M. Daoud

Geometric measure of pairwise quantum discord for superpositions of multipartite generalized coherent states

Abstract We give the explicit expressions of the pairwise quantum correlations present in superpositions of multipartite coherent states. A special attention is devoted to the evaluation of the geometric quantum discord. The dynamics of quantum correlations under a dephasing channel is analyzed. A comparison of geometric measure of quantum discord with that of concurrence shows that quantum discord in multipartite coherent states is more resilient to dissipative environments than is quantum entanglement. To illustrate our results, we consider some special superpositions of Weyl–Heisenberg, SU ( 2 ) and SU ( 1 , 1 ) coherent states which interpolate between Werner and Greenberger–Horne–Zeilinger states.

QUANTUM DISCORD FOR MULTIPARTITE COHERENT STATES INTERPOLATING BETWEEN WERNER AND GREENBERGER–HORNE–ZEILINGER STATES

The quantum discord is used as measure of quantum correlations for two families of multipartite coherent states. The first family interpolates between generalized GHZ states and generalized Werner states. The second one is an interpolation between generalized GHZ and the ground state of the multipartite quantum system. Two inequivalent ways to split the system in a pair of qubits are introduced. The explicit expressions of quantum quantum discord in multipartite coherent states are derived. Its evaluation uses the Koashi–Winter relation in optimizing the conditional entropy. The temporal evolution of quantum correlations (quantum discord and entanglement) is also discussed.

Quantum discord of Bell cat states under amplitude damping

The evolution of pairwise quantum correlations of Bell cat states under amplitude damping is examined using the concept of quantum discord which goes beyond entanglement. A closed expression of the quantum discord is explicitly derived. We used the Koashi?Winter relation, a relation which facilitates the optimization process of the conditional entropy. We also discuss the temporal evolution of bipartite quantum correlations under a dephasing channel and compare the behaviors of quantum discord and entanglement whose properties are characterized through the concurrence.

Effective Wess–Zumino–Witten action for edge states of quantum Hall systems on Bergman ball

Using a group theory approach, we investigate the basic features of the Landau problem on the Bergman ball Bk. This can be done by considering a system of particles living on Bk in the presence of an uniform magnetic field B and realizing the ball as the coset space SU(k,1)/U(k). In quantizing the theory on Bk, we define the wavefunctions as the Wigner D-functions satisfying a set of suitable constraints. The corresponding Hamiltonian is mapped in terms of the right translation generators. In the lowest Landau level, we obtain the wavefunctions as the SU(k,1) coherent states. This are used to define the star product, density matrix and excitation potential in higher dimensions. With these ingredients, we construct a generalized effective Wess–Zumino–Witten action for the edge states and discuss their nature.

QUANTUM HALL EFFECT ON THE FLAG MANIFOLD F2

The Landau problem on the flag manifold F2 = SU(3)/U(1)×U(1) is analyzed from an algebraic point of view. The involved magnetic background is induced by two U(1) Abelian connections. In quantizing the theory, we show that the wave functions, of a nonrelativistic particle living on F2, are the SU(3) Wigner -functions satisfying two constraints. Using the F2 algebraic and geometrical structures, we derive the Landau Hamiltonian as well as its energy levels. The lowest Landau level (LLL) wave functions coincide with the coherent states for the mixed SU(3) representations. We discuss the quantum Hall effect for a filling factor ν = 1, where the obtained particle density is constant and finite for a strong magnetic field. In this limit, we also show that the system behaves like an incompressible fluid. We study the semiclassical properties of the system confined in LLL. These will be used to discuss the edge excitations and construct the corresponding Wess–Zumino–Witten action.

QUANTUM HALL DROPLETS ON DISC AND EFFECTIVE WESS–ZUMINO–WITTEN ACTION FOR EDGE STATES

We algebraically analyze the quantum Hall effect of a system of particles living on the disc B1 in the presence of a uniform magnetic field B. For this, we identify the non-compact disc with the coset space SU(1,1)/U(1). This allows us to use the geometric quantization in order to get the wavefunctions as the Wigner -functions satisfying a suitable constraint. We show that the corresponding Hamiltonian coincides with the Maass Laplacian. Restricting to the lowest Landau level, we introduce the noncommutative geometry through the star product. Also we discuss the state density behavior as well as the excitation potential of the quantum Hall droplet. We show that the edge excitations are described by an effective Wess–Zumino–Witten action for a strong magnetic field and discuss their nature. We finally show that LLL wavefunctions are intelligent states.

STATISTICAL PROPERTIES OF KLAUDER PERELOMOV COHERENT STATES FOR THE MORSE POTENTIAL

We present in this letter a realistic construction of the coherent states for the Morse potential using the Klauder–Perelomov approach. We discuss the statistical properties of these states, by deducing the Q- and P-distribution functions. The thermal expectations for the quantum canonical ideal gas of the Morse oscillators are also calculated.

Entanglement versus Gaussian quantum discord in a double-cavity opto-mechanical system

In this paper, we investigate the robustness of the quantum correlations against the environment effects in various opto-mechanical bipartite systems. For two spatially separated opto-mechanical cavities, we give analytical formula for the global covariance matrix involving two mechanical modes and two optical modes. The logarithmic negativity as an indicator of the degree of entanglement and the Gaussian quantum discord which is a witness of quantumness of correlations are used as quantifiers to evaluate the different pairwise quantum correlations in the whole system. The evolution of the quantum correlations existing in this opto-mechanical system are analyzed in terms of the thermal bath temperature, squeezing parameter and the opto-mechanical cooperativity. We find that with desirable choice of these parameters, it is possible either to enhance or annihilate the quantum correlations in the system. Various scenarios are discussed in detail.

Multipartite quantum correlations in even and odd spin coherent states

The key ingredient of the approach presented in this paper is the factorization property of SU(2) coherent states upon the splitting or decay of a quantum spin system. In this picture, the even and odd spin coherent states are viewed as comprising two, three or more spin sub-systems. From this perspective, we investigate the multipartite quantum correlations defined as the sum of the correlations of all possible bi-partitions. The pairwise quantum correlations are quantified by entanglement of formation and quantum discord. Special attention is devoted to tripartite splitting schemes. We explicitly derive the sum of the entanglement of formation for all possible bi-partitions. It coincides with the sum of all possible occurrences of pairwise quantum discord. The conservation relation between the distribution of entanglement of formation and quantum discord in the tripartite splitting scheme is discussed. We show that entanglement of formation and quantum discord possess the monogamy property for even spin coherent states, in contrast to odd ones which violate the monogamy relation when the overlap of the coherent states approaches unity.

Nonclassical correlations in a two-mode optomechanical system

The pairwise quantum correlations in a tripartite optomechanical system comprising a mechanical mode and two optical modes are analyzed. The Simon criterion is used as a witness of the separability. Whereas the Gaussian discord is employed to capture the quantumness of correlations. Both entanglement and Gaussian discord are evaluated as functions of the parameters characterizing the environment and the system (temperature, squeezing and optomechanical coupling). We work in the resolved-sideband regime. We show that it is possible to reach three simultaneous bipartite entanglements via the quantum correlations transfer from the squeezed light to the system. While, even without squeezed light, the quantumness of correlations can be captured simultaneously between the three modes for a very wide range of parameters. Specifically, we find that the two optical modes exhibit more quantum correlations in comparison with the entangled mechanical–optical modes. Finally, unlike the two hybrid subsystems, the purely optical one seems more resilient against the environmental destructive effects.