We apply the Jaynes principle of maximum entropy for the partial reconstruction of correlated spin states. We determine the minimum set of observables which are necessary for the complete reconstruction of the most correlated states of systems composed of spins-1/2 (e.g., the Bell and the Greenberger-Horne-Zeilinger states). We investigate to what extent an incomplete measurement can reveal nonclassical features of correlated spin states.
The dynamics of an atom on the Jaynes-Cummings model has been studied by an atomic inversion, von Neumann entropy and so on. In this letter, we will treat the Jaynes-Cummings model as a problem in non-equilibrium statistical mechanics and apply quantum mutual entropy to study the irreversible dynamics of a state for the atom on this model.
The linear entropy, the von Neumann entropy and the atomic Wehrl entropy are frequently used to quantify entanglement in the quantum systems. These relations provide typical information on the entanglement in the Jaynes-Cummings model (JCM). In this Letter, we explain the origin of this analytically and derive a closed form for the atomic Wehrl entropy. Moreover, we show that it is more convenient to use the Bloch sphere radius for quantifying entanglement in the JCM instead of these entropic relations.
For a closed bi-partite quantum system partitioned into system proper and environment we interprete the microcanonical and the canonical condition as constraints for the interaction between those two subsystems. In both cases the possible pure-state trajectories are confined to certain regions in Hilbert space. We show that in a properly defined thermodynamical limit almost all states within those accessible regions represent states of some maximum local entropy. For the microcanonical condition this dominant state still depends on the initial state; for the canonical condition it coincides wi…
In this paper, we study the interaction between the two-level atom and a bimodal cavity field, namely, two-mode Jaynes-Cummings model when the atom and the modes are initially in the atomic superposition state and two-mode squeezed vacuum state, respectively. For this system we investigate the atomic inversion, linear entropy and atomic Wehrl entropy. We show that there is a connection between all these quantities. Also we prove that the atomic Wehrl entropy exhibits behaviors similar to those of the linear entropy and the von Neumann entropy. Moreover, we show that the bipartite exhibits peri…
In this paper the interaction between a two-level atom and a single-mode field in the $k$-photon Jaynes-Cummings model (JCM) in the presence of Stark shift and Kerr medium is studied. All terms in the respected Hamiltonian, such as the single-mode field, its interaction with the atom, the contribution of the Stark shift and the Kerr medium effects are considered to be $f$-deformed. In particular, the effect of the initial state of radiation field on the dynamical evolution of some physical properties such as atomic inversion and entropy squeezing are investigated by considering different initi…
The time-dependence of the quantum entropy for a two-level atom interacting with a single-cavity mode is computed using the Jaynes-Cummings model, when the initial state of the radiation field is prepared in a thermal state with temperature fluctuations. In order to describe the out-of-equilibrium situation, the Super Statistics approximation is implemented so that the gamma and the multi-level distribution functions are used to introduce the inverse temperature fluctuations. In the case of the gamma distribution, paralleling the Tsallis non-additive formalism, the entropy for the system is co…
The Jaynes-Cummings model is the simplest fully quantum model that describes the interaction between light and matter. We extend a previous analysis by Phoenix and Knight (S. J. D. Phoenix, P. L. Knight, Annals of Physics 186, 381). of the JCM by considering mixed states of both the light and matter. We present examples of qualitatively different entropic correlations. In particular, we explore the regime of entropy exchange between light and matter, i.e. where the rate of change of the two are anti-correlated. This behavior contrasts with the case of pure light-matter states in which the rate…
We show that the Jaynes principle is indeed a proper inference scheme when applied to compound systems and will correctly produce the entangled maximum entropy states compatible with appropriate data. This is accomplished by including the dispersion of the entanglement along with its mean value as constraints and an application of the uncertainty principle. We also construct a "thermodynamic-like" description of the entanglement arising out of the maximum entropy principle.
In this paper, we examine the effects of the gravitational field on the dynamical evolution of the cavity-field entropy and the creation of the Schrodinger-cat state in the Jaynes-Cummings model. We consider a moving two-level atom interacting with a single mode quantized cavity-field in the presence of a classical homogeneous gravitational field. Based on an su(2) algebra, as the dynamical symmetry group of the model, we derive the reduced density operator of the cavity-field which includes the effects of the atomic motion and the gravitational field. Also, we obtain the exact solution and th…
he Jaynes-Cummings model (JCM) is an very important model for describing interaction between quantized electromagnetic fields and atoms in cavity quantum electrodynamics (QED). This model is generalized in many different direction since it predicts many novel quantum effects that can be verified by modern physics experimental technologies. In this paper, the Berry phase and entropy of the ground state for arbitrary photon number $n$ of a two-atom Jaynes-Cummings model with Kerr like medium are investigated. It is found that there are some correspondence between their images, especially the exi…
We use the microscopic derivation of the Jaynes-Cummings model master equation under field losses to study the dynamics of initial field states beyond the single-excitation manifold. We show that field-qubit detuning, as well as finite temperature, modify the effective decay rate in the model using entropy measures, like qubit-field purity and von Neumann entropy of the field, for initial Fock states. For initial semi-classical states of the field, we show that the microscopic approach, in phase space, provides an evolution to thermal equilibrium that is smoother than the one provided by the s…
We show, by explicit examples, that the Jaynes inference scheme based on maximization of entropy can produce inseparable states even if there exists a separable state compatible with the measured data. It can lead to problems with processing of entanglement. The difficulty vanishes when one uses inference scheme based on minimization of entanglement.
