Related papers: Quantum algorithm for estimating Renyi entropies o…
Relative entropy is a measure of distinguishability for quantum states, and plays a central role in quantum information theory. The family of Renyi entropies generalizes to Renyi relative entropies that include as special cases most entropy…
We present a quantum algorithm to compute the entanglement spectrum of arbitrary quantum states. The interesting universal part of the entanglement spectrum is typically contained in the largest eigenvalues of the density matrix which can…
Characterizing complexity and criticality in quantum systems requires diagnostics that are both computationally tractable and physically insightful. We apply a measure of quantum state complexity for n-qubit systems, defined as the…
In this paper we propose a method to estimate the density matrix \rho of a d-level quantum system by measurements on the N-fold system. The scheme is based on covariant observables and representation theory of unitary groups and it extends…
The quantum Renyi relative entropies play a prominent role in quantum information theory, finding applications in characterizing error exponents and strong converse exponents for quantum hypothesis testing and quantum communication theory.…
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…
Quantum Renyi relative entropies provide a one-parameter family of distances between density matrices, which generalizes the relative entropy and the fidelity. We study these measures for renormalization group flows in quantum field theory.…
Entropy is a fundamental concept in equilibrium statistical mechanics, yet its origin in the non-equilibrium dynamics of isolated quantum systems is not fully understood. A strong consensus is emerging around the idea that the stationary…
We present a technique for enhancing the estimation of quantum state properties by incorporating approximate prior knowledge about the quantum state of interest. This method involves performing randomized measurements on a quantum processor…
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) =…
We implement a Wang-Landau sampling technique in quantum Monte Carlo (QMC) for the purpose of calculating the Renyi entanglement entropies and associated mutual information. The algorithm converges an estimate for an analogue to the density…
We present a detailed account of quantum state estimation by joint maximization of the likelihood and the entropy. After establishing the algorithms for both perfect and imperfect measurements, we apply the procedure to data from simulated…
We calculate the quantum Renyi entropy in a phase space representation for either fermions or bosons. This can also be used to calculate purity and fidelity, or the entanglement between two systems. We show that it is possible to calculate…
We describe a numerical algorithm for approximating the equilibrium-reduced density matrix and the effective (mean force) Hamiltonian for a set of system spins coupled strongly to a set of bath spins when the total system (system+bath) is…
Estimating nonlinear properties such as R\'enyi entropies and observable-weighted moments serves as a central strategy for spectrum spectroscopy, which is fundamental to property prediction and analysis in quantum information science,…
The Renyi entropies constitute a family of information measures that generalizes the well-known Shannon entropy, inheriting many of its properties. They appear in the form of unconditional and conditional entropies, relative entropies or…
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…
We present a scheme for measuring R\'enyi entropies in generic atomic Hubbard and spin models using single copies of a quantum state and for partitions in arbitrary spatial dimension. Our approach is based on the generation of random…
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…
We describe algorithms to obtain an approximate classical description of a $d$-dimensional quantum state when given access to a unitary (and its inverse) that prepares it. For pure states we characterize the query complexity for…