Related papers: Transition Probability (Fidelity) and Its Relative…
The entanglement fidelity provides a measure of how well the entanglement between two subsystems is preserved in a quantum process. By using a simple model we show that in some cases this quantity in its original definition fails in the…
Fidelity is the standard measure for quantifying the similarity between two quantum states. It is equal to the square of the minimum Bhattacharyya coefficient between the probability distributions induced by quantum measurements on the two…
A geometric interpretation for the A-fidelity between two states of a qubit system is presented, which leads to an upper bound of the Bures fidelity. The metrics defined based on the A-fidelity are studied by numerical method. An…
Fidelity plays an important role in quantum information theory. In this letter, we introduce new metric of quantum states induced by fidelity, and connect it with the well-known trace metric, Sine metric and Bures metric for the qubit case.…
We analyze mean fidelity between random density matrices of size N, generated with respect to various probability measures in the space of mixed quantum states: Hilbert-Schmidt measure, Bures (statistical) measure, the measures induced by…
In this paper, we utilize the framework of Markov processes to attain a more probabilistic perspective on the theory of transfer operators. In doing so, we establish a functional central limit theorem (FLCT) for an $O(N)$ model associated…
Realistic quantum mechanics based on complex probability theory is shown to have a frequency interpretation, to coexist with Bell's theorem, to be linear, to include wavefunctions which are expansions in eigenfunctions of Hermitian…
We show the existence of invariant ergodic $\sigma$-additive probability measures with full support on $X$ for a class of linear operators $L: X \to X$, where $L$ is a weighted shift operator and $X$ either is the Banach space…
In the quantum mechanical Hilbert space formalism, the probabilistic interpretation is a later ad-hoc add-on, more or less enforced by the experimental evidence, but not motivated by the mathematical model itself. A model involving a clear…
Fidelity serves as a benchmark for the relieability in quantum information processes, and has recently atracted much interest as a measure of the susceptibility of dynamics to perturbations. A rich variety of regimes for fidelity decay have…
The concept of fidelity has been introduced to characterize the stability of a quantum-mechanical system against perturbations. The fidelity amplitude is defined as the overlap integral of a wave packet with itself after the development…
Entropy can signify different things: For instance, heat transfer in thermodynamics or a measure of information in data analysis. Many entropies have been introduced and it can be difficult to ascertain their different importance and…
Non-relativistic quantum mechanics is reformulated here based on the idea that relational properties among quantum systems, instead of the independent properties of a quantum system, are the most fundamental elements to construct quantum…
The analysis and control of stochastic dynamical systems rely on probabilistic models such as (continuous-space) Markov decision processes, but large or continuous state spaces make exact analysis intractable and call for principled…
It is shown that a normalisable probability density can be defined for the entire complex plane in the modified de Broglie-Bohm quantum mechanics, which gives complex quantum trajectories. This work is in continuation of a previous one that…
I discuss the process of measurement in the context of a communication system. The setting is a transmitter which encodes some physical object and sends it off, a receiver which measures some property of the transmitted physical object…
A trade-off relation on our knowledge about two noncommuting observables of a qubit system in simultaneous measurement is formulated. The obtained inequality offers a quantitative information-theoretic representation of Bohr's principle of…
The quantum mechanical probability densities are compared with the probability densities treated by the theory of random variables. The relevance of their difference for the interpretation of quantum mechanics is commented.
In static classical statistical systems the problem of information transport from a boundary to the bulk finds a simple description in terms of wave functions or density matrices. While the transfer matrix formalism is a type of Heisenberg…
A typical quantum experiment has a bunch of apparatuses placed so that quantum systems can pass between them. We regard each use of an apparatus, along with some given outcome on the apparatus (a certain detector click or a certain meter…