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Coherence and entanglement are fundamental properties of quantum systems, promising to power the near future quantum computers, sensors and simulators. Yet, their experimental detection is challenging, usually requiring full reconstruction…
We investigate the computational hardness of estimating the quantum $\alpha$-R\'enyi entropy ${\rm S}^{\tt R}_{\alpha}(\rho) = \frac{\ln {\rm Tr}(\rho^\alpha)}{1-\alpha}$ and the quantum $q$-Tsallis entropy ${\rm S}^{\tt T}_q(\rho) =…
The efficient simulation of correlated quantum systems is the most promising near-term application of quantum computers. Here, we present a measurement of the second Renyi entropy of the ground state of the two-site Fermi-Hubbard model on a…
A method of representing probabilistic aspects of quantum systems is introduced by means of a density function on the space of pure quantum states. In particular, a maximum entropy argument allows us to obtain a natural density function…
Quantum ensembles form easily accessible architectures for studying various phenomena in quantum physics, quantum information science, and spectroscopy. Here we review some recent protocols for measurements in quantum ensembles by utilizing…
Estimating quantum entropies and divergences is an important problem in quantum physics, information theory, and machine learning. Quantum neural estimators (QNEs), which utilize a hybrid classical-quantum architecture, have recently…
This paper introduces a numerical framework for establishing lower bounds on the conditional von-Neumann entropy in device-independent quantum cryptography and randomness extraction scenarios. Leveraging a hierarchy of semidefinite programs…
We formulate limits to perception under continuous quantum measurements by comparing the quantum states assigned by agents that have partial access to measurement outcomes. To this end, we provide bounds on the trace distance and the…
A general quantum measurement on an unknown quantum state enables us to estimate what the state originally was. Simultaneously, the measurement has a destructive effect on a measured quantum state which is reflected by the decrease of the…
Quantum information-theoretic approach has been identified as a way to understand the foundations of quantum mechanics as early as 1950 due to Shannon. However there hasn't been enough advancement or rigorous development of the subject. In…
Simply and reliably detecting and quantifying entanglement outside laboratory conditions will be essential for future quantum information technologies. Here we address this issue by proposing a method for generating expressions which can…
Renyi entropy associated with spin tomograms of quantum states is shown to obey to new inequalities containing the dependence on quantum Fourier transform. The limiting inequality for the von Neumann entropy of spin quantum states and a new…
We define correlational (von Neumann) entropy for an individual quantum state of a system whose time-independent hamiltonian contains random parameters and is treated as a member of a statistical ensemble. This entropy is representation…
We demonstrate that the Renyi-2 entropy provides a natural measure of information for any multimode Gaussian state of quantum harmonic systems, operationally linked to the phase-space Shannon sampling entropy of the Wigner distribution of…
Information theory provides principled ways to analyze different inference and learning problems such as hypothesis testing, clustering, dimensionality reduction, classification, among others. However, the use of information theoretic…
In this article, we derive a unique procedure for quantum state estimation from a simple, self-evident principle: an experimentalist's estimate of the quantum state generated by an apparatus should be constrained by honesty. A skeptical…
The states of the qubit, the basic unit of quantum information, are $2 \times 2$ positive semi-definite Hermitian matrices with trace 1. We contribute to the program to axiomatize quantum mechanics by characterizing these states in terms of…
Entropy is a central concept in physics, but can be challenging to calculate even for systems that are easily simulated. This is exacerbated out of equilibrium, where generally little is known about the distribution characterizing simulated…
When an informationally complete measurement is not available, the reconstruction of the density operator that describes the state of a quantum system can be accomplish, in a reliable way, by adopting the maximum entropy principle (MaxEnt…
A problem of statistical estimation of a Hermitian nonnegatively definite matrix of unit trace (for instance, a density matrix in quantum state tomography) is studied. The approach is based on penalized least squares method with a…