Related papers: On geometric phases for quantum trajectories
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…
A geometrical approach to quantum computation is presented, where a non-abelian connection is introduced in order to rewrite the evolution operator of an energy degenerate system as a holonomic unitary. For a simple geometrical model we…
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…
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…
A monitored quantum system undergoing a cyclic evolution of the parameters governing its Hamiltonian accumulates a geometric phase that depends on the quantum trajectory followed by the system on its evolution. The phase value will be…
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…
Practical implementations of quantum computing are always done in the presence of decoherence. Geometric phase is useful in the context of quantum computing as a tool to achieve fault tolerance. Recent experimental progresses on coherent…
We illustrate how geometric gauge forces and topological phase effects emerge in quantum systems without employing assumptions that rely on adiabaticity. We show how geometric magnetism may be harnessed to engineer novel quantum devices…
Based on a generic quantum open system model, we study the geometric nature of decoherence by defining a complex-valued geometric phase through stochastic pure states describing non-unitary, non-cyclic and non-adiabatic evolutions. The…
Geometric phases have been shown to be feasible in implementing quantum gates to perform quantum information processing. For all the realistic applications, the environmental influence on the geometric phase and decoherence such as memory…
Geometric phases play a fundamental role in understanding quantum topology, yet extending the Uhlmann phase to non-Hermitian systems poses significant challenges due to parameter-dependent inner product structures. In this work, we develop…
Geometric phase that manifests itself in number of optic and nuclear experiments is shown to be a useful tool for realization of quantum computations in so called holonomic quantum computer model (HQCM). This model is considered as an…
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 present a nonlocal construction of universal gates by means of holonomic (geometric) quantum teleportation. The effect of the errors from imperfect control of the classical parameters, the looping variation of which builds up holonomic…
A periodic change of slow environmental parameters of a quantum system induces quantum holonomy. The phase holonomy is a well-known example. Another is a more exotic kind that exhibits eigenvalue and eigenspace holonomies. We introduce a…
In the first part of this review we introduce the basics theory behind geometric phases and emphasize their importance in quantum theory. The subject is presented in a general way so as to illustrate its wide applicability, but we also…
We consider an ``integral'' extension of the classical notion of affine connection providing a correspondence between paths in the manifold and diffeomorphisms of the manifold. These path-diffeomorphisms are a generalization of parallel…
An adiabatic cyclic evolution of control parameters of a quantum system ends up with a holonomic operation on the system, determined entirely by the geometry in the parameter space. The operation is given either by a simple phase factor (a…
The theory of geometric phase is generalized to a cyclic evolution of the eigenspace of an invariant operator with $N$-fold degeneracy. The corresponding geometric phase is interpreted as a holonomy inherited from the universal connection…
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…