相关论文: Metric and classical fidelity uncertainty relation…

We introduce a new information-theoretic formulation of quantum measurement uncertainty relations, based on the notion of relative entropy between measurement probabilities. In the case of a finite-dimensional system and for any approximate…

We present a universal formulation of uncertainty relation valid for any conceivable quantum measurement and the resultant observation (observer) effect of statistical nature. Owing to its simplicity and operational tangibility, our general…

We establish the geometric ergodicity of the preconditioned Hamiltonian Monte Carlo (HMC) algorithm defined on an infinite-dimensional Hilbert space, as developed in [Beskos et al., Stochastic Process. Appl., 2011]. This algorithm can be…

Heisenberg's uncertainty principle is often cited as an example of a "purely quantum" relation with no analogue in the classical limit where $\hbar \to 0$. However, this formulation of the classical limit is problematic for many reasons,…

The entropic uncertainty relation proven by Maassen and Uffink for arbitrary pairs of two observables is known to be non-optimal. Here, we call an uncertainty relation optimal, if the lower bound can be attained for any value of either of…

Quantum bits can be isolated to perform useful information-theoretic tasks, even though physical systems are fundamentally described by very high-dimensional operator algebras. This is because qubits can be consistently embedded into…

Depth measures are powerful tools for defining level sets in emerging, non--standard, and complex random objects such as high-dimensional multivariate data, functional data, and random graphs. Despite their favorable theoretical properties,…

We show that the Euclidean Snyder non-commutative space implies infinitely many different physical predictions. The distinct frameworks are specified by generalized uncertainty relations underlying deformed Heisenberg algebras. Considering…

The Heisenberg-Robertson uncertainty relation quantitatively expresses the impossibility of jointly sharp preparation of incompatible observables. However it does not capture the concept of incompatible observables because it can be trivial…

Quantum uncertainty relations have deep-rooted significance on the formalism of quantum mechanics. Heisenberg's uncertainty relations attracted a renewed interest for its applications in quantum information science. Robertson derived a…

By considering (non-relativistic) quantum mechanics as it is done in practice in particular in condensed-matter physics, it is argued that a deterministic, unitary time evolution within a chosen Hilbert space always has a limited scope,…

The existence of a minimal observable length has long been suggested, in quantum gravity, as well as in string theory. In this context a generalized uncertainty relation has been derived which quantum theoretically describes the minimal…

The uncertainty principle is one of the fundamental features of quantum mechanics and plays a vital role in quantum information processing. We study uncertainty relations based on metric-adjusted skew information for finite quantum…

In quantum physics, measurement error and disturbance were first naively thought to be simply constrained by the Heisenberg uncertainty relation. Later, more rigorous analysis showed that the error and disturbance satisfy more subtle…

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…

Identifying a reasonably small Hilbert space that completely describes an unknown quantum state is crucial for efficient quantum information processing. We introduce a general dimension-certification protocol for both discrete and…

Heisenberg's uncertainty principle is quantified by error-disturbance tradeoff relations, which have been tested experimentally in various scenarios. Here we shall report improved new versions of various error-disturbance tradeoff relations…

In the course of the last decades entropic uncertainty relations have attracted much attention not only due to their fundamental role as manifestation of non-classicality of quantum mechanics, but also as major tools for applications of…

The most fundamental problem in statistics is the inference of an unknown probability distribution from a finite number of samples. For a specific observed data set, answers to the following questions would be desirable: (1) Estimation:…

The current study aims to examine uncertainty relations for measurements from generalized equiangular tight frames. Informationally overcomplete measurements are a valuable tool in quantum information processing, including tomography and…