Related papers: The Quantum Geometric Phase between Orthogonal Sta…
The geometric measure of entanglement of a pure quantum state is defined to be its distance to the space of product (seperable) states. Given an $n$-partite system composed of subsystems of dimensions $d_1,\ldots, d_n$, an upper bound for…
The theory of generalised measurements is used to examine the problem of discriminating unambiguously between non-orthogonal pure quantum states. Measurements of this type never give erroneous results, although, in general, there will be a…
The connection between the quantum-vacuum geometric phases (which originates from the vacuum zero-point electromagnetic fluctuation) and the non-normal product procedure is considered in the present Letter. In order to investigate this…
We present a characterization of quantum phase transitions in terms of the the overlap function between two ground states obtained for two different values of external parameters. On the examples of the Dicke and XY models, we show that the…
We investigate the differential geometry of bipartite quantum states. In particular the manifold structures of pure bipartite states are studied in detail. The manifolds with respect to all normalized pure states of arbitrarily given…
Topological phase transition is accompanied with a change of topological numbers. It has been believed that the gap closing and the breakdown of the adiabaticity at the transition point is necessary in general. However, the gap closing is…
In the standard geometric approach to a measure of entanglement of a pure state, $\sin^2\theta$ is used, where $\theta$ is the angle between the state to the closest separable state of products of normalized qubit states. We consider here a…
Based on phase-space structures of quantum states, we propose a novel measure to quantify macroscopic quantum superpositions. Our measure simultaneously quantifies two different kinds of essential information for a given quantum state in a…
It has recently been pointed out that phases of matter with intrinsic topological order, like the fractional quantum Hall states, have an extra dynamical degree of freedom that corresponds to quantum geometry. Here we perform extensive…
We predict a geometric quantum phase shift of a moving electric dipole in the presence of an external magnetic field at a distance. On the basis of the Lorentz-covariant field interaction approach, we show that a geometric phase appears…
Studying the geometry of sets appearing in various problems of quantum information helps in understanding different parts of the theory. It is thus worthwhile to approach quantum mechanics from the angle of geometry -- this has already…
We show that the phase shift of {\pi}/2 is crucial for the phase space translation covariance of the measured high-amplitude limit observable in eight-port homodyne detection. However, for an arbitrary phase shift {\theta} we construct…
The effect of entanglement on off-diagonal geometric phases is investigated in the paper. Two spin-1/2 particles in magnetic fields along the $y$ direction are taken as an example. Three parameters (the purity of state $r$, the mixing angle…
Geometric phase plays a fundamental role in quantum theory and accounts for wide phenomena ranging from the Aharanov-Bohm effect, the integer and fractional quantum hall effects, and topological phases of matter, including topological…
We show that sharply defined topological quantum phase transitions are not limited to states of matter with gapped electronic spectra. Such transitions may also occur between two gapless metallic states both with extended Fermi surfaces.…
We describe an algorithm for quantum state tomography that converges in polynomial time to an estimate, together with a rigorous error bound on the fidelity between the estimate and the true state. The result suggests that state tomography…
In an open system, the geometric phase should be described by a distribution. We show that a geometric phase distribution for open system dynamics is in general ambiguous, but the imposition of reasonable physical constraints on the…
The nonorthogonality of coherent states is a fundamental property which prevents them from being perfectly and deterministically discriminated. To circumvent this problem, we present an experimentally feasible protocol for the probabilistic…
The manifold of ground states of a family of quantum Hamiltonians can be endowed with a quantum geometric tensor whose singularities signal quantum phase transitions and give a general way to define quantum phases. In this paper, we show…
We study the influence of geometry of quantum systems underlying space of states on its quantum many-body dynamics. We observe an interplay between dynamical and topological ingredients of quantum non-equilibrium dynamics revealed by the…