Yang–Baxter matrices associated with quantum information based on the topological basis

2016 ◽  
Vol 30 (21) ◽  
pp. 1630013 ◽  
Author(s):  
Li-Wei Yu ◽  
Kang Xue ◽  
Mo-Lin Ge
Keyword(s):  
Quantum Information ◽  
Von Neumann Entropy ◽  
Baxter Equation ◽  
Additivity Rule ◽  
Braid Relation ◽  
Von Neumann

The solutions of Yang–Baxter equation (YBE) associated with quantum information have been reviewed with new progress. The additivity rule for two particles is shown to obey Lorentzian type other than the Gallilean. Acting the braiding operations on the topological basis, it turns out that the [Formula: see text]-dimensional representations obeying YBE are nothing but the Wigner’s [Formula: see text]-functions. The connection between the extremization of [Formula: see text]-norm as well as of von Neumann entropy and the reduction of YBE to braid relation is also discussed.

Quantum Algorithmic Complexities and Entropy

2009 ◽  
Vol 16 (01) ◽  
pp. 1-28 ◽  
Author(s):  
Fabio Benatti
Keyword(s):  
Quantum Computing ◽  
Quantum Information ◽  
Complexity Theory ◽  
Information Sources ◽  
Algorithmic Complexity ◽  
Entropy Rate ◽  
Von Neumann Entropy ◽  
Von Neumann

We review the basics of classical algorithmic complexity theory and two of its quantum extensions that have been prompted by the foreseeable existence of quantum computing devices. In particular, we will examine the relations between these extensions and the von Neumann entropy rate of generic quantum information sources of ergodic type.

Information entropy of multi-qubit Rabi system

2015 ◽  
Vol 13 (06) ◽  
pp. 1550042 ◽  
Author(s):  
D. A. M. Abo-Kahla ◽  
M. Abdel-Aty
Keyword(s):  
Population Dynamics ◽  
Quantum Information ◽  
Information Entropy ◽  
Time Development ◽  
Von Neumann Entropy ◽  
Frequency Detuning ◽  
Coupling Constant ◽  
Von Neumann

We consider quantum information entropy phenomenon for multi-qubit Rabi system. By introducing different measurements schemes, we establish the relation between information entropy approach and Von Neumann entropy. It is shown that the information entropy is more sensitive to the time development than the Von Neumann entropy. Furthermore, the suggested protocol exhibits excellent scaling of relevant characteristics, with respect to population dynamics, such that more accurate dynamical results may be obtained using information entropy due to variation of the frequency detuning and the coupling constant.

scholarly journals Interaction of quantum systems with environment in QCD

2019 ◽  
Vol 204 ◽  
pp. 01002
Author(s):  
Viatcheslav Kuvshinov ◽  
Valery Shaparau ◽  
Eugene Bagashov
Keyword(s):  
Quantum Information ◽  
Von Neumann Entropy ◽  
Asymptotic Freedom ◽  
Squeezed States ◽  
Time Intervals ◽  
Von Neumann ◽  
Confinement Region ◽  
Photon States ◽  
Short Time ◽  
Good Agreement

It is shown that the interaction of quark with the stochastic vacuum of QCD (considered as an environment) leads to the decoherence of quark colour state, associated with the loss of information on the initial quark colour. We propose to consider this process as a reason of the confinement of the quark colour. Asymptotically this leads to confined quarks (fully mixed colourless quark states) in the limit of large distances and time intervals (confinement region) and free coloured quarks in the limit of small distances and time intervals (asymptotic freedom). We propose quantitative characteristics that allow to describe the process of interaction: purity, fidelity, von Neumann entropy, quantum information measure. The cases of two and arbitrary number of quarks are considered, and it is shown that the entanglement in such system disappears in the limit of large distances and time intervals. The process is in good agreement with the known theorems in quantum information theory (no-cloning and no-hiding). We study non-perturbative evolution of the gluon colour states during short time. Fluctuations of gluons are less than those for coherent states. This fact suggests that there gluon squeezed states can arise. Theoretical justification for the occurrence both singe- and two-mode gluon squeezing effects in QCD is given. We show that gluon entangled states which are closely related with two-mode squeezed states of gluon fields can appear at short time non-perturbative evolution by analogy with corresponding photon states in quantum optics.

scholarly journals NO-CLONING THEOREM IN THERMOFIELD DYNAMICS

2012 ◽  
Vol 10 (02) ◽  
pp. 1230001 ◽  
Author(s):  
T. PRUDÊNCIO
Keyword(s):  
Quantum Information ◽  
Von Neumann Entropy ◽  
Mixed States ◽  
Von Neumann

We discuss the relation between the no-cloning theorem from quantum information and the doubling procedure used in the formalism of thermofield dynamics (TFD). We also discuss how to apply the no-cloning theorem in the context of thermofield states defined in TFD. Consequences associated to mixed states, von Neumann entropy and thermofield vacuum are also addressed.

