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.

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.

On the interaction between a time-dependent field and a two-level atom

2019 ◽  
Vol 34 (10) ◽  
pp. 1950081 ◽  
Author(s):  
N. H. Abdel-Wahab ◽  
Ahmed Salah
Keyword(s):  
Quantum Electrodynamics ◽  
Initial Conditions ◽  
Coupling Parameter ◽  
Quantum Systems ◽  
Trapped Ions ◽  
Time Dependent ◽  
Von Neumann Entropy ◽  
Von Neumann ◽  
Level Atom ◽  
Dependent Field

In this paper, we study the interaction between the time-dependent field and a two-level atom with one mode electromagnetic field. We consider that the field of photons is assumed to be coupled with modulated coupling parameter which depends explicitly on time. It is shown that the considered model can be reduced to a well-known form of the time-dependent generalized Jaynes–Cummings model. Under special initial conditions, in which the atom and the field are prepared in the excited and the coherent states, respectively, the explicit time evolution of the wave function of the entire system is analytically obtained. Our proposal has many advantages over the previous optical schemes and can be realized in several multiple experiments, such as trapped ions and quantum electrodynamics cavity. The influence of the time-dependent field parameter on the collapses-revivals, the normal squeezing of the radiation, the anti-bunching of photons and the entanglement phenomena for the considered atomic system is examined. The linear entropy, the von Neumann entropy are used to quantify entanglement in the quantum systems. We noticed that these phenomena are affected by the existence of both the time-dependent coupling field and detuning parameters.

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.

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.

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 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.

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