Related papers: Bargmann invariants and off-diagonal geometric pha…
Bargmann invariants, a class of gauge-invariant quantities arising from the overlaps of quantum state vectors, provide a profound and unifying framework for understanding the geometric structure of quantum mechanics. This survey offers a…
Certain unitary-invariants, known as Bargmann invariants or multivariate traces of quantum states, have recently gained attention due to their applications in quantum information theory. However, determining the boundaries of sets of…
Bargmann invariants have recently emerged as powerful tools in quantum information theory, with applications ranging from geometric phase characterization to quantum state distinguishability. Despite their widespread use, a complete…
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.…
We introduce an operational framework to analyze non-adiabatic Abelian and non-Abelian, cyclic and non-cyclic, geometric phases in open quantum systems. In order to remove the adiabaticity condition, we generalize the theory of dynamical…
Bargmann invariants, also known as multivariate traces of quantum states $\operatorname{Tr}(\rho_1 \rho_2 \cdots \rho_n)$, are unitary invariant quantities used to characterize weak values, Kirkwood-Dirac quasiprobabilities,…
We present a study of the properties of Bargmann Invariants (BI) and Null Phase Curves (NPC) in the theory of the geometric phase for finite dimensional systems. A recent suggestion to exploit the Majorana theorem on symmetric SU(2)…
A generalized connection between the quantum mechanical Bargmann invariants and the geometric phases was established for the Dirac fermions. We extend that formalism for the Majorana fermions by defining proper quantum mechanical ray and…
The concept of off-diagonal geometric phases for mixed quantal states in unitary evolution is developed. We show that these phases arise from three basic ideas: (1) fulfillment of quantum parallel transport of a complete basis, (2) a…
We investigate the adiabatic evolution of a set of non-degenerate eigenstates of a parameterized Hamiltonian. Their relative phase change can be related to geometric measurable quantities that extend the familiar concept of Berry phase to…
We show that topological phases include disordered materials if the underlying invariant is interpreted as originating from coarse geometry. This coarse geometric framework, grounded in physical principles, offers a natural setting for the…
We accept the implicit challenge of A. Uhlmann in his 1994 paper, "Parallel Lifts and Holonomy along Density Operators: Computable Examples Using O(3)-Orbits," by, in fact, computing the holonomy invariants for rotations of certain n-level…
We extend the off-diagonal geometric phase [Phys. Rev. Lett. {\bf 85}, 3067 (2000)] to mixed quantal states. The nodal structure of this phase in the qubit (two-level) case is compared with that of the diagonal mixed state geometric phase…
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…
The concept of off-diagonal geometric phase (GP) has been introduced in order to recover interference information about the geometry of quantal evolution where the standard GPs are not well-defined. In this Letter, we propose a physical…
If a quantum system evolves in a noncyclic fashion the corresponding geometric phase or holonomy may not be fully defined. Off-diagonal geometric phases have been developed to deal with such cases. Here, we generalize these phases to the…
Off-diagonal geometric phases have been developed in order to provide information of the geometry of paths that connect noninterfering quantal states. We propose a kinematic approach to off-diagonal geometric phases for pure and mixed…
We present the first scheme for producing and measuring an Abelian geometric phase shift in a three-level system where states are invariant under a non-Abelian group. In contrast to existing experiments and proposals for experiments, based…
Bargmann invariants, multivariate traces of states, completely characterize any unitary-invariant property of a set of states. Unitary invariants enable the description of quantum resources such as basis-independent coherence and…
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…