Related papers: Phase Dynamics of Two Entangled Qubits
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)…
When an entangled state evolves under local unitaries, the entanglement in the state remains fixed. Here we show the dynamical phase acquired by an entangled state in such a scenario can always be understood as the sum of the dynamical…
We present an unambiguous characterization of the rotation group SO(3) biconnectedness topology using two-qubit maximally entangled states. We show how to generate cyclic evolutions of these states, which are in one-to-one correspondence to…
We consider arbitrary mixed state in unitary evolution and provide a comprehensive description of corresponding geometric phase in which two different points of view prevailing currently can be unified. Introducing an ancillary system and…
We discuss the appearance of fractional topological phases on cyclic evolutions of entangled qudits. The original result reported in Phys. Rev. Lett. \textbf{106}, 240503 (2011) is detailed and extended to qudits of different dimensions.…
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…
The geometric phase for a pure quantal state undergoing an arbitrary evolution is a ``memory'' of the geometry of the path in the projective Hilbert space of the system. We find that Uhlmann's geometric phase for a mixed quantal state…
We investigate the topological structure of entangled qudits under unitary local operations. Different sectors are identified in the evolution, and their geometrical and topological aspects are analyzed. The geometric phase is explicitly…
We propose an experiment to observe the topological phases associated with cyclic evolutions, generated by local SU(2) operations, on three-qubit entangled states prepared on different degrees of freedom of entangled photon pairs. The…
This thesis, explores the quantum entanglement and evolution through both a geometric and dynamical perspective. The first part focuses on classical phase space and its central role in Hamiltonian mechanics, emphasizing the importance of…
In this work, we study a bipartite system composed by a pair of entangled qudits coupled to an environment. Initially, we derive a master equation and show how the dynamics can be restricted to a "diagonal" sector that includes a maximally…
We calculate the geometric phase of a bipartite two-level system coupled to an external environment. We analyze the reduced density matrix for an arbitrary initial state of the composite system and compute the correction to the unitary…
We introduce a connection between entanglement induced by interaction and geometric phases acquired by a composite quantum spin system. We begin by analyzing the evaluation of cyclic (Aharonov-Anandan) and non-cyclic (Mukunda-Simon)…
We study a kind of geometric phases for entangled quantum systems, and particularly a spin driven by a magnetic field and entangled with another spin. The new kind of geometric phase is based on an analogy between open quantum systems and…
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…
It is known that an interacting bipartite system evolves as an entangled state in general, even if it is initially in a separable state. Due to the entanglement of the state, the geometric phase of the system is not equal to the sum of the…
Through the quantum trajectory approach, we calculate the geometric phase acquired by a bipartite system subjected to decoherence. The subsystems that compose the bipartite system interact with each other, and then are entangled in the…
Global phase factors of topological origin, resulting from cyclic local $\rm{SU}$ evolution, called topological phases, were first described in [Phys. Rev. Lett. {\bf 90}, 230403 (2003)], in the case of entangled qubit pairs. In this paper…
The dynamics of a two-qubit system is considered with the aim of a general categorization of the different ways in which entanglement can disappear in the course of the evolution, e.g., entanglement sudden death. The dynamics is described…
The geometric phases of cyclic evolutions for mixed states are discussed in the framework of unitary evolution. A canonical one-form is defined whose line integral gives the geometric phase which is gauge invariant. It reduces to the…