Related papers: The Quantum Union Bound made easy
A reformulation of a physical theory in which measurements at the initial and final moments of time are treated independently is discussed, both on the classical and quantum levels. Methods of the standard quantum mechanics are used to…
We give a novel derivation of Holevo's bound using an important result from nonequilibrium statistical physics, the fluctuation theorem. To do so we develop a general formalism of quantum fluctuation theorems for two-time measurements,…
Elementary particles are found in two different situations: (i) bound to metastable states of matter, for which angular momentum is quantized, and (ii) free, for which, due to their high energy-momentum and leaving aside inner a.m. or spin,…
This paper first reviews quantum measure and integration theory. A new representation of the quantum integral is presented. This representation is illustrated by computing some quantum (Lebesgue)${}^2$ integrals. The rest of the paper only…
We consider the situation of a two-level quantum system undergoing a continuous indirect measurement, giving rise to so-called "quantum trajectories". We first describe these quantum trajectories in a physically realistic discrete-time…
Quantum computation offers a promising new kind of information processing, where the non-classical features of quantum mechanics can be harnessed and exploited. A number of models of quantum computation exist, including the now well-studied…
Quantifying quantum entanglement is a pivotal challenge in quantum information science, particularly for high-dimensional systems, due to its computational complexity. This thesis extends the geometric measure of entanglement (GME) to…
This paper presents a simple model for repeated measurement of a quantum system: the evolution of a free particle, simulated by discretising the particle's position. This model is easily simulated by computer and provides a useful arena to…
Gentle measurements of quantum states do not entirely collapse the initial state. Instead, they provide a post-measurement state at a prescribed trace distance $\alpha$ from the initial state together with a random variable used for quantum…
If the block universe view is correct, the future and the past have similar status and one would expect physical theories to involve final as well as initial boundary conditions. A plausible consistency condition between the initial and…
The history based formalism known as Quantum Measure Theory (QMT) generalizes the concept of probability-measure so as to incorporate quantum interference. The resulting \textit{quantum measure} $\mu$ is defined for arbitrary events (sets…
Concurrence introduced by Hill and Wootters [Phys. Rev. Lett. 78, 5022 (1997)], provides an important measure of entanglement for a general pair of qubits that is strictly positive entangled states and vanishes for all separable states. We…
We describe a quantum mechanical measurement as a variational principle including interaction between the system under measurement and the measurement apparatus. Augmenting the action with a nonlocal term (a double integration over the…
Quantum measurement is a fundamental cornerstone of experimental quantum computations. The main issues in current quantum measurement strategies are the high number of measurement rounds to determine a global optimal measurement output and…
Effective bounds on the union probability are well known to be beneficial in the analysis of stochastic problems in many areas, including probability theory, information theory, statistical communications, computing and operations research.…
We produce a new, shorter construction of a minor-universal planar graph.
The polynomial method by Beals, Buhrman, Cleve, Mosca, and de Wolf (FOCS 1998, J. ACM 2001), the adversary method by Ambainis (STOC 2000, J. Comput. Syst. Sci. 2002), and the compressed oracle method by Zhandry (CRYPTO 2019) have been shown…
In this paper, we present a thought experiment that demonstrates that the equivalence of quantum reduced states and statistical mixed states of ensembles is not merely a simple mathematical formulation in quantum mechanics, but rather…
Quantum metrology derives its capabilities from the careful employ of quantum resources for carrying out measurements. This advantage, however, relies on refined data postprocessing, assessed based on the variance of the estimated…
We first review and critically examine some basic concepts and ambiguities related to quantum mechanics and quantum measurement to understand the success and shortcomings of current theories. We also touch on ideas regarding expression of…