Fisher Information and Quantum Squeezing Properties of Gaussian Pure States

2012 ◽  
Vol 571 ◽  
pp. 283-286
Author(s):  
Jia Qiang Zhao ◽  
Lian Zhen Cao ◽  
Huai Xin Lu
Keyword(s):  
Fisher Information ◽  
Quantum States ◽  
Pure States ◽  
Definition Of ◽  
Fisher Length

In this paper the Fisher information of Gaussian pure States is studied. Based on the definition of joint non-classical properties, we calculate the non-classical properties of Gaussian pure States. The results show that the Fisher information and Fisher length are efficacious tools to study the non-classical properties of quantum States.

scholarly journals Generalized Wavelet Fisher’s Information of1/fαSignals

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Julio Ramírez-Pacheco ◽  
Homero Toral-Cruz ◽  
Luis Rizo-Domínguez ◽  
Joaquin Cortez-Gonzalez
Keyword(s):  
Fisher Information ◽  
Gaussian Noise ◽  
Structural Breaks ◽  
Wavelet Domain ◽  
Fractional Gaussian Noise ◽  
Domain Definition ◽  
Potential Applications ◽  
Definition Of ◽  
The Time Domain ◽  
Fisher's Information

This paper defines the generalized wavelet Fisher information of parameterq. This information measure is obtained by generalizing the time-domain definition of Fisher’s information of Furuichi to the wavelet domain and allows to quantify smoothness and correlation, among other signals characteristics. Closed-form expressions of generalized wavelet Fisher information for1/fαsignals are determined and a detailed discussion of their properties, characteristics and their relationship with waveletq-Fisher information are given. Information planes of1/fsignals Fisher information are obtained and, based on these, potential applications are highlighted. Finally, generalized wavelet Fisher information is applied to the problem of detecting and locating weak structural breaks in stationary1/fsignals, particularly for fractional Gaussian noise series. It is shown that by using a joint Fisher/F-Statistic procedure, significant improvements in time and accuracy are achieved in comparison with the sole application of theF-statistic.

scholarly journals Clustering and enhanced classification using a hybrid quantum autoencoder

2021 ◽  
Author(s):  
Maiyuren Srikumar ◽  
Charles Daniel Hill ◽  
Lloyd Hollenberg
Keyword(s):  
Machine Learning ◽  
Supervised Classification ◽  
Quantum Information Theory ◽  
Quantum States ◽  
Data Sets ◽  
New Paradigm ◽  
Novel Approach ◽  
Representational Space ◽  
Quantum Machine Learning ◽  
Pure States

Abstract Quantum machine learning (QML) is a rapidly growing area of research at the intersection of classical machine learning and quantum information theory. One area of considerable interest is the use of QML to learn information contained within quantum states themselves. In this work, we propose a novel approach in which the extraction of information from quantum states is undertaken in a classical representational-space, obtained through the training of a hybrid quantum autoencoder (HQA). Hence, given a set of pure states, this variational QML algorithm learns to identify – and classically represent – their essential distinguishing characteristics, subsequently giving rise to a new paradigm for clustering and semi-supervised classification. The analysis and employment of the HQA model are presented in the context of amplitude encoded states – which in principle can be extended to arbitrary states for the analysis of structure in non-trivial quantum data sets.

scholarly journals Pure States of Maximum Uncertainty with Respect to a Given POVM

2020 ◽  
Vol 27 (01) ◽  
pp. 2050002
Author(s):  
Anna Szymusiak
Keyword(s):  
Shannon Entropy ◽  
Pure State ◽  
Quantum States ◽  
Maximal Amount ◽  
Dimension 2 ◽  
Pure States

One of the differences between classical and quantum world is that in the former we can always perform a measurement that gives certain outcomes for all pure states, while such a situation is not possible in the latter one. The degree of randomness of the distribution of the measurement outcomes can be quantified by the Shannon entropy. While it is well known that this entropy, as a function of quantum states, needs to be minimized by some pure states, we would like to address the question how ‘badly’ can we end by choosing initially any pure state, i.e., which pure states produce the maximal amount of uncertainty under given measurement. We find these maximizers for all highly symmetric POVMs in dimension 2, and for all SIC-POVMs in any dimension.

scholarly journals Average of Uncertainty Product for Bounded Observables

2018 ◽  
Vol 25 (02) ◽  
pp. 1850008 ◽  
Author(s):  
Lin Zhang ◽  
Jiamei Wang
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Quantum States ◽  
Density Matrices ◽  
Finite Dimensional ◽  
Uncertainty Product ◽  
Schmidt Norm ◽  
Rank One ◽  
Pure States ◽  
Average Uncertainty

The goal of this paper is to calculate exactly the average of uncertainty product of two bounded observables and to establish its typicality over the whole set of finite dimensional quantum pure states. Here we use the uniform ensembles of pure and isospectral states as well as the states distributed uniformly according to the measure induced by the Hilbert-Schmidt norm. Firstly, we investigate the average uncertainty of an observable over isospectral density matrices. By letting the isospectral density matrices be of rank-one, we get the average uncertainty of an observable restricted to pure quantum states. These results can help us check how large is the gap between the uncertainty product and any lower bounds obtained for the uncertainty product. Although our method in the present paper cannot give a tighter lower bound of uncertainty product for bounded observables, it can help us drop any one that is not substantially tighter than the known one.

scholarly journals Schrödinger-like quantum dynamics in loop quantized black holes

