Related papers: On the geometric phase for Gaussian states
A general framework is described which associates geometrical structures to any set of $D$ finite-dimensional hermitian matrices $X^a, \ a=1,...,D$. This framework generalizes and systematizes the well-known examples of fuzzy spaces, and…
Gaussian quantum mechanics is a powerful tool regularly used in quantum optics to model linear and quadratic Hamiltonians efficiently. Recent interest in qubit-CV hybrid models has revealed a simple, yet important gap in our knowledge,…
Continuous-variable Gaussian entanglement is an attractive notion, both as a fundamental concept in quantum information theory, based on the well-established Gaussian formalism for phase-space variables, and as a practical resource in…
We solve stationarity equations of the geometric measure of entanglement for multi-qubit W-type states. In this way we compute analytically the maximal overlap of one-parameter $n$-qubit and two-parameter four-qubit W-type states and their…
We show that the geometric phase for mixed state during a cyclic evolution suggested in 2004 J. Phys. A 37 3699 is U(1) invariant and can be observed by nowaday techniques.
Gaussian quantum states of bosonic systems are an important class of states. In particular, they play a key role in quantum optics as all processes generated by Hamiltonians up to second order in the field operators (i.e. linear optics and…
The Groverian measures are analytically computed in various types of three-qubit states. The final results are also expressed in terms of local-unitary invariant quantities in each type. This fact reflects the manifest local-unitary…
Off-diagonal geometric phases have been developed in order to provide information of the geometry of paths that connect noninterfering quantal states. We propose a kinematic approach to off-diagonal geometric phases for pure and mixed…
The two-mode relative phase associated with Gaussian states plays an important role in quantum information processes in optical, atomic and electronic systems. In this work, the origin and structure of the two-mode relative phase in pure…
The geometric phase is usually treated as a quantity modulo 2\pi, a convention carried over from early work on the subject. The results of a series of optical interference experiments involving polarization of light, done by the present…
Finite-dimensional Quantum Mechanics can be geometrically formulated as a proper classical-like Hamiltonian theory in a projective Hilbert space. The description of composite quantum systems within the geometric Hamiltonian framework is…
Entanglement of formation is a fundamental measure that quantifies the entanglement of bipartite quantum states. This measure has recently been extended into multipartite states taking the name $\alpha$-entanglement of formation. In this…
We examine evolutions where each component of a given decomposition of a mixed quantal state evolves independently in a unitary fashion. The geometric phase and parallel transport conditions for this type of decomposition dependent…
We analyze generalized Gaussian cat states obtained by superposing arbitrary Gaussian states, e.g., a coherent state and a squeezed state. The Wigner functions of such states exhibit the typical pair of Gaussian hills plus an interference…
The notion of partial trace of a density operator is essential for the understanding of the entanglement and separability properties of quantum states. In this paper we investigate these notions putting an emphasis on the geometrical…
We suggest a scheme to reconstruct the covariance matrix of a two-mode state using a single homodyne detector plus a polarizing beam splitter and a polarization rotator. It can be used to fully characterize bipartite Gaussian states and to…
Different constructions for Hilbert state space for constrained systems are investigated. Properties of Gaussian states analogous to quantum mechanical Gaussian wave functions are studied. Their evolution for quadratic Hamiltonian case are…
The wave description of geometric phase uses the superposition of light waves to explain the geometric phase's origin. While our previous work focused on a basis of linearly polarized waves, here we show that the same concepts can be…
Geometric phases play a central role in a variety of quantum phenomena, especially in condensed matter physics. Recently, it was shown that this fundamental concept exhibits a connection to quantum phase transitions where the system…
We study the geometric phase factors underlying the classical and the corresponding quantum dynamics of a driven nonlinear oscillator exhibiting chaotic dynamics. For the classical problem, we compute the geometric phase factors associated…