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.

Lorentz Invariance of Entanglement

2002 ◽  
Vol 2 (6) ◽  
pp. 487-512
Author(s):  
P.M. Alsing ◽  
G. Milburn
Keyword(s):  
Lorentz Invariance ◽  
Bell States ◽  
Explicit Calculation ◽  
Particle State ◽  
Lorentz Transformations ◽  
Wigner Rotation ◽  
Bipartite State ◽  
Relativistic Analog ◽  
Massive Spin ◽  
Inertial Frames

We study the transformation of maximally entangled states under the action of Lorentz transformations in a fully relativistic setting. By explicit calculation of the Wigner rotation, we describe the relativistic analog of the Bell states as viewed from two inertial frames moving with constant velocity with respect to each other. Though the finite dimensional matrices describing the Lorentz transformations are non-unitary, each single particle state of the entangled pair undergoes an effective, momentum dependent, local unitary rotation, thereby preserving the entanglement fidelity of the bipartite state. The details of how these unitary transformations are manifested are explicitly worked out for the Bell states comprised of massive spin $1/2$ particles and massless photon polarizations. The relevance of this work to non-inertial frames is briefly discussed.

scholarly journals ENTANGLED MARKOV CHAINS GENERATED BY SYMMETRIC CHANNELS

2005 ◽  
Vol 08 (03) ◽  
pp. 497-504 ◽  
Author(s):  
TAKAYUKI MIYADERA
Keyword(s):  
Markov Chains ◽  
Entropy Density ◽  
Dimensional Case ◽  
Von Neumann Entropy ◽  
Quantum Random Walk ◽  
Von Neumann ◽  
Infinite Dimensional ◽  
Symmetric Channel ◽  
Finite Dimensional ◽  
Finite Dimensional Case

A notion of entangled Markov chain was introduced by Accardi and Fidaleo in the context of quantum random walk. They proved that, in the finite-dimensional case, the corresponding states have vanishing entropy density, but they did not prove that they are entangled. In this note this entropy result is extended to the infinite-dimensional case under the assumption of finite speed of hopping. Then the entanglement problem is discussed for spin-1/2, entangled Markov chains generated by a binary symmetric channel with hopping probability 1-q. The von Neumann entropy of these states, restricted on a sublattice is explicitly calculated and shown to be independent of the size of the sublattice. This is a new, purely quantum, phenomenon. Finally the entanglement property between the sublattices [Formula: see text] and [Formula: see text] is investigated using the PPT criterium. It turns out that, for q≠ 0, 1, ½ the states are non-separable, thus truly entangled, while for q = 0, 1, ½, they are separable.

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 Entanglement of Pseudo-Hermitian Random States

Entropy ◽  
2020 ◽  
Vol 22 (10) ◽  
pp. 1109
Author(s):  
Cleverson Andrade Goulart ◽  
Mauricio Porto Pato
Keyword(s):  
Density Matrix ◽  
Random Matrices ◽  
Bell States ◽  
Von Neumann Entropy ◽  
Abstract Model ◽  
Von Neumann ◽  
Fock States ◽  
Bosonic System ◽  
Random States

In a recent paper (A. Fring and T. Frith, Phys. Rev A 100, 101102 (2019)), a Dyson scheme to deal with density matrix of non-Hermitian Hamiltonians has been used to investigate the entanglement of states of a PT-symmetric bosonic system. They found that von Neumann entropy can show a different behavior in the broken and unbroken regime. We show that their results can be recast in terms of an abstract model of pseudo-Hermitian random matrices. It is found however that although the formalism is practically the same, the entanglement is not of Fock states but of Bell states.

scholarly journals THE VON NEUMANN ENTROPY OF EPR SPIN CORRELATION FOR THE RELATIVISTIC PAIRS

2008 ◽  
Vol 23 (27n28) ◽  
pp. 4449-4466 ◽  
Author(s):  
YOSHIHISA NISHIKAWA
Keyword(s):  
Lorentz Transformation ◽  
Center Of Mass ◽  
Spin Correlation ◽  
Laboratory Frame ◽  
Von Neumann Entropy ◽  
Superposition State ◽  
Von Neumann ◽  
Spin Singlet ◽  
Mass Frame ◽  
Reduced Density

Variation of the von Neumann entropy by the Lorentz transformation is discussed. Taking the spin-singlet state in the center-of-mass frame, the von Neumann entropy in the laboratory frame is calculated from the reduced density matrix obtained by taking the trace over 4-momentum after the Lorentz transformation. As the model to discuss the EPR spin correlation, it is supposed that one parent particle splits into a superposition state of various pair states in various directions. Computing the von Neumann entropy and the Shannon entropy, we have shown a global behavior of the entropy to see a relativistic effect. We discuss also the superrelativistic limit, distinguishability between the two particles of the pair and so on.

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.

Density matrix and purity evolution in dissipative two-level systems: I. Theory and path integral results for tunneling dynamics

2021 ◽  
Vol 23 (9) ◽  
pp. 5113-5124
Author(s):  
Sambarta Chatterjee ◽  
Nancy Makri
Keyword(s):  
Density Matrix ◽  
Path Integral ◽  
Von Neumann Entropy ◽  
Level System ◽  
Von Neumann ◽  
Bacteriochlorophyll Dimer ◽  
Two Level Systems ◽  
Tunneling Dynamics ◽  
Reduced Density ◽  
Harmonic Bath

The time evolution of the purity (the trace of the square of the reduced density matrix) and von Neumann entropy in a symmetric two-level system coupled to a dissipative harmonic bath is investigated through analytical arguments and accurate path integral calculations on simple models and the singly excited bacteriochlorophyll dimer.

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.

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