Related papers: General Description of Mixed State Geometric Phase

The geometric phase is of fundamental interest and plays an important role in quantum information processing. However, the definition and calculation of this phase for open systems remains a problem due to the lack of agreement on…

We explore geometric phases of coherent states and some of their properties. A better and elegant expression of geometric phase for coherent state is derived. It is used to obtain the explicit form of the geometric phase for entangled…

By viewing entanglement as a state function, a new kind of phase transition takes place: the geometric phase transition. This phenomenon occurs due to singularities in the shape of the entangled states set. It is shown how this result can…

The gauge invariance of geometric phases for mixed states is analyzed by using the hidden local gauge symmetry which arises from the arbitrariness of the choice of the basis set defining the coordinates in the functional space. This…

The aim of the paper is to propose geometric descriptions of multipartite entangled states using algebraic geometry. In the context of this paper, geometric means each stratum of the Hilbert space, corresponding to an entangled state, is an…

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…

This paper focuses on the geometric phase of entangled states of bi-partite systems under bi-local unitary evolution. We investigate the relation between the geometric phase of the system and those of the subsystems. It is shown that (1)…

We use tools from the theory of dynamical systems with symmetries to stratify Uhlmann's standard purification bundle and derive a new connection for mixed quantum states. For unitarily evolving systems, this connection gives rise to the…

Pure-state manifestations of geometric phase are well established and have found applications across essentially all branches of physics, yet their generalization to mixed-state regimes remains largely unexplored experimentally. The Uhlmann…

Uhlmann's mixed state geometric phase [Rep. Math. Phys. {\bf 24}, 229 (1986)] is analyzed in the case of a qubit affected by isotropic decoherence treated in the Markovian approximation. It is demonstrated that this phase decreases rapidly…

We investigate the evolution of a state which is dominated by a finite-dimensional non-Hermitian time-dependent Hamiltonian operator with a nondegenerate spectrum by using a biorthonormal approach. The geometric phase between any two…

In this paper we propose a geometrization of the non-relativistic quantum mechanics for mixed states. Our geometric approach makes use of the Uhlmann's principal fibre bundle to describe the space of mixed states and as a novelty tool, to…

It is shown that space-time may be not only in a state which is described by Riemann geometry but also in states which are described by Finsler geometry. Transitions between various metric states of space-time have the meaning of phase…

It was shown that quantum mechanical qubit states as elements of two dimensional complex space can be generalized to elements of even subalgebra of geometric (Clifford) algebra over Euclidian space. The construction critically depends on…

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…

We illustrate the geometric phase associated with the cyclic dynamics of a classical system of coupled oscillators. We use an analogy between a classical coupled oscillator and a two-state quantum mechanical system to represent the…

In a neutron polarimetry experiment the mixed state relative phases between spin eigenstates are determined from the maxima and minima of measured intensity oscillations. We consider evolutions leading to purely geometric, purely dynamical…

Examples of geometric phases abound in many areas of physics. They offer both fundamental insights into many physical phenomena and lead to interesting practical implementations. One of them, as indicated recently, might be an inherently…

In this thesis we provide a uniform treatment of two non-adiabatic geometric phases for dynamical systems of mixed quantum states, namely those of Uhlmann and of Sj\"{o}qvist et al. We develop a holonomy theory for the latter which we also…

The role of mixed states in topological quantum matter is less known than that of pure quantum states. Generalisations of topological phases appearing in pure states had received only quite recently attention in the literature. In…