scholarly journals Lindbladian operators, von Neumann entropy and energy conservation in time-dependent quantum open systems

2017 ◽  
Vol 466 ◽  
pp. 450-454 ◽  
Author(s):  
Congjie Ou ◽  
Ralph V. Chamberlin ◽  
Sumiyoshi Abe
Keyword(s):  
Energy Conservation ◽  
Open Systems ◽  
Time Dependent ◽  
Von Neumann Entropy ◽  
Von Neumann ◽  
Quantum Open Systems

scholarly journals Quantum Weak Invariants: Dynamical Evolution of Fluctuations and Correlations

Entropy ◽  
2020 ◽  
Vol 22 (11) ◽  
pp. 1219
Author(s):  
Zeyi Shi ◽  
Sumiyoshi Abe
Keyword(s):  
Time Evolution ◽  
Open Quantum System ◽  
Dynamical Evolution ◽  
Time Dependent ◽  
Von Neumann Entropy ◽  
Completely Positive Map ◽  
Expectation Values ◽  
Completely Positive ◽  
Temporal Asymmetry ◽  
Von Neumann

Weak invariants are time-dependent observables with conserved expectation values. Their fluctuations, however, do not remain constant in time. On the assumption that time evolution of the state of an open quantum system is given in terms of a completely positive map, the fluctuations monotonically grow even if the map is not unital, in contrast to the fact that monotonic increases of both the von Neumann entropy and Rényi entropy require the map to be unital. In this way, the weak invariants describe temporal asymmetry in a manner different from the entropies. A formula is presented for time evolution of the covariance matrix associated with the weak invariants in cases where the system density matrix obeys the Gorini–Kossakowski–Lindblad–Sudarshan equation.

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 Quantumness Measures for a System of Two Qubits Interacting with a Field in the Presence of the Time-Dependent Interaction and Kerr Medium

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 635
Author(s):  
Sayed Abdel-Khalek ◽  
Kamal Berrada ◽  
Eied M. Khalil ◽  
Abdel-Shafy F. Obada ◽  
Esraa Reda ◽  
...  
Keyword(s):  
Single Mode ◽  
Dynamical Behaviour ◽  
Time Dependent ◽  
Von Neumann Entropy ◽  
Kerr Medium ◽  
Von Neumann ◽  
Mode Field ◽  
Mandel’S Parameter ◽  
Qubit System ◽  
Dependent Interaction

In this work, we introduce the standard Tavis-Cummings model to describe two-qubit system interacting with a single-mode field associated to power-law (PL) potentials. We explore the effect of the time-dependent interaction and the Kerr-like medium. We solve the Schrödinger equation to obtain the density operator that allows us to investigate the dynamical behaviour of some quantumness measures, such as von Neumann entropy, negativity and Mandel’s parameter. We provide how these entanglement measures depend on the system parameters, which paves the way towards better control of entanglement generation in two-qubit systems. We find that the enhancement and preservation of the atoms-field entanglement and atom-atom entanglement can be achieved by a proper choice of the initial parameters of the field in the absence and presence of the time-dependent interaction and Kerr medium. We examine the photons distribution of the field and determine the situations for which the field exhibits super-poissonian, poissonian or sub-poissonian distribution.

Entanglement in composite systems due to external influences

2018 ◽  
Vol 33 (21) ◽  
pp. 1850128
Author(s):  
D. M. Gitman ◽  
M. S. Meireles ◽  
A. D. Levin ◽  
A. A. Shishmarev ◽  
R. A. Castro
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Density Operator ◽  
Time Dependent ◽  
Von Neumann Entropy ◽  
Entanglement Measure ◽  
Photon Beams ◽  
Von Neumann ◽  
Electron Positron ◽  
In The Beginning

