Related papers: Time-Efficient Quantum Entropy Estimator via Sampl…
For a given quantum state $\rho$ and two quantum operations $\Phi$ and $\Psi$, the information encoded in the quantum state $\rho$ is quantified by its von Neumann entropy $\S(\rho)$. By the famous Choi-Jamio{\l}kowski isomorphism, the…
We introduce the problem of \emph{entropy equivalence testing} for probability distributions, a relaxation of the well-studied closeness testing problem, where the distribution testing algorithm is now only required to distinguish, given…
Block-encodings have become one of the most common oracle assumptions in the circuit model. I present an algorithm that uses von Neumann's measurement procedure to measure a phase, using time evolution on a block-encoded Hamiltonian as a…
After a brief introduction to the concept of entanglement in quantum systems, I apply these ideas to many-body systems and show that the von Neumann entropy is an effective way of characterising the entanglement between the degrees of…
The von Neumann entropy is a key quantity in quantum information theory and, roughly speaking, quantifies the amount of quantum information contained in a state when many identical and independent i.i.d. copies of the state are available,…
Subentropy is an entropy-like quantity that arises in quantum information theory; for example, it provides a tight lower bound on the accessible information for pure state ensembles, dual to the von Neumann entropy upper bound in Holevo's…
This article focuses on the development of scalable and quantum bit-efficient algorithms for computing power functions of random quantum states. Two algorithms, based on Hadamard testing and Gate Set Tomography, are proposed. We provide a…
The Kalman filter and Rauch-Tung-Striebel (RTS) smoother are optimal for state estimation in linear dynamic systems. With nonlinear systems, the challenge consists in how to propagate uncertainty through the state transitions and output…
The weak law of large numbers implies that, under mild assumptions on the source, the Renyi entropy per produced symbol converges (in probability) towards the Shannon entropy rate. This paper quantifies the speed of this convergence for…
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…
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…
Entropy Estimation is an important problem with many applications in cryptography, statistic,machine learning. Although the estimators optimal with respect to the sample complexity have beenrecently developed, there are still some…
The problem of quantum state estimation is crucial in the development of quantum technologies. In particular, the use of symmetric quantum states is useful in many relevant applications. In this work, we analyze the task of reconstructing…
In this Thesis, several results in quantum information theory are collected, most of which use entropy as the main mathematical tool. *While a direct generalization of the Shannon entropy to density matrices, the von Neumann entropy behaves…
Quantum metrology aims to exploit quantum phenomena to overcome classical limitations in the estimation of relevant parameters. We consider a probe undergoing a phase shift $\varphi$ whose generator is randomly sampled according to a…
The major problem in information theoretic analysis of neural responses and other biological data is the reliable estimation of entropy--like quantities from small samples. We apply a recently introduced Bayesian entropy estimator to…
We provide the notion of entropy for a classical Klein-Gordon real wave, that we derive as particular case of a notion entropy for a vector in a Hilbert space with respect to a real linear subspace. We then consider a localised automorphism…
Non-stabilizerness (colloquially "magic") characterizes genuinely quantum (beyond-Clifford) operations necessary for preparation of quantum states, and can be measured by stabilizer R\'enyi entropy (SRE). For permutationally symmetric…
The entropy is one of the most applicable uncertainty measures in many statistical and en- gineering problems. In statistical literature, the entropy is used in calculation of the Kullback- Leibler (KL) information which is a powerful mean…
It is well known that to estimate the Shannon entropy for symbolic sequences accurately requires a large number of samples. When some aspects of the data are known it is plausible to attempt to use this to more efficiently compute entropy.…