scholarly journals Quantifying Athermality and Quantum Induced Deviations from Classical Fluctuation Relations

Entropy ◽  
2020 ◽  
Vol 22 (1) ◽  
pp. 111
Author(s):  
Zoë Holmes ◽  
Erick Hinds Mingo ◽  
Calvin Chen ◽  
Florian Mintert
Keyword(s):  
Energy Supply ◽  
Quantum Coherence ◽  
Informational Content ◽  
Thermal System ◽  
Information Theoretic ◽  
Fluctuation Relations ◽  
Average Work ◽  
Increasing Process ◽  
Binomial State ◽  
Thermal States

In recent years, a quantum information theoretic framework has emerged for incorporating non-classical phenomena into fluctuation relations. Here, we elucidate this framework by exploring deviations from classical fluctuation relations resulting from the athermality of the initial thermal system and quantum coherence of the system’s energy supply. In particular, we develop Crooks-like equalities for an oscillator system which is prepared either in photon added or photon subtracted thermal states and derive a Jarzynski-like equality for average work extraction. We use these equalities to discuss the extent to which adding or subtracting a photon increases the informational content of a state, thereby amplifying the suppression of free energy increasing process. We go on to derive a Crooks-like equality for an energy supply that is prepared in a pure binomial state, leading to a non-trivial contribution from energy and coherence on the resultant irreversibility. We show how the binomial state equality fits in relation to a previously derived coherent state equality and offers a richer feature-set.

scholarly journals Distillation of maximally correlated bosonic matter from many-body quantum coherence

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 330
Author(s):  
Tyler J. Volkoff
Keyword(s):  
Quantum Coherence ◽  
Particle Number ◽  
Fock Space ◽  
Continuous Variable ◽  
Squeezed States ◽  
Discrete Variable ◽  
Many Body ◽  
Information Theoretic ◽  
Bose Einstein ◽  
Single Particle Basis

We construct quantum coherence resource theories in symmetrized Fock space (QCRTF), thereby providing an information-theoretic framework that connects analyses of quantum coherence in discrete-variable (DV) and continuous variable (CV) bosonic systems. Unlike traditional quantum coherence resource theories, QCRTF can be made independent of the single-particle basis and allow to quantify coherence within and between particle number sectors. For example, QCRTF can be formulated in such a way that neither Bose-Einstein condensates nor Heisenberg-Weyl coherent states are considered as quantum many-body coherence resources, whereas spin-squeezed and quadrature squeezed states are. The QCRTF framework is utilized to calculate the optimal asymptotic distillation rate of maximally correlated bosonic states both for particle number conserving resource states and resource states of indefinite particle number. In particular, we show how to generate a uniform superposition of maximally correlated bosonic states from a state of maximal bosonic coherence with asymptotically unit efficiency using only free operations in the QCRTF.

A Note on the Residual Entropy Function

1993 ◽  
Vol 7 (3) ◽  
pp. 413-420 ◽  
Author(s):  
Pietro Muliere ◽  
Giovanni Parmigiani ◽  
Nicholas G. Polson
Keyword(s):  
Information Theory ◽  
Probability Distribution ◽  
Random Variable ◽  
Reliability Theory ◽  
Entropy Function ◽  
Informational Content ◽  
Residual Entropy ◽  
Regularity Conditions ◽  
Information Theoretic ◽  
Information Theoretic Measures

Interest in the informational content of truncation motivates the study of the residual entropy function, that is, the entropy of a right truncated random variable as a function of the truncation point. In this note we show that, under mild regularity conditions, the residual entropy function characterizes the probability distribution. We also derive relationships among residual entropy, monotonicity of the failure rate, and stochastic dominance. Information theoretic measures of distances between distributions are also revisited from a similar perspective. In particular, we study the residual divergence between two positive random variables and investigate some of its monotonicity properties. The results are relevant to information theory, reliability theory, search problems, and experimental design.

scholarly journals Quantum coherence fluctuation relations

2018 ◽  
Vol 51 (41) ◽  
pp. 414007 ◽  
Author(s):  
Benjamin Morris ◽  
Gerardo Adesso
Keyword(s):  
Quantum Coherence ◽  
Fluctuation Relations

scholarly journals Decomposable coherence and quantum fluctuation relations

Quantum ◽  
2019 ◽  
Vol 3 ◽  
pp. 202 ◽  
Author(s):  
Erick Hinds Mingo ◽  
David Jennings
Keyword(s):  
Quantum Coherence ◽  
Composite System ◽  
Classical Mechanics ◽  
Newtonian Mechanics ◽  
Early Analysis ◽  
Work Processes ◽  
Temperature Dependent ◽  
Work Process ◽  
Fluctuation Relations ◽  
New Perspective