2016 ◽  
Vol 25 (08) ◽  
pp. 1642006 ◽  
Author(s):  
Rodolfo Gambini ◽  
Javier Olmedo ◽  
Jorge Pullin
Keyword(s):  
Black Holes ◽  
Quantum Theory ◽  
Quantum Dynamics ◽  
Local Information ◽  
Quantum States ◽  
Spherically Symmetric ◽  
Definition Of ◽  
Symmetric Spacetime ◽  
Spherically Symmetric Spacetime

We show, following a previous quantization of a vacuum spherically symmetric spacetime carried out in [R. Gambini, J. Olmedo and J. Pullin, Class. Quantum Grav. 31 (2014) 095009.] that this setting admits a Schrödinger-like picture. More precisely, the technique adopted there for the definition of parametrized Dirac observables (that codify local information of the quantum theory) can be extended in order to accommodate different pictures. In this new picture, the quantum states are parametrized in terms of suitable gauge parameters and the observables constructed out of the kinematical ones on this space of parametrized states.

Distribution of x ⋅ p for quantum states on a circle

2015 ◽  
Vol 12 (07) ◽  
pp. 1550078
Author(s):  
Q. H. Liu ◽  
L. Qin ◽  
X. L. Huang ◽  
D. Y. Zhang ◽  
D. M. Xun
Keyword(s):  
Flat Space ◽  
Quantum States ◽  
Free Motion ◽  
Two Dimensional ◽  
Proper Definition ◽  
Dot Product ◽  
Definition Of

We first give the proper definition of the particle's position-momentum dot product, the so-called posmomx ⋅ p, to quantum states on a circular circle, in which the momentum turns out to be the geometric one that is recently intensively studied. Second, we carry out the posmom distributions for eigenstates of the free motion on the circle, i.e. [Formula: see text], (m = 0, ±1, ±2, …). The results are not only potentially experimentally testable, but also reflect a fact that the embedding of the circle S1 in two-dimensional flat space R2 is physically reasonable.

Fisher information of accelerated two-qubit systems

2018 ◽  
Vol 32 (05) ◽  
pp. 1850050 ◽  
Author(s):  
N. Metwally
Keyword(s):  
Analytical Solution ◽  
Fisher Information ◽  
General State ◽  
Initial State ◽  
Werner State ◽  
Pure States ◽  
X State ◽  
Different Parts ◽  
Degree Of Entanglement

In this paper, Fisher information for an accelerated system initially prepared in the X-state is discussed. An analytical solution, which consists of three parts: classical, the average over all pure states and a mixture of pure states, is derived for the general state and for Werner state. It is shown that the Unruh acceleration has a depleting effect on the Fisher information. This depletion depends on the degree of entanglement of the initial state settings. For the X-state, for some intervals of Unruh acceleration, the Fisher information remains constant, irrespective to the Unruh acceleration. In general, the possibility of estimating the state’s parameters decreases as the acceleration increases. However, the precision of estimation can be maximized for certain values of the Unruh acceleration. We also investigate the contribution of the different parts of the Fisher information on the dynamics of the total Fisher information.

scholarly journals Deciding unitary equivalence between matrix polynomials and sets of bipartite quantum states

2011 ◽  
Vol 11 (9&10) ◽  
pp. 813-819
Author(s):  
Eric Chitambar ◽  
Carl Miller ◽  
Yaoyun Shi
Keyword(s):  
Success Probability ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Quantum States ◽  
Unitary Equivalence ◽  
Matrix Polynomials ◽  
Unitary Transformations ◽  
The Matrix ◽  
Pure States ◽  
High Success Probability

In this brief report, we consider the equivalence between two sets of $m+1$ bipartite quantum states under local unitary transformations. For pure states, this problem corresponds to the matrix algebra question of whether two degree $m$ matrix polynomials are unitarily equivalent; i.e. $UA_iV^\dagger=B_i$ for $0\leq i\leq m$ where $U$ and $V$ are unitary and $(A_i, B_i)$ are arbitrary pairs of rectangular matrices. We present a randomized polynomial-time algorithm that solves this problem with an arbitrarily high success probability and outputs transforming matrices $U$ and $V$.

scholarly journals Fisher Concord: Efficiency of Quantum Measurement

2016 ◽  
Vol 3 (1) ◽  
Author(s):  
Nan Li ◽  
Shunlong Luo
Keyword(s):  
Fisher Information ◽  
Fisher Information Matrix ◽  
Symmetric Matrix ◽  
Information Matrix ◽  
Quantum Fisher Information ◽  
Quantum Measurements ◽  
Quantum States ◽  
Information Theoretic ◽  
Information Conservation ◽  
Relative Accessibility

AbstractBy comparing measurement-induced classical Fisher information of parameterized quantum states with quantum Fisher information,we study the notion of Fisher concord (as abbreviation of the concord between the classical and the quantum Fisher information), which is an information-theoretic measure of quantum states and quantum measurements based on both classical and quantum Fisher information. Fisher concord is defined by multiplying the inverse square root of quantum Fisher information matrix to measurement-induced classical Fisher information matrix on both sides, and quantifies the relative accessibility of parameter information from quantum measurements (alternatively, the efficiency of quantum measurements in extracting parameter information). It reduces to the ratio of the classical Fisher information to quantum Fisher information in any single parameter scenario. In general, Fisher concord is a symmetric matrix which depends on both quantum states and quantum measurements. Some basic properties of Fisher concord are elucidated. The significance of Fisher concord in quantifying the interplay between classicality and quantumness in parameter estimation and in characterizing the ef- ficiency of quantum measurements are illustrated through several examples, and some information conservation relations in terms of Fisher concord are exhibited.

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