A Strengthened Monotonicity Inequality of Quantum Relative Entropy: A Unifying Approach Via Rényi Relative Entropy

We derive a strengthened monotonicity inequality for quantum relative entropy by employing properties of \({\alpha}\)-Rényi relative entropy. We develop a unifying treatment toward the improvement of some quantum entropy inequalities. In particular, an emphasis is put on a lower bound of quantum conditional mutual information (QCMI) as it gives a Pinsker-like lower bound for the QCMI. We also give some improved entropy inequalities based on Rényi relative entropy. The inequalities obtained, thus, extend some well-known ones. We also obtain a condition under which a tripartite operator becomes a Markov state. As a by-product we provide some trace inequalities of operators, which are of independent interest.     

Relative Entropy of Entanglement of a Kind of Two-Qubit Entangled States

We strictly prove that some block diagonalizable two-qubit entangled state with six non-zero elements reaches its quantum relative entropy entanglement by a separable state having the same matrix structure. The entangled state comprises local filtering result state as a special case.     

Kolmogorov–Sinaj Entropy on MV-Algebras

There is given a construction of the entropy of a dynamical system on arbitrary MV-algebra M. If M is the MV-algebra of characteristic functions of a σ-algebra (isomorphic to the σ-algebra), then the construction leads to the Kolmogorov–Sinaj entropy. If M is the MV-algebra (tribe) of fuzzy sets, then the construction coincides with the Maličky modification of the Kolmogorov–Sinaj entropy for fuzzy sets (Maličky and Riečan, 1986; Riečan and Mundici, 2002; Riečan and Neubrunn, 1997).     

Nonlinear Jaynes–Cummings Model of Atom–Field Interaction

Interaction of a two-level atom with a single mode of electromagnetic field including Kerr nonlinearity for the field and intensity-dependent atom-field coupling is discussed. The Hamiltonian for the atom-field system is written in terms of the generatorsof a closed algebra, which has SU(1,1) and Heisenberg–Weyl algebras as limitingcases. Eigenstates and eigenvalues of the Hamiltonian are constructed. With the field being in a coherent state initially, the dynamical behavior of atomic inversion, field statistics, and uncertainties in the field quadratures are studied. Appearance of nonclassical features during the evolution of the field is shown. Further, we explore the overlap of initial and time-evolved field states.     

Entropy squeezing for a two-level atom in the Jaynes－Cummings model with an intensity-depend coupling

We study the squeezing for a two-level atom in the Jaynes－Cummings model with intensity-dependent coupling using quantum information entropy, and examine the influences of the initial state of the system on the squeezed component number and direction of the information entropy squeezing. Our results show that, the squeezed component number depends on the atomic initial distribution angle, while the squeezed direction is determined by both the phases of the atom and the field for the information entropy squeezing. Quantum information entropy is shown to be a remarkable precision measure for atomic squeezing.     

Entropy of the Kerr–Sen black hole

We study the entropy of Kerr–Sen black hole of heterotic string theory beyond semiclassical approximations. Applying the properties of exact differentials for three variables to the first law of thermodynamics, we derive the corrections to the entropy of the black hole. The leading (logarithmic) and non-leading corrections to the area law are obtained.     

Jaynes–Cummings model: Solutions without rotating-wave approximation

The Jaynes–Cummings model in the general nonresonant case without rotating-wave approximation is considered. The analysis is carried out using the resolvent formalism. It is shown that one, given the matrix of Hamiltonian resolvent, can easily find all basic physical quantities corresponding to the given model. The matrix of the resolvent of the total Hamiltonian for the given model is found. Matrix elements of the resolvent are expressed in terms of continued fractions. It is shown that these fractions uniformly converge to meromorphic functions, which corresponds to a purely point spectrum of the total Hamiltonian. The time evolution in the case of exact resonance for different coupling constants is numerically studied. It is shown that the rotating- wave approximation is not satisfactory for large coupling constants even in the case of exact resonance. In this case, probabilities of multiphoton transitions increase with increasing coupling constant.     