Recently, it has been known that a quantum entangled state plays an important role in the field ofquantum information theory such as quantum teleportation and quantum computation. The research on quantifying entangled states has been done by several measures. In this letter, we will adopt the method using quantum mutual entropy to measure the degree of entanglement of Jaynes-Cummings model.
Quantum phase transitions and entanglement entropy in a non-Hermitian Jaynes-Cummings model
School of Physics and Astronomy, Rochester Institute of Technology（罗切斯特理工学院物理与天文学院）；Department of Physics, Banaras Hindu University（贝拿勒斯印度教大学物理系）；School of Basic Sciences, Indian Institute of Technology Bhubaneswar（布巴内斯瓦尔印度理工学院基础科学学院）
We study the entanglement in a system consisting of two non-interacting atoms located in separate cavities, both in their ground states. A single incoming photon has a non-zero probability of entering either of the two cavities. The Jaynes-Cummings interaction in the rotating wave approximation describes the coupling of each atom with the radiation field. We compute and analyze the atom-atom entanglement, the entanglement between the two photon modes, and also the entanglement between each atom and each photon mode. The measure of entanglement is the von Neumann entropy. For the case in which …
In the previous paper, we adopted the method using quantum mutual entropy to measure the degree of entanglement in the time development of the Jaynes-Cummings model. In this paper, we formulate the entanglement in the time development of the Jaynes-Cummings model with squeezed states, and then show that the entanglement can be controlled by means of squeezing.
We show the existence of dynamical purity swapping phenomena in the Jaynes-Cummings model. Moreover we show that purity swapping between a qubit and a generic quantum system is possible, provided they are coupled via non-unitary matrix elements interaction. We particularize to the case of a quantum optical Ramsey interferometer. We show that using purity swapping, a perfect interference pattern can be obtained at the output port of the interferometer even if we start from totally unpolarized sources. This feature is shown to be associated with the phenomena of recreation of the state vector at…
We present a scheme for a reconstruction of states of quantum systems from incomplete tomographic-like data. The proposed scheme is based on the Jaynes principle of Maximum Entropy. We apply our algorithm for a reconstruction of motional quantum states of neutral atoms. As an example we analyze the experimental data obtained by the group of C. Salomon at the ENS in Paris and we reconstruct Wigner functions of motional quantum states of Cs atoms trapped in an optical lattice.
The rise in linear entropy of a subsystem in the N-atom Jaynes-Cummings model is shown to be strongly influenced by the shape of the classical orbits of the underlying classical phase space: we find a one-to-one correspondence between maxima (minima) of the linear entropy and maxima (minima) of the expectation value of atomic excitation J_z. Since the expectation value of this operator can be viewed as related to the orbit radius in the classical phase space projection associated to the atomic degree of freedom, the proximity of the quantum wave packet to this atomic phase space borderline pro…
We derive an expression for a density operator estimated via Bayesian quantum inference in the limit of an infinite number of measurements. This expression is derived under the assumption that the reconstructed system is in a pure state. In this case the estimation corresponds to an averaging over a generalized microcanonical ensemble of pure states satisfying a set of constraints imposed by the measured mean values of the observables under consideration. We show that via the ``purification'' ansatz, statistical mixtures can also be consistently reconstructed via the quantum Bayesian inference…
We analyze the connections between entanglement dynamics and classical trajectories in a semiclassi-cal regime for two systems: A pair of coupled oscillators and the Jaynes-Cummings model. We find that entanglement production depends on classical invariant tori and such phenomenon is closely related to the power spectra of classical trajectories. Classical power spectrum with a larger number of frequency com-ponents corresponds to larger entanglement. We introduce a frequency entropy to describe the classical frequency distribution, and find that there is good correspondence between the classi…
A concern has been expressed that ``the Jaynes principle can produce fake entanglement'' [R. Horodecki et al., Phys. Rev. A {\bf 59}, 1799 (1999)]. In this paper we discuss the general problem of distilling maximally entangled states from $N$ copies of a bipartite quantum system about which only partial information is known, for instance in the form of a given expectation value. We point out that there is indeed a problem with applying the Jaynes principle of maximum entropy to more than one copy of a system, but the nature of this problem is classical and was discussed extensively by Jaynes. …
The interaction of a two-level atom with a single-mode quantized field is one of the simplest models in quantum optics. Under the rotating wave approximation, it is known as the Jaynes-Cummings model and without it as the Rabi model. Real-world realizations of the Jaynes-Cummings model include cavity, ion trap and circuit quantum electrodynamics. The Rabi model can be realized in circuit quantum electrodynamics. As soon as nonlinear couplings are introduced, feasible experimental realizations in quantum systems are drastically reduced. We propose a set of two photonic lattices that classically…
We introduce a new notion of entropy for quantum states, called contextual entropy, and show how it unifies Shannon and von Neumann entropy. The main result is that from the knowledge of the contextual entropy of a quantum state of a finite-dimensional system, one can reconstruct the quantum state, i.e., the density matrix, if the Hilbert space is of dimension 3 or greater. We present an explicit algorithm for this state reconstruction and relate our result to Gleason's theorem.
