scholarly journals HOW "HOT" ARE MIXED QUANTUM STATES?

2007 ◽  
Vol 05 (01n02) ◽  
pp. 311-317
Author(s):  
GEORGE PARFIONOV ◽  
ROMÀN R. ZAPATRIN
Keyword(s):  
Mixed State ◽  
Density Operator ◽  
Gibbs Distribution ◽  
The State ◽  
Quantum States ◽  
Gibbs Ensemble ◽  
Differential Entropy ◽  
Average Value ◽  
Temperature Parameter ◽  
Pure States

Given a mixed quantum state ρ of a qudit, we consider any observable M as a kind of "thermometer" in the following sense. Given a source which emits pure states with certain distributions, we select distributions such that the appropriate average value of the observable M is equal to the average Tr M ρ of M in the state ρ. Among those distributions we find the most typical, namely, having the highest differential entropy. We call this distribution the conditional Gibbs ensemble as it turns out to be a Gibbs distribution characterized by a temperature-like parameter β. The expressions establishing the liaisons between the density operator ρ and its temperature parameter β are provided. Within this approach, the uniform mixed state has the highest "temperature," which tends to zero as the state in question approaches a pure state.

Outgrowth of quasi pure states in isolated coupled-harmonic-oscillator

2021 ◽  
Vol 35 (05) ◽  
pp. 2150075
Author(s):  
Tianhai Zeng ◽  
Zhaobin Liu ◽  
Kai Li ◽  
Feng Wang ◽  
Bin Shao
Keyword(s):  
Harmonic Oscillator ◽  
Reference Frame ◽  
Interaction Potential ◽  
Mixed State ◽  
Pure State ◽  
Center Of Mass ◽  
Quantum States ◽  
Pure States ◽  
Position Representation ◽  
Coupled Harmonic Oscillator

Isolated coupled-harmonic-oscillator here is the system of two distinguishable particles coupled with a harmonic oscillator interaction potential. Each particle stays in a mixed state due to entanglement. However, in center-of-mass reference frame, we obtain quasi wavefunction of the first particle expressing quasi pure state by replacing the second coordinate in the total wavefunction. We discuss the similar systems with the first particle and the potential being same and the second mass changing from micro to macro one. Measured by fidelity and coherence, the quasi pure state approaches to the pure state of a usual harmonic oscillator with same mass and similar potential. It conversely shows that the latter purely superposed state in position representation and its coherence originate from those of the first particle, which are related with some neglected macro object and the interaction between them. The current results provide a possible clue to new insights into quantum states.

scholarly journals Purification and redistribution of entanglement via single local filtering

2014 ◽  
Vol 12 (01) ◽  
pp. 1450004 ◽  
Author(s):  
K. O. Yashodamma ◽  
P. J. Geetha ◽  
Sudha
Keyword(s):  
Quantum State ◽  
The State ◽  
Quantum States ◽  
Local Action ◽  
Entanglement Transfer ◽  
Local Filtering

The effect of filtering operation with respect to purification and concentration of entanglement in quantum states are discussed in this paper. It is shown, through examples, that the local action of the filtering operator on a part of the composite quantum state allows for purification of the remaining part of the state. The redistribution of entanglement in the subsystems of a noise affected state is shown to be due to the action of local filtering on the non-decohering part of the system. The varying effects of the filtering parameter, on the entanglement transfer between the subsystems, depending on the choice of the initial quantum state is illustrated.

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.

Quantum Error Correction

2020 ◽  
Author(s):  
Todd A. Brun
Keyword(s):  
Error Correction ◽  
Quantum Computation ◽  
Single Photon ◽  
Error Correcting Code ◽  
Quantum Systems ◽  
Quantum Error Correction ◽  
The State ◽  
Quantum States ◽  
Quantum Code ◽  
Quantum Error

