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Physics and Information
In recent years the physics of information [1{7] has received increasing attention [5, 6, 8{16]. There is a growing consensus that information is endowed with physical reality, not in the least because the ultimate limits of any physical device that processes or transmits information are determined by the fundamental laws of physics [6, 12{14]. That is, the physics of information and computation is an interdisciplinary eld which has promoted our understanding of how the underlying physics in uences our ability to both manipulate and use information.
By the same token a plenitude of theoretical developments indicate that the concept of information constitutes an essential ingredient for a deep understanding of physical systems and processes [1{6]. The physics of information also comprises a set of ideas, concepts and techniques that provide a natural \bridge » between theoretical physics and other branches of Science, particularly biology [17]. Landauer’s principle is one of the most fundamental results in the physics of information and is generally associated with the statement \information is physical ». It constitutes a historical turning point in the eld by directly connecting information processing with (more) conventional physical quantities [18].
According to Landauer’s principle a minimal amount of energy is required to be dissipated in order to erase a bit of information in a computing device working at temperature T. This minimum energy is given by kT ln 2, where k denotes Boltzmann’s constant [19{21]. Landauer’s principle has deep implications, as it allows for the derivation of several important results in classical and quantum information theory [22]. It also constitutes a rather useful heuristic tool for estab-lishing new links etween, or obtaining new derivations of, fundamental aspects of thermodynamics and other areas of physics [23].
Information is something that is encoded in a physical state of a system and a computation is something that can be carried out on a physically realizable device with real physical degrees of freedom. In order to quantify information one will need a measure of how much information is encoded in a system or process. Shannon entropy, Renyi entropy (which is a generalization of Shannon entropy) and Tsallis’ S(T) q power-law entropies will be discussed. Since the universe is quantum mechanical at a fundamental level, the question naturally arises as to how quantum theory can enhance our insight into the nature of information.
Physics and Information
1.1 Information and entropic measures
1.2 Conservation of information
1.3 Quantum no-cloning
2 Quantum Entanglement in Distinguishable and Indistinguishable Subsystems
2.1 Entanglement measures for composite systems with distinguishable subsystems
2.2 Quantum entanglement in a many-body system exhibiting multiple quantum phase transitions .
2.3 Measures of quantum correlations: quantum discord
2.4 Distinguishable and indistinguishable particles
2.5 Systems of identical fermions .
2.6 Relevant properties and techniques related to uncertainty relations and entropic inequalities .
2.7 Uncertainty relations for distinguishable particles
3 Extensions of Landauer’s Principle and Conservation of Infor- mation in General Probabilistic Theories
3.1 Landauer’s Principle and Divergenceless Dynamical Systems
3.2 Fidelity Measure and Conservation of Information in General Probabilistic
Theories
4 Separability Criteria for Fermions
4.1 Uncertainty Relations and Entanglement in Fermion Systems .
4.2 Entropic Entanglement Criteria for Fermion Systems .
4.2.4 Two-fermion systems with a single-particle Hilbert space of
dimension four
5 Characterization of Correlations in Fermion Systems Based on Measurement Induced Disturbances
6 Conclusions
