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Preparing the ground state of a system is an important task in physics. We propose a quantum algorithm for preparing the ground state of a physical system that can be simulated on a quantum computer. The system is coupled to an ancillary…
We study an entropy measure for quantum systems that generalizes the von Neumann entropy as well as its classical counterpart, the Gibbs or Shannon entropy. The entropy measure is based on hypothesis testing and has an elegant formulation…
Information plays an important role in our understanding of the physical world. We hence propose an entropic measure of information for any physical theory that admits systems, states and measurements. In the quantum and classical world,…
We investigate the universal inequalities relating the alpha-Renyi entropies of the marginals of a multi-partite quantum state. This is in analogy to the same question for the Shannon and von Neumann entropy (alpha=1) which are known to…
A new axiomatic characterization with a minimum of conditions for entropy as a function on the set of states in quantum mechanics is presented. Traditionally unspoken assumptions are unveiled and replaced by proven consequences of the…
Quantum physics, despite its observables being intrinsically of a probabilistic nature, does not have a quantum entropy assigned to them. We propose a quantum entropy that quantify the randomness of a pure quantum state via a conjugate pair…
Entropy is a fundamental property of both classical and quantum systems, spanning myriad theoretical and practical applications in physics and computer science. We study the problem of obtaining estimates to within a multiplicative factor…
It is shown that, despite strong nonlinearity, entanglement of formation of two-qubit state can be measured without prior state reconstruction. Collective measurements on small number of copies are provided that allow to determine quantum…
The quantum relative entropy is a fundamental quantity in quantum information science, characterizing the distinguishability between two quantum states. However, this quantity is not additive in general for correlated quantum states,…
An initial unknown quantum state can be determined with a single measurement apparatus by letting it interact with an auxiliary, "Ancilla", system as proposed by Allahverdyan, Balian and Nieuwenhuizen [Phys. Rev. Lett. 92, 120402 (2004)].…
We construct a complete set of Wannier functions which are localized at both given positions and momenta. This allows us to introduce the quantum phase space, onto which a quantum pure state can be mapped unitarily. Using its probability…
We develop a nonequilibrium increment method in quantum Monte Carlo simulations to obtain the R\'enyi entanglement entropy of various quantum many-body systems with high efficiency and precision. To demonstrate its power, we show the…
How much information about an unknown quantum state can be obtained by a measurement? We propose a model independent answer: the information obtained is equal to the minimum entropy of the outputs of the measurement, where the minimum is…
Observational entropy is interpreted as the uncertainty an observer making measurements associates with a system. So far, properties that make such an interpretation possible rely on the assumption of ideal projective measurements. We show…
We compute analytically the statistics of the Renyi and von Neumann entropies (standard measures of entanglement), for a random pure state in a large bipartite quantum system. The full probability distribution is computed by first mapping…
A large class of strongly correlated quantum systems can be described in certain large-N limits by quadratic in field actions along with self-consistency equations that determine the two-point functions. We use the replica approach and the…
Understanding the limitations imposed by noise on current and next-generation quantum devices is a crucial step towards demonstrating practical quantum advantage. In this work, we investigate the accumulation of entropy density as a…
Bipartite entanglement entropies, calculated from the reduced density matrix of a subsystem, provide a description of the resources available within a system for performing quantum information processing. However, these quantities are not…
We generalize the concept of the Wehrl entropy of quantum states which gives a basis-independent measure of their localization in phase space. We discuss the minimal values and the typical values of these R{enyi-Wehrl entropies for pure…
Estimating statistical properties is fundamental in statistics and computer science. In this paper, we propose a unified quantum algorithm framework for estimating properties of discrete probability distributions, with estimating R\'enyi…