In Newtonian mechanics, any closed-system dynamics of a composite system in a microstate will leave all its individual subsystems in distinct microstates, however this fails dramatically in quantum mechanics due to the existence of quantum entanglement. Here we introduce the notion of a `coherent work process', and show that it is the direct extension of a work process in classical mechanics into quantum theory. This leads to the notion of `decomposable' and `non-decomposable' quantum coherence and gives a new perspective on recent results in the theory of asymmetry as well as early analysis in the theory of classical random variables. Within the context of recent fluctuation relations, originally framed in terms of quantum channels, we show that coherent work processes play the same role as their classical counterparts, and so provide a simple physical primitive for quantum coherence in such systems. We also introduce a pure state effective potential as a tool with which to analyze the coherent component of these fluctuation relations, and which leads to a notion of temperature-dependent mean coherence, provides connections with multi-partite entanglement, and gives a hierarchy of quantum corrections to the classical Crooks relation in powers of inverse temperature.

scholarly journals Coherent fluctuation relations: from the abstract to the concrete

Quantum ◽  
2019 ◽  
Vol 3 ◽  
pp. 124 ◽  
Author(s):  
Zoë Holmes ◽  
Sebastian Weidt ◽  
David Jennings ◽  
Janet Anders ◽  
Florian Mintert
Keyword(s):  
Quantum Systems ◽  
Theoretic Approach ◽  
Information Theoretic ◽  
Trapped Ion ◽  
Fluctuation Relations ◽  
Cat States ◽  
Information Theoretic Approach ◽  
Abstract Framework ◽  
Autonomous Evolution ◽  
Coherent Fluctuation

Recent studies using the quantum information theoretic approach to thermodynamics show that the presence of coherence in quantum systems generates corrections to classical fluctuation theorems. To explicate the physical origins and implications of such corrections, we here convert an abstract framework of an autonomous quantum Crooks relation into quantum Crooks equalities for well-known coherent, squeezed and cat states. We further provide a proposal for a concrete experimental scenario to test these equalities. Our scheme consists of the autonomous evolution of a trapped ion and uses a position dependent AC Stark shift.

scholarly journals Coherence Dynamics of Two Interacting Bosonic Modes in a Thermal Environment

2020 ◽  
Vol 226 ◽  
pp. 01006
Author(s):  
Aurelian Isar
Keyword(s):  
Open System ◽  
Quantum Coherence ◽  
Open Systems ◽  
Thermal Environment ◽  
Reservoir Temperature ◽  
Initial State ◽  
Completely Positive ◽  
Thermal Reservoir ◽  
Quantum Dynamical ◽  
Thermal States

We describe the time evolution of the quantum coherence in an open system consisting of two coupled bosonic modes embedded in a thermal reservoir. We discuss the influence of the environment in terms of the covariance matrix for initial squeezed thermal states. The coherence is quantified using the relative entropy as a measure, and its dynamics is studied in the framework of the theory of open systems based on completely positive quantum dynamical semigroups. We show that the evolution of the quantum coherence strongly depends on the initial state of the system (squeezing parameter and thermal photon numbers), the parameters characterizing the thermal reservoir (temperature and dissipation coefficient) and the intensity of the coupling between the two modes.

Redox Reactions in Lipid Membranes as a Model for Primordial Energy-Conserving Systems

1997 ◽  
Vol 161 ◽  
pp. 437-442
Author(s):  
Salvatore Di Bernardo ◽  
Romana Fato ◽  
Giorgio Lenaz
Keyword(s):  
Experimental Evidence ◽  
Lipid Membranes ◽  
Energy Supply ◽  
Redox Reactions ◽  
Living Systems ◽  
Asymmetric Distribution ◽  
Conservation Of Energy ◽  
Asymmetrical Distribution ◽  
Energy Conserving ◽  
Living Organisms

AbstractOne of the peculiar aspects of living systems is the production and conservation of energy. This aspect is provided by specialized organelles, such as the mitochondria and chloroplasts, in developed living organisms. In primordial systems lacking specialized enzymatic complexes the energy supply was probably bound to the generation and maintenance of an asymmetric distribution of charged molecules in compartmentalized systems. On the basis of experimental evidence, we suggest that lipophilic quinones were involved in the generation of this asymmetrical distribution of charges through vectorial redox reactions across lipid membranes.

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