arXiv subjects

Chiranjib Mukhopadhyay

Publications and source records attributed to Chiranjib Mukhopadhyay.

29 records · Page 2Linked to original sources

arXiv2018

Quantum uncertainty relation based on the mean deviation

Traditional forms of quantum uncertainty relations are invariably based on the standard deviation. This can be understood in the historical context of simultaneous development of quantum theory and mathematical statistics. Here, we present alternative forms of uncertainty relations, in both state dependent and state independent forms, based on the mean deviation. We illustrate the robustness of this formulation in situations where the standard deviation based uncertainty relation is inapplicable. We apply the mean deviation based uncertainty relation to detect EPR violation in a lossy scenario for a higher inefficiency threshold than that allowed by the standard deviation based approach. We demonstrate that the mean deviation based uncertainty relation can perform equally well as the standard deviation based uncertainty relation as non-linear witness for entanglement detection.

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arXiv2018

Stronger classes of sum uncertainty and reverse uncertainy relations

Uncertainty relations are old, yet potentially rewarding to explore. By introducing a quantity called the uncertainty matrix, we provide a link between purity and observable incompatibility, and derive several stronger uncertainty relations in both forward and reverse directions for arbitrary quantum states, i.e., mixed as well as pure, and arbitrary incompatible quantum observables, none of which suffer from the problem of triviality. Besides the tightness, the interpretations of terms in these uncertainty relations may be of independent inter- est. We provide the possible generalization of stronger uncertainty relations to sum of variances of more than two observables. We also demonstrate applications of techniques used here to, firstly, obtain a simple reverse quantum speed limit for quantum states undergoing Markovian dynamical evolution, and secondly, to provide a lower bound for fidelity between two quantum states.

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arXiv2018

Coherence makes quantum systems 'magical'

Two primary facets of quantum technological advancement that hold great promise are quantum communication and quantum computation. For quantum communication, the canonical resource is entanglement. For quantum gate implementation, the resource is 'magic' in an auxiliary system. It has already been shown that quantum coherence is the fundamental resource for the creation of entanglement. We argue on the similar spirit that quantum coherence is the fundamental resource when it comes to the creation of magic. This unifies the two strands of modern development in quantum technology under the common underpinning of existence of quantum superposition, quantified by the coherence in quantum theory. We also attempt to obtain magic monotones inspired from coherence monotones and vice versa. We further study the interplay between quantum coherence and magic in a qutrit system and that between quantum entanglement and magic in a qutrit-qubit setting.

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arXiv2018

Generating steady quantum coherence and magic through an autonomous thermodynamic machine by utilizing a spin bath

Generation of steady quantumness in the presence of an environment is of utmost importance if we are to build practical quantum devices. We propose a scheme of generating steady coherence and magic in a qubit system attached to a heat bath at a certain temperature through its interaction with another qubit system attached to a spin bath. Coherence generation in the reduced qubit is always possible in this model. The steady coherence in the reduced qubit attached to the heat bath may be used to enhance the subsequent transient performance of a quantum absorption refrigerator. For the case of generation of magic, which is the quantum resource responsible for implementation of gates which are not simulable via stabilizer computation, we show that there exists a critical temperature of the heat bath beyond which it is not possible to create magic in the reduced qubit attached to the heat bath. Below the critical temperature, the strength of interaction between the qubits must lie within a certain region for creation of magic. We further note that by increasing the strength of coupling of the second qubit to the spin bath, typified by the reset probability, keeping the coupling strength of the first qubit to the heat bath fixed, it is possible to increase the critical temperature of the heat bath for creation of magic.

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arXiv2018

Quantum speed limit constraints on a nanoscale autonomous refrigerator

Quantum speed limit, furnishing a lower bound on the required time for the evolution of a quantum system through the state space, imposes an ultimate natural limitation to the dynamics of physical devices. Quantum absorption refrigerators, on the other hand, have attracted a great deal of attention in the last few years. In this article, we discuss the effects of quantum speed limit on the performance of a quantum absorption refrigerator. In particular, we show that there exists a trade-off relation between the steady cooling rate of the refrigerator and the minimum time taken to reach the steady state. Based on this, we define a figure of merit called "bounding second order cooling rate" and show that this scales linearly with the unitary interaction strength among the constituent qubits. We also study the increase of bounding second order cooling rate with the thermalization strength. We subsequently demonstrate that coherence in the initial three qubit system can significantly increase the bounding second order cooling rate. We study the efficiency of the refrigerator at maximum bounding second order cooling rate and, in a limiting case, we show that the efficiency at maximum bounding second order cooling rate is given by a simple formula reminiscent of the Curzon-Ahlborn relation.