In this paper, we consider two examples of an entanglement in two-qubit systems and an example of entanglement in quantum field theory (QFT). In the beginning, we study the entanglement of two spin states by a magnetic field. A nonzero entanglement appears for interacting spins. When the coupling between the spins is constant, we study the entanglement by several types of time-dependent magnetic fields. In the case of a constant difference between [Formula: see text] components of magnetic fields acting on each spin, we find several time-dependent coupling functions [Formula: see text] that also allow us to analyze analytically and numerically the entanglement measure. Considering two photons moving in an electron medium, we demonstrate that they can be entangled in a controlled way by applying an external magnetic field. The magnetic field affecting electrons of the medium affects photons and, thus, causes an entanglement of the photon beams. The third example is related to the effect of production of electron–positron pairs from the vacuum by a strong external electric field. Here, we have used a general nonperturbative expression for the density operator of the system under consideration. Applying a reduction procedure to this density operator, we construct mixed states of electron and positron subsystems. Calculating the von Neumann entropy of such states, we obtain the loss of information due to the reduction and, at the same time, the entanglement measure of electron and positron subsystems. This entanglement can be considered as an example of an entanglement in QFT.

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.

THE UNREASONABLE EFFECTIVENESS OF EXPONENTIALLY SUPPRESSED CORRECTIONS IN PRESERVING INFORMATION

2013 ◽  
Vol 22 (12) ◽  
pp. 1342030 ◽  
Author(s):  
KYRIAKOS PAPADODIMAS ◽  
SUVRAT RAJU
Keyword(s):  
Hilbert Space ◽  
Black Hole ◽  
Quantum Mechanics ◽  
Nonperturbative Effects ◽  
Von Neumann Entropy ◽  
Von Neumann ◽  
Information Theoretic ◽  
Black Hole Evaporation ◽  
Strong Subadditivity ◽  
Unreasonable Effectiveness

We point out that nonperturbative effects in quantum gravity are sufficient to reconcile the process of black hole evaporation with quantum mechanics. In ordinary processes, these corrections are unimportant because they are suppressed by e-S. However, they gain relevance in information-theoretic considerations because their small size is offset by the corresponding largeness of the Hilbert space. In particular, we show how such corrections can cause the von Neumann entropy of the emitted Hawking quanta to decrease after the Page time, without modifying the thermal nature of each emitted quantum. Second, we show that exponentially suppressed commutators between operators inside and outside the black hole are sufficient to resolve paradoxes associated with the strong subadditivity of entropy without any dramatic modifications of the geometry near the horizon.

Generalized information and entanglement entropy, gravitation and holography

2015 ◽  
Vol 30 (16) ◽  
pp. 1530039 ◽  
Author(s):  
O. Obregón
Keyword(s):  
Entanglement Entropy ◽  
Ideal Gas ◽  
Einstein Equations ◽  
Von Neumann Entropy ◽  
Nonextensive Statistical Mechanics ◽  
Von Neumann ◽  
H Theorem ◽  
Gauge Gravity ◽  
Gravity Duality ◽  
Correction Terms

A nonextensive statistical mechanics entropy that depends only on the probability distribution is proposed in the framework of superstatistics. It is based on a Γ(χ2) distribution that depends on β and also on pl. The corresponding modified von Neumann entropy is constructed; it is shown that it can also be obtained from a generalized Replica trick. We further demonstrate a generalized H-theorem. Considering the entropy as a function of the temperature and volume, it is possible to generalize the equation of state of an ideal gas. Moreover, following the entropic force formulation a generalized Newton's law is obtained, and following the proposal that the Einstein equations can be deduced from the Clausius law, we discuss on the structure that a generalized Einstein's theory would have. Lastly, we address the question whether the generalized entanglement entropy can play a role in the gauge/gravity duality. We pay attention to 2d CFT and their gravity duals. The correction terms to the von Neumann entropy result more relevant than the usual UV ones and also than those due to the area dependent AdS3 entropy which result comparable to the UV ones. Then the correction terms due to the new entropy would modify the Ryu–Takayanagi identification between the CFT entanglement entropy and the AdS entropy in a different manner than the UV ones or than the corrections to the AdS3 area dependent entropy.

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