Floquet–Gibbs state in open quantum systems

We study long-time asymptotic states of periodically driven quantum systems coupled to a thermal bath. In order to describe a class of such a system, we introduce the Floquet–Gibbs state, i.e. the state whose density matrix is diagonalized in the basis of the Floquet state of the system Hamiltonian, and its diagonal element obeys the Boltzmann distribution over its Floquet quasienergy. We obtain sufficient conditions for the realization of the Floquet–Gibbs state in a system with infinitesimal system-bath coupling [T. Shirai et al., Phys. Rev. E 91, 030101 (2015)]. These conditions severely restrict a class of suitable physical models attaining the Floquet–Gibbs state. We also show that some of the conditions can be lifted by imposing conditions on timescales of the thermal bath with the aid of the truncated Floquet Hamiltonian in the Floquet–Magnus expansion [T. Shirai et al., New J. Phys. 18, 053008 (2016)]. In this paper, we give an overview of this theory and reconsider it by looking at the dynamics from a rotating frame.     

Entropy of Reissner–Nordström–anti-de Sitter Black Hole

By using the method of quantum statistics, we directly derive the partition function of bosonic and fermionic field in Reissner-Nordström-anti-de Sitter black hole and obtain the integral expression of black hole's entropy. It avoids the difficulty in solving the wave equation of various particles. Then via the improved brick-wall method, membrane model, we calculate the statistical entropy of a film with the thickness of (N – 1) around the outside of horizon. In our result we can choose proper parameter in order to let the thickness of film tend to zero and have it approach the surface of horizon. Consequently, the entropy of black hole is proportional to the area of horizon. The stripped term and the divergent logarithmic term in the original brick-wall method no longer exist. In the whole process, physics idea is clear; calculation is simple. We offer a new simple and direct way of calculating the entropy of different complicated black holes.     

Gravitational Jaynes–Cummings model beyond the rotating wave approximation

In this paper, the quantum properties of a two-level atom and the cavity-field in the Jaynes?CCummings model with the gravity beyond the rotating wave approximation are investigated. For this purpose, by solving the Schr?dinger equation in the interaction picture, the evolving state of the system is found by which the influence of the counter-rotating terms on the dynamical behaviour of atomic population inversion and the probability distribution of the cavity-field as quantum properties is explored. The results in the atom?Cfield system beyond the rotating wave approximation with the gravity show that the quantum properties are not completely suppressed under certain conditions.     

Grassmann phase space theory and the Jaynes–Cummings model

The Jaynes-Cummings model of a two-level atom in a single mode cavity is of fundamental importance both in quantum optics and in quantum physics generally, involving the interaction of two simple quantum systems—one fermionic system (the TLA), the other bosonic (the cavity mode). Depending on the initial conditions a variety of interesting effects occur, ranging from ongoing oscillations of the atomic population difference at the Rabi frequency when the atom is excited and the cavity is in an n$n$-photon Fock state, to collapses and revivals of these oscillations starting with the atom unexcited and the cavity mode in a coherent state. The observation of revivals for Rydberg atoms in a high-Q microwave cavity is key experimental evidence for quantisation of the EM field. Theoretical treatments of the Jaynes-Cummings model based on expanding the state vector in terms of products of atomic and n$n$-photon states and deriving coupled equations for the amplitudes are a well-known and simple method for determining the effects.     

Black Hole and Cosmic Entropy for Schwarzschild–de Sitter Space–Time

We calculate the free energy and the entropy of a scalar field in terms of the brick-wall method in the background of the Schwarzschild–de Sitter space–time. We obtain the entropy of a black hole and the cosmic entropy at nonasymptotic flat space. When the cut-off satisfies the proper condition, the entropy of a black hole is proportional to the area of a black hole horizon, and the cosmic entropy is proportional to the cosmic horizon area.     

Information and Entropy Flow in the Kalman–Bucy Filter

We investigate the information theoretic properties of Kalman–Bucy filters in continuous time, developing notions of information supply, storage and dissipation. Introducing a concept of energy, we develop a physical analogy in which the unobserved signal describes a statistical mechanical system interacting with a heat bath. The abstract universe comprising the signal and the heat bath obeys a non-increase law of entropy; however, with the introduction of partial observations, this law can be violated. The Kalman–Bucy filter behaves like a Maxwellian demon in this analogy, returning signal energy to the heat bath without causing entropy increase. This is made possible by the steady supply of new information. In a second analogy the signal and filter interact, setting up a stationary non-equilibrium state, in which energy flows between the heat bath, the signal and the filter without causing any overall entropy increase. We introduce a rate of interactive entropy flow that isolates the statistical mechanics of this flow from marginal effects. Both analogies provide quantitative examples of Landauers Principle.     

