Related papers: Quantum algorithm for estimating Renyi entropies o…
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…
The estimation of the density matrix of a $k$-level quantum system is studied when the parametrization is given by the real and imaginary part of the entries and they are estimated by independent measurements. It is established that the…
We develop a universal approximation for the Renyi entropies of a pure state at late times in a non-integrable many-body system, which macroscopically resembles an equilibrium density matrix. The resulting expressions are fully determined…
New algorithm for quantum state estimation based on the maximum likelihood estimation is proposed. Existing techniques for state reconstruction based on the inversion of measured data are shown to be overestimated since they do not…
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…
We extend algorithmic information theory to quantum mechanics, taking a universal semicomputable density matrix (``universal probability'') as a starting point, and define complexity (an operator) as its negative logarithm. A number of…
The measured relative entropy and measured R\'enyi relative entropy are quantifiers of the distinguishability of two quantum states $\rho$ and $\sigma$. They are defined as the maximum classical relative entropy or R\'enyi relative entropy…
Density estimation is a central task in statistics and machine learning. This problem aims to determine the underlying probability density function that best aligns with an observed data set. Some of its applications include statistical…
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,…
We study the problem of computing energy density in one-dimensional quantum systems. We show that the ground-state energy per site or per bond can be computed in time (i) independent of the system size and subexponential in the desired…
It was recently shown that estimating the Shannon entropy $H({\rm p})$ of a discrete $k$-symbol distribution ${\rm p}$ requires $\Theta(k/\log k)$ samples, a number that grows near-linearly in the support size. In many applications $H({\rm…
The development of quantum computation has resulted in many quantum algorithms for a wide array of tasks. Recently, there is a growing interest in using quantum computing techniques to estimate or compute quantum information-theoretic…
In this work, we study the Renyi-alpha entropies S_{alpha}(\hat{rho}) = (1 - alpha)^{-1} \ln{Tr(\hat{rho}^{alpha})} of quantum states for N bosons in the phase-space representation. With the help of the Bopp rule, we derive the entropies of…
When working with quantum states, analysis of the final quantum state generated through probabilistic measurements is essential. This analysis is typically conducted by constructing the density matrix from either partial or full tomography…
We propose an iterative algorithm for incomplete quantum process tomography, with the help of quantum state estimation, based on the combined principles of maximum-likelihood and maximum-entropy. The algorithm yields a unique estimator for…
We propose a new field theoretic method for calculating Renyi entropy of a sub-system of many interacting Bosons without using replica methods. This method is applicable to dynamics of both open and closed quantum systems starting from…
Non-linear properties of quantum states, such as entropy or entanglement, quantify important physical resources and are frequently used in quantum information science. They are usually calculated from a full description of a quantum state,…
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…
The density matrix is a positive semidefinite operator of trace 1 characterizing the state of a quantum system. We consider the inverse problem to reconstruct such density matrices from indirect measurements, also known as quantum state…
We define and investigate a notion of entropy for quantum error correcting codes. The entropy of a code for a given quantum channel has a number of equivalent realisations, such as through the coefficients associated with the Knill-Laflamme…