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Quantum coherence and non-classical correlation are key features of quantum world. Quantifying coherence and non-classical correlation are two key tasks in quantum information theory. First, we present a bona fide measure of quantum…

Quantum Physics · Physics 2018-06-29 Zhi-Xiang Jin , Shao-Ming Fei

This work considers the asymptotic behavior of the distance between two sample covariance matrices (SCM). A general result is provided for a class of functionals that can be expressed as sums of traces of functions that are separately…

Statistics Theory · Mathematics 2023-12-25 Roberto Pereira , Xavier Mestre , David Gregoratti

Given a quantum system on many qubits split into a few different parties, how many total correlations are there between these parties? Such a quantity, aimed to measure the deviation of the global quantum state from an uncorrelated state…

Quantum Physics · Physics 2022-02-15 Zhenhuan Liu , Pei Zeng , You Zhou , Mile Gu

Loosely speaking, the concept of quantum typicality refers to the fact that a single pure state can imitate the full statistical ensemble. This fact has given rise to a rather simple but remarkably useful numerical approach to simulate the…

Statistical Mechanics · Physics 2020-05-18 Tjark Heitmann , Jonas Richter , Dennis Schubert , Robin Steinigeweg

Preparing the ground state of a local Hamiltonian is a crucial problem in understanding quantum many-body systems, with applications in a variety of physics fields and connections to combinatorial optimization. While various quantum…

Quantum Physics · Physics 2025-02-06 Benjamin F. Schiffer , Jordi Tura

In the paper of F.A. Mele, A.A. Mele, L. Bittel, J. Eisert, V. Giovannetti, L. Lami, L. Leone, S.F.E. Oliviero, ArXiv:2405.01431, estimates for the trace-norm distance between two quantum Gaussian states in terms of the mean vectors and…

Quantum Physics · Physics 2025-09-01 A. S. Holevo

Quantum state tomography is a fundamental tool in quantum information processing. It allows us to estimate the state of a quantum system by measuring different observables on many identically prepared copies of the system. This is, in…

Quantum Physics · Physics 2011-11-28 Carlos A. Riofrío

We describe two quantum algorithms to approximate the mean value of a black-box function. The first algorithm is novel and asymptotically optimal while the second is a variation on an earlier algorithm due to Aharonov. Both algorithms have…

Quantum Physics · Physics 2011-06-22 Gilles Brassard , Frederic Dupuis , Sebastien Gambs , Alain Tapp

We study the average case approximation of the Boolean mean by quantum algorithms. We prove general query lower bounds for classes of probability measures on the set of inputs. We pay special attention to two probabilities, where we show…

Quantum Physics · Physics 2007-05-23 A. Papageorgiou

The goal of this paper is to calculate exactly the average of uncertainty-product of two bounded observables and to establish its typicality over the whole set of finite dimensional quantum pure states. Here we use the uniform ensembles of…

Quantum Physics · Physics 2018-07-24 Lin Zhang , Jiamei Wang

The algorithmic error of digital quantum simulations is usually explored in terms of the spectral norm distance between the actual and ideal evolution operators. In practice, this worst-case error analysis may be unnecessarily pessimistic.…

Quantum Physics · Physics 2023-02-02 Qi Zhao , You Zhou , Alexander F. Shaw , Tongyang Li , Andrew M. Childs

We investigate the tradeoff between the quality of an approximate version of a given measurement and the disturbance it induces in the measured quantum system. We prove that if the target measurement is a non-degenerate von Neumann…

Quantum Physics · Physics 2019-01-23 Anna-Lena K. Hashagen , Michael M. Wolf

We introduce and apply Hilbert's projective metric in the context of quantum information theory. The metric is induced by convex cones such as the sets of positive, separable or PPT operators. It provides bounds on measures for statistical…

Mathematical Physics · Physics 2011-08-16 David Reeb , Michael J. Kastoryano , Michael M. Wolf

Armed with quantum correlations, quantum sensors in a network have shown the potential to outclass their classical counterparts in distributed sensing tasks such as clock synchronization and reference frame alignment. On the other hand,…

Quantum Physics · Physics 2024-05-24 Yuxiang Yang , Benjamin Yadin , Zhen-Peng Xu

Gaussian states of bosonic quantum systems enjoy numerous technological applications and are ubiquitous in nature. Their significance lies in their simplicity, which in turn rests on the fact that they are uniquely determined by two…

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…

Quantum Physics · Physics 2026-04-15 Sanchari Chakraborti , Rafael D. Sorkin , Urbasi Sinha

We introduce a quantum measurement process that is capable of characterizing an unknown state of a system almost without disturbing or collapsing it. The underlying idea is to extract information of a system from the thermodynamic…

Quantum Physics · Physics 2019-11-26 Mohit Lal Bera , Manabendra Nath Bera

The achievement of quantum supremacy boosted the need for a robust medium of quantum information. In this task, higher-dimensional qudits show remarkable noise tolerance and enhanced security for quantum key distribution applications.…

We study quantum statistical inference tasks of hypothesis testing and their canonical variations, in order to review relations between their corresponding figures of merit---measures of statistical distance---and demonstrate the crucial…

Quantum Physics · Physics 2020-09-25 Marcin Jarzyna , Jan Kolodynski

In this work we determine a lower bound to the mean value of the quantum potential for an arbitrary state. Furthermore, we derive a generalized uncertainty relation that is stronger than the Robertson-Schr\"odinger inequality and hence also…

Quantum Physics · Physics 2020-05-08 F. Nicacio , F. T. Falciano