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arXiv2022

Quantum speed limits for information and coherence

The quantum speed limit indicates the maximal evolution speed of the quantum system. In this work, we determine speed limits on the informational measures, namely the von Neumann entropy, maximal information, and coherence of quantum systems evolving under dynamical processes. These speed limits ascertain the fundamental limitations on the evolution time required by the quantum systems for the changes in their informational measures. Erasing of quantum information to reset the memory for future use is crucial for quantum computing devices. We use the speed limit on the maximal information to obtain the minimum time required to erase the information of quantum systems via some quantum processes of interest.

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arXiv2022

Extraction of Product and Higher Moment Weak Values: Applications in Quantum State Reconstruction and Entanglement Detection

Weak measurements introduced by Aharonov, Albert and Vaidman (AAV) can provide informations about the system with minimal back action. Weak values of product observables (commuting) or higher moments of an observable are informationally important in the sense that they are useful to resolve some paradoxes, realize strange quantum effects, reconstruct density matrices, etc. In this work, we show that it is possible to access the higher moment weak values of an observable using weak values of that observable with pairwise orthogonal post-selections. Although the higher moment weak values of an observable are inaccessible with Gaussian pointer states, our method allows any pointer state. We have calculated product weak values in a bipartite system for any given pure and mixed pre selected states. Such product weak values can be obtained using only the measurements of local weak values (which are defined as single system weak values in a multi-partite system). As an application, we use higher moment weak values and product weak values to reconstruct unknown quantum states of single and bipartite systems, respectively. Further, we give a necessary separability criteria for finite dimensional systems using product weak values and certain class of entangled states violate this inequality by cleverly choosing the product observables and the post selections. By such choices, positive partial transpose (PPT) criteria can be achieved for these classes of entangled states. Robustness of our method which occurs due to inappropriate choices of quantum observables and noisy post-selections is also discussed here. Our method can easily be generalized to the multi-partite systems.

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arXiv2021

Quantum Superposition of Two Temperatures

In the classical world, temperature is a measure of how hot or cold a physical object is. We never find a physical system which can be both hot and cold at the same time. Here, we show that for a quantum system, it is possible to have superposition of two temperatures which can lead to a situation that it can be found both in hot and cold state. We propose a physical mechanism for how to create a quantum state which is superposition of two temperatures. Furthermore, we define an operator for the inverse temperature and show that the thermal state is, in fact, an eigenstate of this operator. The quantum state which represents superposition of two temperatures is not an eigenstate of the inverse temperature operator. Our findings can have new applications in quantum thermodynamics, quantum nano scale devices and quantum statistical mechanics.

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arXiv2021

Reverse Quantum Speed Limit: How Slow Quantum Battery can Discharge?

We introduce the notion of reverse quantum speed limit for arbitrary quantum evolution which answers a fundamental question: ``how slow a quantum system can evolve in time?" Using the geometrical approach to quantum mechanics, the reverse speed limit follows from the fact that the gauge invariant length of the reference section is always greater than the Fubini-Study distance on the projective Hilbert space of the quantum system. We illustrate the reverse speed limit for two-level quantum systems with an external driving Hamiltonian and show that our results hold well. We find several examples where our bound is tight. We also find one practical application of the reverse speed limit in discharging process of quantum batteries which answers the question: ``how slow quantum batteries can discharge?" Our result provides a lower bound on the average discharging power of quantum batteries.

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arXiv2021

Wave and particle properties can be spatially separated in a quantum entity

Wave and particle are two fundamental properties of Nature. The wave-particle duality has indicated that a quantum object may exhibit the behaviours of both wave and particle, depending upon the circumstances of the experiment. The major significance of wave-particle duality has led to a fundamental equation in quantum mechanics, the Schr{\" o}dinger equation. At present, the principle of wave-particle duality has been deeply rooted in people's hearts. This gives rise to a common sense perception that wave property and particle property coexist simultaneously in a quantum entity, and these two physical attributes cannot be completely separated from each other. In classical physics, a similar common sense is that a physical system is inseparable from its physical properties. However, this has been recently challenged and beaten by a quantum phenomenon called the "quantum Cheshire cat", for which a cat and its grin can be separated spatially. In this work, we propose a thought experiment based on the similar technology of quantum Cheshire cat. We find that wave and particle attributes of a quantum entity can be completely separated, thus successfully dismantling the wave-particle duality for a quantum entity. Our result is still consistent with the complementarity principle and deepens the understanding of quantum foundations.

