scholarly journals Quantum Features of Macroscopic Fields: Entropy and Dynamics

Entropy ◽  
2019 ◽  
Vol 21 (7) ◽  
pp. 705
Author(s):  
Robert Alicki
Keyword(s):  
Wave Equations ◽  
Particle Density ◽  
Von Neumann Entropy ◽  
Quantum Field ◽  
Von Neumann ◽  
Single Particle Density ◽  
Definition Of ◽  
Thermal Sources ◽  
Reduced State ◽  
State Of The Field

Macroscopic fields such as electromagnetic, magnetohydrodynamic, acoustic or gravitational waves are usually described by classical wave equations with possible additional damping terms and coherent sources. The aim of this paper is to develop a complete macroscopic formalism including random/thermal sources, dissipation and random scattering of waves by environment. The proposed reduced state of the field combines averaged field with the two-point correlation function called single-particle density matrix. The evolution equation for the reduced state of the field is obtained by reduction of the generalized quasi-free dynamical semigroups describing irreversible evolution of bosonic quantum field and the definition of entropy for the reduced state of the field follows from the von Neumann entropy of quantum field states. The presented formalism can be applied, for example, to superradiance phenomena and allows unifying the Mueller and Jones calculi in polarization optics.

scholarly journals WIGNER ROTATIONS, BELL STATES, AND LORENTZ INVARIANCE OF ENTANGLEMENT AND VON NEUMANN ENTROPY

2004 ◽  
Vol 02 (02) ◽  
pp. 183-200 ◽  
Author(s):  
CHOPIN SOO ◽  
CYRUS C. Y. LIN
Keyword(s):  
Lorentz Invariance ◽  
Zeta Functions ◽  
Bell States ◽  
Von Neumann Entropy ◽  
Lorentz Transformations ◽  
Von Neumann ◽  
Infinite Dimensional ◽  
Einstein Podolsky Rosen ◽  
Definition Of ◽  
Reduced Density

We compute, for massive particles, the explicit Wigner rotations of one-particle states for arbitrary Lorentz transformations; and the explicit Hermitian generators of the infinite-dimensional unitary representation. For a pair of spin 1/2 particles, Einstein–Podolsky–Rosen–ell entangled states and their behaviour under the Lorentz group are analyzed in the context of quantum field theory. Group theoretical considerations suggest a convenient definition of the Bell states which is slightly different from the conventional assignment. The behaviour of Bell states under arbitrary Lorentz transformations can then be described succinctly. Reduced density matrices applicable to systems of identical particles are defined through Yang's prescription. The von Neumann entropy of each of the reduced density matrix is Lorentz invariant; and its relevance as a measure of entanglement is discussed, and illustrated with an explicit example. A regularization of the entropy in terms of generalized zeta functions is also suggested.

RELATIVE VON NEUMANN ENTROPY FOR EVALUATING AMINO ACID CONSERVATION

2010 ◽  
Vol 08 (05) ◽  
pp. 809-823 ◽  
Author(s):  
FREDRIK JOHANSSON ◽  
HIROYUKI TOH
Keyword(s):  
Amino Acid ◽  
Sequence Analysis ◽  
Shannon Entropy ◽  
Von Neumann Entropy ◽  
Sequence Alignments ◽  
Multiple Sequence ◽  
Von Neumann ◽  
Multiple Sequence Alignments ◽  
Previous Definition ◽  
Definition Of

The Shannon entropy is a common way of measuring conservation of sites in multiple sequence alignments, and has also been extended with the relative Shannon entropy to account for background frequencies. The von Neumann entropy is another extension of the Shannon entropy, adapted from quantum mechanics in order to account for amino acid similarities. However, there is yet no relative von Neumann entropy defined for sequence analysis. We introduce a new definition of the von Neumann entropy for use in sequence analysis, which we found to perform better than the previous definition. We also introduce the relative von Neumann entropy and a way of parametrizing this in order to obtain the Shannon entropy, the relative Shannon entropy and the von Neumann entropy at special parameter values. We performed an exhaustive search of this parameter space and found better predictions of catalytic sites compared to any of the previously used entropies.

scholarly journals Switching and Swapping of Quantum Information: Entropy and Entanglement Level

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 717
Author(s):  
Marek Sawerwain ◽  
Joanna Wiśniewska ◽  
Roman Gielerak
Keyword(s):  
Quantum Information ◽  
Quantum Systems ◽  
Von Neumann Entropy ◽  
Crucial Issue ◽  
Schmidt Decomposition ◽  
Intrinsic Decoherence ◽  
Von Neumann ◽  
Local Quantum ◽  
Definition Of ◽  
Moriya Interaction