We present analytical results for the time-dependent information entropy in exactly solvable two-state (qubit) models. The first model describes dephasing (decoherence) in a qubit coupled to a bath of harmonic oscillators. The entropy production for this model in the regimes of "complete" and "incomplete" decoherence is discussed. As another example, we consider the damped Jaynes-Cummings model describing a spontaneous decay of a two-level system into the field vacuum. It is shown that, for all strengths of coupling, the open system passes through the mixed state with the maximum information e…
A quantum state is fully characterized by its density matrix or equivalently by its quasiprobabilities in phase space. A scheme to identify the quasiprobabilities of a quantum state is an important tool in the recent development of quantum technologies. Based on our highly efficient vacuum measurement scheme, we measure the quasiprobability $Q$-function of the vibrational motion for a \Yb ion {\it resonantly} interacting with its internal energy states. This interaction model is known as the Jaynes-Cummings model which is one of the fundamental models in quantum electrodynamics. We apply the c…
Using tomographic reconstruction we determine the complete internuclear quantum state, represented by the Wigner function, of a dissociating I2 molecule based on femtosecond time resolved position and momentum distributions of the atomic fragments. The experimental data are recorded by timed ionization of the photofragments with an intense 20 fs laser pulse. Our reconstruction method, which relies on Jaynes' maximum entropy principle, will also be applicable to time resolved position or momentum data obtained with other experimental techniques.
Our point of departure are the unitary dynamics of closed quantum systems as generated from the Schrödinger equation. We focus on a class of quantum models that typically exhibit roughly exponential relaxation of some observable within this framework. Furthermore, we focus on pure state evolutions. An entropy in accord with Jaynes principle is defined on the basis of the quantum expectation value of the above observable. It is demonstrated that the resulting deterministic entropy dynamics are in a sense in accord with a transient fluctuation theorem. Moreover, we demonstrate that the dynamics …
In this paper we have analysed in detail two different purification protocols. The first one, proposed by Sudarshan, is based on the preservation of probabilities.We have constructed a second protocol here based on optimisation of fidelities. We have considered both complete and partial measurements and have established bounds and inequalities for various fidelities. For every type of measurement, we have analysed post-measurement states based on the Maximum entropy principle as well as what we have proposed as unbiased states. We show that our purification protocol always leads to better stat…
We present a fully quantum solution to the Gibbs paradox (GP) with an illustration based on a gedanken experiment with two particles trapped in an infinite potential well. The well is divided into two cells by a solid wall, which could be removed for mixing the particles. For the initial thermal state with correct two-particle wavefunction according to their quantum statistics, the exact calculations shows the entropy changes are the same for boson, fermion and non-identical particles. With the observation that the initial unmixed state of identical particles in the conventional presentations …
In the dynamics of open quantum systems, the backflow of information to the reduced system under study has been suggested as the actual physical mechanism inducing memory and thus leading to non-Markovian quantum dynamics. To this aim, the trace-distance or Bures-distance revivals between distinct evolved system states have been shown to be subordinated to the establishment of system-environment correlations or changes in the environmental state. We show that this interpretation can be substantiated also for a class of entropic quantifiers. We exploit a suitably regularized version of Umegaki'…
In the framework of quantum information geometry, we derive, from quantum relative Tsallis entropy, a family of quantum metrics on the space of full rank, N level quantum states, by means of a suitably defined coordinate free differential calculus. The cases N = 2, N = 3 are discussed in detail and notable limits are analyzed. The radial limit procedure has been used to recover quantum metrics for lower rank states, such as pure states. By using the tomographic picture of quantum mechanics we have obtained the Fisher- Rao metric for the space of quantum tomograms and derived a reconstruction f…
We consider the problem of reconstructing global quantum states from local data. Because the reconstruction problem has many solutions in general, we consider the reconstructed state of maximum global entropy consistent with the local data. We show that unique ground states of local Hamiltonians are exactly reconstructed as the maximal entropy state. More generally, we show that if the state in question is a ground state of a local Hamiltonian with a degenerate space of locally indistinguishable ground states, then the maximal entropy state is close to the ground state projector. We also show …
