Related papers: Phases of quantum states in completely positive no…
The representation of measurements by positive operator valued measures and the description of the most general state transformations by means of completely positive maps are two basic concepts of quantum information theory. These concepts…
Completely positive quantum operations are frequently discussed in the contexts of statistical mechanics and quantum information. They are customarily given by maps forming positive operator-values measures. To intuitively understand…
We interpret quantum computing as a geometric evolution process by reformulating finite quantum systems via Connes' noncommutative geometry. In this formulation, quantum states are represented as noncommutative connections, while gauge…
A generalised notion of geometric phase for pure states is proposed and its physical manifestations are shown. An appreciation of fact that the interference phenomenon also manifests in the average of an observable, allows us to define the…
We show that the geometric phase between any two states, including orthogonal states, can be computed and measured using the notion of projective measurement, and we show that a topological number can be extracted in the geometric phase…
In presence of dissipation, quantal states may acquire complex-valued phase effects. We suggest a notion of dissipative interferometry that accommodates this complex-valued structure and that may serve as a tool for analyzing the effect of…
We characterize operationally meaningful quantum gains in a paradigmatic model of lossless multiple-phase interferometry and stress insufficiency of the analysis based solely on the concept of quantum Fisher information. We show that the…
The basic elements of the mathematical theory of states of thermal equilibrium of infinite systems of quantum anharmonic oscillators (quantum crystals) are outlined. The main concept of this theory is to describe the states of finite…
We develop the widest possible generalisation of the well-known connection between quantum mechanical Bargmann invariants and geometric phases. The key notion is that of null phase curves in quantum mechanical ray and Hilbert spaces.…
Quantum groups lead to an algebraic structure that can be realized on quantum spaces. These are noncommutative spaces that inherit a well defined mathematical structure from the quantum group symmetry. In turn such quantum spaces can be…
Everett's concept of relative state is used to introduce a geometric phase that depends nontrivially on entanglement in a pure quantum state. We show that this phase can be measured in multiparticle interferometry. A correlation-dependent…
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…
Distinct from the dynamical phase, in a cyclic evolution, a system's state may acquire an additional component, a.k.a. geometric phase. The latter is a manifestation of a closed path in state space. Geometric phases underlie various…
We show how interferometry can be used to characterise certain aspects of general quantum processes, in particular, the coherence of completely positive maps. We derive a measure of coherent fidelity, maximum interference visibility and the…
The Pancharatnam phase is a generalization of the Berry phase that applies to discrete sequences of quantum states. Here, we show that the Pancharatnam phase is a natural invariant for a wide class of quantum many-body dynamics involving…
The dipole-coupled two-level atoms(qubits) in a single-mode resonant cavity is studied by extended bosonic coherent states. The numerically exact solution is presented. For finite systems, the first-order quantum phase transitions occur at…
Two geometric phases of mixed quantum states, known as the interferometric phase and Uhlmann phase, are generalizations of the Berry phase of pure states. After reviewing the two geometric phases and examining their parallel-transport…
We analyze the dynamics of neutron beams in interferometry experiments using quantum dynamical semigroups. We show that these experiments could provide stringent limits on the non-standard, dissipative terms appearing in the extended…
An effective Hamiltonian describing interaction between generic "fast" and a "slow" systems is obtained in the strong interaction limit. The result is applied for studying the effect of quantum phase transition as a bifurcation of the…
We explore the main processes involved in the evolution of general quantum systems by means of Diagrams of States, a novel method to graphically represent and analyze how quantum information is elaborated during computations performed by…