Related papers: A thermofield-double model of Uhlmann anholonomy
The time-dependent pseudo-Hermitian formulation of quantum mechanics allows to study open system dynamics in analogy to Hermitian quantum systems. In this setting, we show that the notion of holonomic quantum computation can equally be…
A microscopic definition of the thermodynamic entropy in an isolated quantum system must satisfy (i) additivity, (ii) extensivity and (iii) the second law of thermodynamics. We show that the diagonal entropy, which is the Shannon entropy in…
Abelian and non-Abelian geometric phases, known as quantum holonomies, have attracted considerable attention in the past. Here, we show that it is possible to associate nonequivalent holonomies to discrete sequences of subspaces in a…
This PHD thesis is concerned with uncertainty relations in quantum probability theory, state estimation in quantum stochastics, and natural bundles in differential geometry. After some comments on the nature and necessity of decoherence in…
This work demonstrates that the Deutsch algorithm can be effectively modelled using a two-level harmonic oscillator within the second quantization formalism. By adopting this framework, evolution operators are derived. We present a…
Topological phases are generally characterized by topological invariants denoted by integer numbers. However, different topological systems often require different topological invariants to measure, such as geometric phases, topological…
In a series of recent papers we have proved rigorously that time travel is a reality and very much feasible by using quantum mechanical processes. There are plenty of indirect experimental support untill a direct experiment is conducted.…
Geometric phase (GP) independent of energy and time rely only on the geometry of state space. It has been argued to have potential fault tolerance and plays an important role in quantum information and quantum computation. We present the…
The change of a quantum state can generally only be fully monitored through simultaneous measurements of two non-commuting observables X and Y spanning a phase space. A measurement device that is coupled to the thermal environment provides…
The measures of distances between points in a Hilbert space are one of the basic theoretical concepts used to characterize properties of a quantum system with respect to some etalon state. These are not only used in studying fidelity of…
The aim of this thesis is to investigate quantum entanglement and quantum nonlocality of bipartite finite-dimensional systems (bipartite qudits). Entanglement is one of the most fascinating non-classical features of quantum theory, and…
One-dimensional systems of interacting atoms are an ideal laboratory to study the Kosterlitz-Thouless phase transition. In the renormalization group picture there is essentially a two-parameter phase diagram to explore. We first present how…
We find for the unitary evolution of spin-1/2 systems that the "purely mathematical mixed state holonomy of Uhlmann limitedly agrees, in the case of evolution over geodesic spherical triangles, with the holonomy "in the experimental context…
The quantum measurement problem still finds no consensus. Nonlocal interferometry provides an unprecedented experimental probe by entangling two photons in the "measurement state" (MS). The experiments show that each photon "measures" the…
Equilibrium phase transitions usually emerge from the microscopic behavior of many-body systems and are associated to interesting phenomena such as the generation of long-range order and spontaneous symmetry breaking. They can be defined…
Quantum thermodynamics is a promising route to unambiguous detections of Majorana bound states. Being fundamentally different from quantum transport, this approach reveals unique Majorana thermodynamic behavior and deepens our insight into…
The statistical analysis of data lying on a differentiable, locally Euclidean, manifold introduces a variety of challenges because the analogous measures to standard Euclidean statistics are local, that is only defined within a…
We construct a topological invariant that classifies density matrices of symmetry-protected topological orders in two-dimensional fermionic systems. As it is constructed out of the previously introduced Uhlmann phase, we refer to it as the…
The Gr\"uneisen ratio $\Gamma$, i.e., the singular part of the ratio of thermal expansion to the specific heat, has been broadly employed to explore both finite-$T$ and quantum critical points (QCPs). For a genuine quantum phase transition…
A central feature of quantum mechanics is that a measurement is intrinsically probabilistic. As a result, continuously monitoring a quantum system will randomly perturb its natural unitary evolution. The ability to control a quantum system…