Fermionic Entropy in Kerr Black Hole Space–Time Background

Making use of brick-wall model proposed by 't Hooft, we have obtained the free energy and the entropy of Fermionic field and given out their expressions under the Kerr space–time background.     

Fast–Slow Partially Hyperbolic Systems Versus Freidlin–Wentzell Random Systems

We consider a simple class of fast-slow partially hyperbolic dynamical systems and show that the (properly rescaled) behaviour of the slow variable is very close to a Freidlin–Wentzell type random system for times that are rather long, but much shorter than the metastability scale. Also, we show the possibility of a “sink” with all the Lyapunov exponents positive, a phenomenon that turns out to be related to the lack of absolutely continuity of the central foliation.     

Nernst Theorem and Entropy of the Axisymmetric Einstein–Maxwell–Dilaton-Axion Black Hole

The free energy and the entropy of scalar field are calculated by brick-wall in the axisymmetric Einstein–Maxwell–Dilaton-axion black hole. It is shown that when the black hole has inner and outer horizons, the entropy is not only related to the area of an outer horizon but also is the function of the area of an inner horizon. When the area of an inner horizon approaches zero, we can obtain the known conclusion. The entropy expressed by location parameter of outer horizon and inner horizons approaches absolute zero. It obeys Nernst theorem. It can be taken as Planck absolute entropy of a black hole.     

Effective Hamiltonian of the Jaynes–Cummings model beyond rotating-wave approximation

The Jaynes–Cummings model with or without rotating-wave approximation plays a major role to study the interaction between atom and light. We investigate the Jaynes–Cummings model beyond the rotating-wave approximation. Treating the counter-rotating terms as periodic drivings, we solve the model in the extended Floquet space. It is found that the full energy spectrum folded in the quasi-energy bands can be described by an effective Hamiltonian derived in the highfrequency regime. In contrast to the Z_2 symmetry of the original model, the effective Hamiltonian bears an enlarged U(1)symmetry with a unique photon-dependent atom-light detuning and coupling strength. We further analyze the energy spectrum, eigenstate fidelity and mean photon number of the resultant polaritons, which are shown to be in accordance with the numerical simulations in the extended Floquet space up to an ultra-strong coupling regime and are not altered significantly for a finite atom-light detuning. Our results suggest that the effective model provides a good starting point to investigate the rich physics brought by counter-rotating terms in the frame of Floquet theory.     

Constraints on Determinism: Bell Versus Conway–Kochen

Bell’s Theorem from Physics 36:1–28 (1964) and the (Strong) Free Will Theorem of Conway and Kochen from Notices AMS 56:226–232 (2009) both exclude deterministic hidden variable theories (or, in modern parlance, ‘ontological models’) that are compatible with some small fragment of quantum mechanics, admit ‘free’ settings of the archetypal Alice and Bob experiment, and satisfy a locality condition akin to parameter independence. We clarify the relationship between these theorems by giving reformulations of both that exactly pinpoint their resemblance and their differences. Our reformulation imposes determinism in what we see as the only consistent way, in which the ‘ontological state’ initially determines both the settings and the outcome of the experiment. The usual status of the settings as ‘free’ parameters is subsequently recovered from independence assumptions on the pertinent (random) variables. Our reformulation also clarifies the role of the settings in Bell’s later generalization of his theorem to stochastic hidden variable theories.     

Entanglement Degree in the Time Development of the Jaynes–Cummings Model

Recently, it has been become known that a quantum entangled state plays an important role in fields of quantum information theory, such as quantum teleportation and quantum computation. Research on quantifying entangled states has been carried out using several measures. In this Letter, we will adopt this method using quantum mutual entropy to measure the degree of entanglement in the time development of the Jaynes–Cummings model.