Information switching and swapping seem to be fundamental elements of quantum communication protocols. Another crucial issue is the presence of entanglement and its level in inspected quantum systems. In this article, a formal definition of the operation of the swapping local quantum information and its existence proof, together with some elementary properties analysed through the prism of the concept of the entropy, are presented. As an example of the local information swapping usage, we demonstrate a certain realisation of the quantum switch. Entanglement levels, during the work of the switch, are calculated with the Negativity measure and a separability criterion based on the von Neumann entropy, spectral decomposition and Schmidt decomposition. Results of numerical experiments, during which the entanglement levels are estimated for systems under consideration with and without distortions, are presented. The noise is generated by the Dzyaloshinskii-Moriya interaction and the intrinsic decoherence is modelled by the Milburn equation. This work contains a switch realisation in a circuit form—built out of elementary quantum gates, and a scheme of the circuit which estimates levels of entanglement during the switch’s operating.

scholarly journals ENTANGLEMENT IN VALENCE-BOND-SOLID STATES

2010 ◽  
Vol 24 (11) ◽  
pp. 1361-1440 ◽  
Author(s):  
VLADIMIR E. KOREPIN ◽  
YING XU
Keyword(s):  
Density Matrix ◽  
Condensed Matter ◽  
Valence Bond ◽  
Von Neumann Entropy ◽  
Information Measurement ◽  
Von Neumann ◽  
Solid States ◽  
The Subject ◽  
Definition Of ◽  
Valence Bond Solid

This article reviews the quantum entanglement in Valence-Bond-Solid (VBS) states defined on a lattice or a graph. The subject is presented in a self-contained and pedagogical way. The VBS state was first introduced in the celebrated paper by I. Affleck, T. Kennedy, E. H. Lieb and H. Tasaki (abbreviation AKLT is widely used). It became essential in condensed matter physics and quantum information (measurement-based quantum computation). Many publications have been devoted to the subject. Recently entanglement was studied in the VBS state. In this review, we start with the definition of a general AKLT spin chain and the construction of VBS ground state. In order to study entanglement, a block subsystem is introduced and described by the density matrix. Density matrices of 1-dimensional models are diagonalized and the entanglement entropies (the von Neumann entropy and Rényi entropy) are calculated. In the large block limit, the entropies also approach finite limits. Study of the spectrum of the density matrix led to the discovery that the density matrix is proportional to a projector.

scholarly journals Entanglement entropy between virtual and real excitations in quantum electrodynamics

2018 ◽  
Vol 33 (13) ◽  
pp. 1850081 ◽  
Author(s):  
Juan Sebastián Ardenghi
Keyword(s):  
Quantum Electrodynamics ◽  
Degrees Of Freedom ◽  
Entanglement Entropy ◽  
Perturbation Expansion ◽  
Inner Product ◽  
Von Neumann Entropy ◽  
Von Neumann ◽  
Virtual Particles ◽  
Quantum Operators ◽  
Definition Of

The aim of this work is to introduce the entanglement entropy of real and virtual excitations of fermion and photon fields. By rewriting the generating functional of quantum electrodynamics theory as an inner product between quantum operators, it is possible to obtain quantum density operators representing the propagation of real and virtual particles. These operators are partial traces, where the degrees of freedom traced out are unobserved excitations. Then the von Neumann definition of entropy can be applied to these quantum operators and in particular, for the partial traces taken over by the internal or external degrees of freedom. A universal behavior is obtained for the entanglement entropy for different quantum fields at zeroth order in the coupling constant. In order to obtain numerical results at different orders in the perturbation expansion, the Bloch–Nordsieck model is considered, where it is shown that for some particular values of the electric charge, the von Neumann entropy increases or decreases with respect to the noninteracting case.

scholarly journals Intrinsic Entropy of Squeezed Quantum Fields and Nonequilibrium Quantum Dynamics of Cosmological Perturbations

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1544
Author(s):  
Jen-Tsung Hsiang ◽  
Bei-Lok Hu
Keyword(s):  
Quantum Dynamics ◽  
Coarse Graining ◽  
Von Neumann Entropy ◽  
Quantum Field ◽  
Matrix Elements ◽  
Cosmological Perturbations ◽  
Von Neumann ◽  
Particle Pairs ◽  
Field Fluctuations ◽  
The Universe