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arXiv2018

Quantifying coherence with quantum addition

Quantum addition channels have been recently introduced in the context of deriving entropic power inequalities for finite dimensional quantum systems. We prove a reverse entropy power equality which can be used to analytically prove an inequality conjectured recently for arbitrary dimension and arbitrary addition weight. We show that the relative entropic difference between the output of such a quantum additon channel and the corresponding classical mixture quantitatively captures the amount of coherence present in a quantum system. This new coherence measure admits an upper bound in terms of the relative entropy of coherence and is utilized to formulate a state-dependent uncertainty relation for two observables. Our results may provide deep insights to the origin of quantum coherence for mixed states that truly come from the discrepancy between quantum addition and the classical mixture.

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arXiv2017

Dynamics and thermodynamics of a central spin immersed in a spin bath

An exact reduced dynamical map along with its operator sum representation is derived for a central spin interacting with a thermal spin environment. The dynamics of the central spin shows high sustainability of quantum traits such as coherence and entanglement in the low-temperature regime. However, for sufficiently high temperature and when the number of bath particles approaches the thermodynamic limit, this feature vanishes and the dynamics closely mimics Markovian evolution. The properties of the long-time-averaged state and the trapped information of the initial state for the central qubit are also investigated in detail, confirming that the nonergodicity of the dynamics can be attributed to the finite temperature and finite size of the bath. It is shown that if a certain stringent resonance condition is satisfied, the long-time-averaged state retains quantum coherence, which can have far reaching technological implications in engineering quantum devices. An exact time-local master equation of the canonical form is derived. With the help of this master equation, the nonequilibrium properties of the central spin system are studied by investigating the detailed balance condition and irreversible entropy production rate. The result reveals that the central qubit thermalizes only in the limit of very high temperature and large number of bath spins.

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arXiv2017

A note on robustness of coherence for multipartite quantum states

In this brief report, we prove that robustness of coherence (ROC), in contrast to many popular quantitative measures of quantum coherence derived from the resource theoretic framework of coherence, may be sub-additive for a specific class of multipartite quantum states. We investigate how the sub-additivity is affected by admixture with other classes of states for which ROC is super-additive. We show that pairs of quantum states may have different orderings with respect to relative entropy of coherence, $l_{1}$-norm of coherence and ROC and numerically study the difference in ordering for coherence measures chosen pairwise.

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arXiv2016

Exact master equation for a spin interacting with a spin bath: Non-Markovianity and negative entropy production rate

An exact canonical master equation of the Lindblad form is derived for a central spin interacting uniformly with a sea of completely unpolarized spins. The Kraus operators for the dynamical map are also derived. The non-Markovianity of the dynamics in terms of the divisibility breaking of the dynamical map and increase of the trace distance fidelity between quantum states is shown. Moreover, it is observed that the irreversible entropy production rate is always negative (for a fixed initial state) whenever the dynamics exhibits non-Markovian behavior. In continuation with the study of witnessing non-Markovianity, it is shown that the positive rate of change of the purity of the central qubit is a faithful indicator of the non-Markovian information back flow. Given the experimental feasibility of measuring the purity of a quantum state, a possibility of experimental demonstration of non-Markovianity and the negative irreversible entropy production rate is addressed. This gives the present work considerable practical importance for detecting the non-Markovianity and the negative irreversible entropy production rate.

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arXiv2016

Stronger Error Disturbance Relations for Incompatible Quantum Measurements

We formulate a new error-disturbance relation, which is free from explicit dependence upon variances in observables. This error-disturbance relation shows improvement over the one provided by the Branciard inequality and the Ozawa inequality for some initial states and for particular class of joint measurements under consideration. We also prove a modified form of Ozawa's error-disturbance relation. The later relation provides a tighter bound compared to the Ozawa and the Branciard inequalities for a small number of states.

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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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