QUANTUM MEASUREMENTS, INFORMATION AND ENTROPY PRODUCTION (original) (raw)
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Information and entropy in quantum theory
Arxiv preprint quant-ph/0411172, 2004
We look at certain thought experiments based upon the 'delayed choice' and 'quantum eraser' interference experiments, which present a complementarity between information gathered from a quantum measurement and interference effects. It has been argued that these experiments show the Bohm interpretation of quantum theory is untenable. We demonstrate that these experiments depend critically upon the assumption that a quantum optics device can operate as a measuring device, and show that, in the context of these experiments, it cannot be consistently understood in this way. By contrast, we then show how the notion of 'active information' in the Bohm interpretation provides a coherent explanation of the phenomena shown in these experiments. We then examine the relationship between information and entropy. The thought experiment connecting these two quantities is the Szilard Engine version of Maxwell's Demon, and it has been suggested that quantum measurement plays a key role in this. We provide the first complete description of the operation of the Szilard Engine as a quantum system. This enables us to demonstrate that the role of quantum measurement suggested is incorrect, and further, that the use of information theory to resolve Szilard's paradox is both unnecessary and insufficient. Finally we show that, if the concept of 'active information' is extended to cover thermal density matrices, then many of the conceptual problems raised by this paradox appear to be resolved.
AIP Conference Proceedings, 2002
The Kullback-Leibler inequality is a way of comparing any two density matrices. A technique to set up the density matrix for a physical system is to use the maximum entropy principle, given the entropy as a functional of the density matrix, subject to known constraints. In conjunction with the master equation for the density matrix, these two ingredients allow us to formulate the second law of thermodynamics in its widest possible setting. Thus problems arising in both quantum statistical mechanics and quantum information can be handled. Aspects of thermodynamic concepts such as the Carnot cycle will be discussed. A model is examined to elucidate the role of entanglement in the Landauer erasure problem.
The role of quantum information in thermodynamics—a topical review
Journal of Physics A: Mathematical and Theoretical, 2016
This topical review article gives an overview of the interplay between quantum information theory and thermodynamics of quantum systems. We focus on several trending topics including the foundations of statistical mechanics, resource theories, entanglement in thermodynamic settings, fluctuation theorems and thermal machines. This is not a comprehensive review of the diverse field of quantum thermodynamics; rather, it is a convenient entry point for the thermo-curious information theorist. Furthermore this review should facilitate the unification and understanding of different interdisciplinary approaches emerging in research groups around the world.
The Von Neumann Entropy: A Reply to Shenker
The British Journal for the Philosophy of Science, 2003
Shenker has claimed that Von Neumann's argument for identifying the quantum mechanical entropy with the Von Neumann entropy, SðrÞ ¼ Àktrðr log rÞ, is invalid. Her claim rests on a misunderstanding of the idea of a quantum mechanical pure state. I demonstrate this, and provide a further explanation of Von Neumann's argument.
Information and the second law of thermodynamics
2018
The second law of classical thermodynamics, based on the positivity of the entropy production, only holds for deterministic processes. Therefore the Second Law in stochastic quantum thermodynamics may not hold. By making a fundamental connection between thermodynamics and information theory we will introduce a new way of defining the Second Law which holds for both deterministic classical and stochastic quantum thermodynamics. Our work incorporates information well into the Second Law and also provides a thermodynamic operational meaning for negative and positive entropy production.
2013
The quantum measurement problem is revisited and discussed in terms of a new solvable measurement model which basic ingredient is the quantum model of a controlled single-bit memory. The structure of this model involving strongly coupled spin and quantum harmonic oscillator allows to define stable pointer states as well-separated Gaussian states of the quantum oscillator and analyze the transition from quantum to classical regime. The relations between accuracy of measurement, stability of pointer states, effective temperature of joint thermal and quantum noise and minimal work needed to perform the bit-flip are derived. They differ from those based on the Landauer principle and are used to analyze thermodynamic efficiency of quantum Szilard engine and imply more realistic estimations of minimal amount of work needed to perform long computations.
Entropy and information gain in quantum continual measurements
2001
Inspired by works on information transmission through quantum channels, we propose the use of a couple of mutual entropies to quantify the efficiency of continual measurement schemes in extracting information on the measured quantum system. Properties of these measures of information are studied and bounds on them are derived. 1 Quantum measurements and entropies We speak of quantum continual measurements when a quantum system is taken under observation with continuity in time and the output is not a single random variable, but rather a stochastic process [1, 2]. The aim of this paper is to quantify, by means of entropic quantities, the effectiveness of a continual measurement in extracting information from the underlying quantum system. Various types of entropies and bounds on informational quantities can be introduced and studied in connection with continual measurements [3–5]. In particular, in Ref. [5] the point of view was the one of information transmission: the quantum system...
Thermodynamics of Quantum Information Systems — Hamiltonian Description
Open Systems & Information Dynamics (OSID), 2004
It is often claimed, that from a quantum system of d levels, and entropy S and heat bath of temperature T one can draw kT ln d − T S amount of work. However, the usual arguments basing on Szilard engine, are not fully rigorous. Here we prove the formula within Hamiltonian description of drawing work from a quantum system and a heat bath, at the cost of entropy of the system. We base on the derivation of thermodynamical laws and quantities in [10] within weak coupling limit. Our result provides fully physical scenario for extracting thermodynamical work form quantum correlations . We also derive Landauer's principle as a consequence of the second law within the considered model.
Information-thermodynamics link revisited
Journal of Physics A: Mathematical and Theoretical, 2019
The so-called information-thermodynamics link created by a thought experiment of Szilard became a core of the modern orthodoxy in the field of quantum information and resources theory in quantum thermodynamics. We remind existing objections against standard interpretation of Szilard engine operation and illustrate them by two quantum models: particle in a box with time-dependent thin potential barrier and the spin-boson model. The consequences of the emerging superselection rules for thermodynamics and foundations of quantum mechanics are discussed. The role of nonergodic systems as information carriers and the thermodynamic cost of stability and accuracy of information processing is briefly discussed and compared to the generally accepted Landauer's principle.