Quantum error correction is a set of methods to protect quantum information—that is, quantum states—from unwanted environmental interactions (decoherence) and other forms of noise. The information is stored in a quantum error-correcting code, which is a subspace in a larger Hilbert space. This code is designed so that the most common errors move the state into an error space orthogonal to the original code space while preserving the information in the state. It is possible to determine whether an error has occurred by a suitable measurement and to apply a unitary correction that returns the state to the code space without measuring (and hence disturbing) the protected state itself. In general, codewords of a quantum code are entangled states. No code that stores information can protect against all possible errors; instead, codes are designed to correct a specific error set, which should be chosen to match the most likely types of noise. An error set is represented by a set of operators that can multiply the codeword state. Most work on quantum error correction has focused on systems of quantum bits, or qubits, which are two-level quantum systems. These can be physically realized by the states of a spin-1/2 particle, the polarization of a single photon, two distinguished levels of a trapped atom or ion, the current states of a microscopic superconducting loop, or many other physical systems. The most widely used codes are the stabilizer codes, which are closely related to classical linear codes. The code space is the joint +1 eigenspace of a set of commuting Pauli operators on n qubits, called stabilizer generators; the error syndrome is determined by measuring these operators, which allows errors to be diagnosed and corrected. A stabilizer code is characterized by three parameters [[n,k,d]], where n is the number of physical qubits, k is the number of encoded logical qubits, and d is the minimum distance of the code (the smallest number of simultaneous qubit errors that can transform one valid codeword into another). Every useful code has n>k; this physical redundancy is necessary to detect and correct errors without disturbing the logical state. Quantum error correction is used to protect information in quantum communication (where quantum states pass through noisy channels) and quantum computation (where quantum states are transformed through a sequence of imperfect computational steps in the presence of environmental decoherence to solve a computational problem). In quantum computation, error correction is just one component of fault-tolerant design. Other approaches to error mitigation in quantum systems include decoherence-free subspaces, noiseless subsystems, and dynamical decoupling.

scholarly journals Analysis of the cannabinoid content of strains available in the New Jersey Medicinal Marijuana Program

2019 ◽  
Vol 1 (1) ◽  
Author(s):  
Thomas A. Coogan
Keyword(s):  
New Jersey ◽  
Relative Concentration ◽  
The State ◽  
High Concentration ◽  
Dominant Type ◽  
Average Value ◽  
Department Of Health ◽  
Different Strains ◽  
Single Laboratory

Abstract Background The six licensed operators in the New Jersey Medicinal Marijuana Program submit their strains of cannabis flower to a single laboratory, administered by the state’s Department of Health, for testing. The results of these tests are made available by the State on a web page for patients, allowing a study of the range of cannabinoid profiles available in the program. Methods Reports on cannabinoid concentrations were collected from 245 test reports released by the State lab; the relative quantities of cannabinoids on all strains was evaluated, as well as trends in the strain types being tested. Results The collection of strain profiles available in New Jersey conforms to results of other population studies, revealing three broad classification of strains based on their relative concentration of cannabinoids: the overwhelmingly majority of strains contain only trace (< 1%) CBDA but high THCA concentration; a handful are balanced in CBDA and THCA content; and a very few strains have a high concentration of CBDA and minimal THCA (< 1%). In those strains that contain more than 1% of both THCA and CBDA, those two substances are present in comparable quantities. The concentration of CBGA is higher in those strains that have the highest THCA concentration, though there are strains that have high THCA (> 20%) with CBGA concentrations at the low end of the range (< 0.5%). In the high CBD strains, the concentration of CBGA is positively correlated with CBDA, but the CBGA concentrations are several fold less in CBD-dominant strains than in THC-dominant strains: the highest measured CBGA concentration in a CBD-dominant strain is only at the average value of CBGA concentration in THC-dominant strains. The most-recently tested strains are overwhelmingly of the THC-dominant type. Conclusions Though some high CBD strains are available in the New Jersey medical marijuana program, the vast majority of strains that have been tested are the THC-dominant strains which contain less than 1% CBDA. The data available from the State does not include any information on how well the different strains sell, but it can be inferred from the trend in strain types tested that the demand in the New Jersey medical market is for THC-dominant strains.

scholarly journals COMPARISON BETWEEN THE DOUBLE BUFFER METHOD AND THE EQUIVALENT RECTANGLE METHOD FOR THE QUANTIFICATION OF DISCREPANCIES BETWEEN LINEAR FEATURES