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arXiv2021

Protocol for unambiguous quantum state discrimination using quantum coherence

Roa et al. showed that quantum state discrimination between two nonorthogonal quantum states does not require quantum entanglement but quantum dissonance only. We find that quantum coherence can also be utilized for unambiguous quantum state discrimination. We present a protocol and quantify the required coherence for this task. We discuss the optimal unambiguous quantum state discrimination strategy in some cases. In particular, our work illustrates an avenue to find the optimal strategy for discriminating two nonorthogonal quantum states by measuring quantum coherence.

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arXiv2021

Greenberger-Horne-Zeilinger States: Their Identifications and Robust Violations

The $N$-qubit Greenberger-Horne-Zeilinger (GHZ) states are the maximally entangled states of $N$ qubits, which have had many important applications in quantum information processing, such as quantum key distribution and quantum secret sharing. Thus how to distinguish the GHZ states from other quantum states becomes a significant problem. In this work, by presenting a family of the generalized Clauser-Horne-Shimony-Holt (CHSH) inequality, we show that the $N$-qubit GHZ states can be indeed identified by the maximal violations of the generalized CHSH inequality under some specific measurement settings. The generalized CHSH inequality is simple and contains only four correlation functions for any $N$-qubit system, thus has the merit of facilitating experimental verification. Furthermore, we present a quantum phenomenon of robust violations of the generalized CHSH inequality, in which the maximal violation of Bell's inequality can be robust under some specific noises adding to the $N$-qubit GHZ states.

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arXiv2021

Classical Communications with Indefinite Causal Order for $N$ completely depolarizing channels

If two identical copies of a completely depolarizing channel are put into a superposition of their possible causal orders, they can transmit non-zero classical information. Here, we study how well we can transmit classical information with $N$ depolarizing channels put in superposition of $M$ causal orders via quantum SWITCH. We calculate Holevo quantity if the superposition uses only cyclic permutations of channels and find that it increases with $M$ and it is independent of $N$. For a qubit it never reaches $1$ if we are increasing $M$. On the other hand, the classical capacity decreases with the dimension $d$ of the message system. Further, for $N=3$ and $N=4$ we studied superposition of all causal orders and uniformly superposed causal orders belonging to different cosets created by cyclic permutation subgroup.

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arXiv2020

Quantum precision thermometry with weak measurement

As the minituarization of electronic devices, which are sensitive to temperature, grows apace, sensing of temperature with ever smaller probes is more important than ever. Genuinely quantum mechanical schemes of thermometry are thus expected to be crucial to future technological progress. We propose a new method to measure the temperature of a bath using the weak measurement scheme with a finite dimensional probe. The precision offered by the present scheme not only shows similar qualitative features as the usual Quantum Fisher Information based thermometric protocols, but also allows for flexibility over setting the optimal thermometric window through judicious choice of post selection measurements.

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arXiv2020

Can Two Quantum Cheshire Cats Exchange Grins?

A common-sense perception of a physical system is that it is inseparable from its physical properties. The notion of Quantum Cheshire Cat challenges this, as far as quantum systems are concerned. It shows that a quantum system can be decoupled from its physical property under suitable pre and postselections. However, in the Quantum Cheshire Cat setup, the decoupling is not permanent. The photon, for example, and its circular polarization is separated and then recombined. In this paper, we present a thought experiment where we decouple two photons from their respective polarizations and then interchange them during recombination. Thus, our proposal shows that the belongingness of a property for a physical system is very volatile in the quantum world. This raises the question of reality of an observable at a much deeper level.

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arXiv2020

Coherence as witness for quantumness of gravity

We propose an interferometric set-up that utilizes the concept of quantum coherence to provide quantum signatures of gravity. The gravitational force comes into nontrivial play due to the existence of an extra mass in the set-up that transforms an incoherent state to a coherent state. The implication uses the fact that quantum coherence at a certain site cannot be altered by local actions at a separate site. The ability to transform an incoherent state to a coherent one in the presence of gravitational field provides a signature of quantumness of gravity. We also observe that the results remain unaltered in presence of a nontrivial quantity of depolarising noise.

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arXiv2019

Direct Experimental Test of Forward and Reverse Uncertainty Relations

The canonical Robertson-Schrödinger uncertainty relation provides a loose bound for the product of variances of two non-commuting observables. Recently, several tight forward and reverse uncertainty relations have been proved which go beyond the traditional uncertainty relations. Here we experimentally test multifold of state-dependent uncertainty relations for the product as well as the sum of variances of two incompatible observables for photonic qutrits. These uncertainty relations are independent of any optimization and still tighter than the Robertson-Schrödinger uncertainty relation and other ones found in current literatures. For the first time, we also test the state-dependent reverse uncertainty relations for the sum of variances of two incompatible observables, which implies another unique feature of preparation uncertainty in quantum mechanics. Our experimental results not only foster insight into a fundamental limitation on preparation uncertainty but also may contribute to the study of upper limit of precession measurements for incompatible observables.

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