Density contrasts in the universe are governed by scalar cosmological perturbations which, when expressed in terms of gauge-invariant variables, contain a classical component from scalar metric perturbations and a quantum component from inflaton field fluctuations. It has long been known that the effect of cosmological expansion on a quantum field amounts to squeezing. Thus, the entropy of cosmological perturbations can be studied by treating them in the framework of squeezed quantum systems. Entropy of a free quantum field is a seemingly simple yet subtle issue. In this paper, different from previous treatments, we tackle this issue with a fully developed nonequilibrium quantum field theory formalism for such systems. We compute the covariance matrix elements of the parametric quantum field and solve for the evolution of the density matrix elements and the Wigner functions, and, from them, derive the von Neumann entropy. We then show explicitly why the entropy for the squeezed yet closed system is zero, but is proportional to the particle number produced upon coarse-graining out the correlation between the particle pairs. We also construct the bridge between our quantum field-theoretic results and those using the probability distribution of classical stochastic fields by earlier authors, preserving some important quantum properties, such as entanglement and coherence, of the quantum field.

scholarly journals An intuitive proof of the data processing inequality

2012 ◽  
Vol 12 (5&6) ◽  
pp. 432-441
Author(s):  
Normand J. Beaudry ◽  
Renato Renner
Keyword(s):  
Data Processing ◽  
Short Proof ◽  
Relevant Information ◽  
Von Neumann Entropy ◽  
Von Neumann ◽  
Fundamental Feature ◽  
Asymptotic Equipartition Property ◽  
Data Processing Inequality ◽  
Definition Of ◽  
Intuitive Proof

The data processing inequality (DPI) is a fundamental feature of information theory. Informally it states that you cannot increase the information content of a quantum system by acting on it with a local physical operation. When the smooth min-entropy is used as the relevant information measure, then the DPI follows immediately from the definition of the entropy. The DPI for the von Neumann entropy is then obtained by specializing the DPI for the smooth min-entropy by using the quantum asymptotic equipartition property (QAEP). We provide a short proof of the QAEP and therefore obtain a self-contained proof of the DPI for the von Neumann entropy.

scholarly journals Classical black hole scattering from a worldline quantum field theory

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Gustav Mogull ◽  
Jan Plefka ◽  
Jan Steinhoff
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Black Hole ◽  
Quantum Field ◽  
Expectation Values ◽  
Path Integral Representation ◽  
S Matrix ◽  
Feynman Rules ◽  
Definition Of ◽  
Three Body

Abstract A precise link is derived between scalar-graviton S-matrix elements and expectation values of operators in a worldline quantum field theory (WQFT), both used to describe classical scattering of black holes. The link is formally provided by a worldline path integral representation of the graviton-dressed scalar propagator, which may be inserted into a traditional definition of the S-matrix in terms of time-ordered correlators. To calculate expectation values in the WQFT a new set of Feynman rules is introduced which treats the gravitational field hμν(x) and position $$ {x}_i^{\mu}\left({\tau}_i\right) $$ x i μ τ i of each black hole on equal footing. Using these both the 3PM three-body gravitational radiation 〈hμv(k)〉 and 2PM two-body deflection $$ \Delta {p}_i^{\mu } $$ Δ p i μ from classical black hole scattering events are obtained. The latter can also be obtained from the eikonal phase of a 2 → 2 scalar S-matrix, which we show corresponds to the free energy of the WQFT.

scholarly journals Islands in linear dilaton black holes

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Georgios K. Karananas ◽  
Alex Kehagias ◽  
John Taskas
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Entanglement Entropy ◽  
Von Neumann Entropy ◽  
Two Dimensional ◽  
Extremal Case ◽  
Von Neumann ◽  
Dimensional Black Hole ◽  
Linear Dilaton ◽  
Linear Dilaton Black Hole

Abstract We derive a novel four-dimensional black hole with planar horizon that asymptotes to the linear dilaton background. The usual growth of its entanglement entropy before Page’s time is established. After that, emergent islands modify to a large extent the entropy, which becomes finite and is saturated by its Bekenstein-Hawking value in accordance with the finiteness of the von Neumann entropy of eternal black holes. We demonstrate that viewed from the string frame, our solution is the two-dimensional Witten black hole with two additional free bosons. We generalize our findings by considering a general class of linear dilaton black hole solutions at a generic point along the σ-model renormalization group (RG) equations. For those, we observe that the entanglement entropy is “running” i.e. it is changing along the RG flow with respect to the two-dimensional worldsheet length scale. At any fixed moment before Page’s time the aforementioned entropy increases towards the infrared (IR) domain, whereas the presence of islands leads the running entropy to decrease towards the IR at later times. Finally, we present a four-dimensional charged black hole that asymptotes to the linear dilaton background as well. We compute the associated entanglement entropy for the extremal case and we find that an island is needed in order for it to follow the Page curve.

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