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 Order-Stability in Complex Biological, Social, and AI-Systems from Quantum Information Theory

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 355
Author(s):  
Andrei Khrennikov ◽  
Noboru Watanabe
Keyword(s):  
Information Theory ◽  
Quantum Information ◽  
Quantum Information Theory ◽  
Von Neumann Entropy ◽  
Order Structure ◽  
Compound System ◽  
Von Neumann ◽  
Local Disorder ◽  
Low Entropy ◽  
The Brain

This paper is our attempt, on the basis of physical theory, to bring more clarification on the question “What is life?” formulated in the well-known book of Schrödinger in 1944. According to Schrödinger, the main distinguishing feature of a biosystem’s functioning is the ability to preserve its order structure or, in mathematical terms, to prevent increasing of entropy. However, Schrödinger’s analysis shows that the classical theory is not able to adequately describe the order-stability in a biosystem. Schrödinger also appealed to the ambiguous notion of negative entropy. We apply quantum theory. As is well-known, behaviour of the quantum von Neumann entropy crucially differs from behaviour of classical entropy. We consider a complex biosystem S composed of many subsystems, say proteins, cells, or neural networks in the brain, that is, S=(Si). We study the following problem: whether the compound system S can maintain “global order” in the situation of an increase of local disorder and if S can preserve the low entropy while other Si increase their entropies (may be essentially). We show that the entropy of a system as a whole can be constant, while the entropies of its parts rising. For classical systems, this is impossible, because the entropy of S cannot be less than the entropy of its subsystem Si. And if a subsystems’s entropy increases, then a system’s entropy should also increase, by at least the same amount. However, within the quantum information theory, the answer is positive. The significant role is played by the entanglement of a subsystems’ states. In the absence of entanglement, the increasing of local disorder implies an increasing disorder in the compound system S (as in the classical regime). In this note, we proceed within a quantum-like approach to mathematical modeling of information processing by biosystems—respecting the quantum laws need not be based on genuine quantum physical processes in biosystems. Recently, such modeling found numerous applications in molecular biology, genetics, evolution theory, cognition, psychology and decision making. The quantum-like model of order stability can be applied not only in biology, but also in social science and artificial intelligence.

A simple proof of the strong subadditivity inequality

2005 ◽  
Vol 5 (6) ◽  
pp. 507-513
Author(s):  
M.A. Nielsen ◽  
D. Petz
Keyword(s):  
Quantum Mechanics ◽  
Quantum Information ◽  
Linear Algebra ◽  
Simple Proof ◽  
Von Neumann Entropy ◽  
Von Neumann ◽  
Strong Subadditivity ◽  
Math Phys

Arguably the deepest fact known about the von~Neumann entropy, the strong subadditivity inequality is a potent hammer in the quantum information theorist's toolkit. This short tutorial describes a simple proof of strong subadditivity due to Petz [Rep. on Math. Phys. \textbf{23} (1), 57--65 (1986)]. It assumes only knowledge of elementary linear algebra and quantum mechanics.

scholarly journals Entropic singularities give rise to quantum transmission

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Vikesh Siddhu
Keyword(s):  
Quantum Information ◽  
General Theorem ◽  
Low Noise ◽  
Von Neumann Entropy ◽  
Quantum Devices ◽  
Von Neumann ◽  
Quantum Transmission ◽  
Quantum Capacity ◽  
Coherent Information ◽  
Quantum Technology

AbstractWhen can noiseless quantum information be sent across noisy quantum devices? And at what maximum rate? These questions lie at the heart of quantum technology, but remain unanswered because of non-additivity— a fundamental synergy which allows quantum devices (aka quantum channels) to send more information than expected. Previously, non-additivity was known to occur in very noisy channels with coherent information much smaller than that of a perfect channel; but, our work shows non-additivity in a simple low-noise channel. Our results extend even further. We prove a general theorem concerning positivity of a channel’s coherent information. A corollary of this theorem gives a simple dimensional test for a channel’s capacity. Applying this corollary solves an open problem by characterizing all qubit channels whose complement has non-zero capacity. Another application shows a wide class of zero quantum capacity qubit channels can assist an incomplete erasure channel in sending quantum information. These results arise from introducing and linking logarithmic singularities in the von-Neumann entropy with quantum transmission: changes in entropy caused by this singularity are a mechanism responsible for both positivity and non-additivity of the coherent information. Analysis of such singularities may be useful in other physics problems.

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