2018 ◽  
Vol 24 (3) ◽  
pp. 300-317 ◽  
Author(s):  
Leandro Luiz Silva de França ◽  
Luiz Felipe Coutinho Ferreira da Silva
Keyword(s):  
The State ◽  
Vector Data ◽  
Positional Accuracy ◽  
Linear Features ◽  
Average Value ◽  
Second Stage ◽  
Traditional Procedure ◽  
Method R

Abstract Currently, in Brazil, for the assessment of the Positional Accuracy of non-point features (lines and polygons), there is no standard norm of execution. This work aims to compare the results of two methodologies that allow determining the average value of the discrepancies between linear features. The first, Equivalent Rectangle Method, aims to determine the discrepancy by considering an equivalent rectangle for the polygon obtained from the two homologous lines. The second, Double Buffer Method applies a buffer on both lines and obtains the average discrepancy value based on the relation of the areas of the generated polygons. These methods were compared in two steps. Initially, an experiment was performed with features of known measurements, where the displacement of the homologous lines was controlled in azimuth and distance. In this step, it was verified that the shape of the feature and the direction of the displacement interfere in the results of both methods when compared to the traditional procedure of measurement of discrepancies by homologous points. In the second stage, we evaluated the vector data of the OpenStreetMap (class of roads), with reference to a more accurate vector dataset produced for the Mapping of the State of Bahia. As a result, for the 1:25,000, 1:50,000, 1:100,000 and 1:250,000 scales, it was obtained, respectively, the PEC-PCD for the Equivalent Rectangle Method "C", "B", "A" and "A" and the PEC-PCD for the Double Buffer Method "R", "C", "B" and "A", where "R" means that it has not achieved the minimum PEC-PCD classification.

scholarly journals CUMULATIVE MEASURE OF CORRELATION FOR MULTIPARTITE QUANTUM STATES

2014 ◽  
Vol 28 (07) ◽  
pp. 1450050 ◽  
Author(s):  
ANDRÉ L. FONSECA DE OLIVEIRA ◽  
EFRAIN BUKSMAN ◽  
JESÚS GARCÍA LÓPEZ DE LACALLE
Keyword(s):  
Phase Transitions ◽  
State Space ◽  
Present Article ◽  
Critical Points ◽  
Quantum Phase Transitions ◽  
The State ◽  
Quantum States ◽  
Quantum Phase ◽  
Mixed States ◽  
Different Dimensions

The present article proposes a measure of correlation for multiqubit mixed states. The measure is defined recursively, accumulating the correlation of the subspaces, making it simple to calculate without the use of regression. Unlike usual measures, the proposed measure is continuous additive and reflects the dimensionality of the state space, allowing to compare states with different dimensions. Examples show that the measure can signal critical points (CPs) in the analysis of Quantum Phase Transitions (QPTs) in Heisenberg models.

scholarly journals Entanglement, Purity, and Information Entropies in Continuous Variable Systems

2005 ◽  
Vol 12 (02) ◽  
pp. 189-205 ◽  
Author(s):  
Gerardo Adesso ◽  
Alessio Serafini ◽  
Fabrizio Illuminati
Keyword(s):  
Tomographic Reconstruction ◽  
Continuous Variable ◽  
The State ◽  
Upper And Lower Bounds ◽  
Mixed States ◽  
Gaussian States ◽  
Pure States ◽  
Classical Correlations ◽  
Quantum And Classical Correlations

Quantum entanglement of pure states of a bipartite system is defined as the amount of local or marginal (i.e. referring to the subsystems) entropy. For mixed states this identification vanishes, since the global loss of information about the state makes it impossible to distinguish between quantum and classical correlations. Here we show how the joint knowledge of the global and marginal degrees of information of a quantum state, quantified by the purities or, in general, by information entropies, provides an accurate characterization of its entanglement. In particular, for Gaussian states of continuous variable systems, we classify the entanglement of two-mode states according to their degree of total and partial mixedness, comparing the different roles played by the purity and the generalized p-entropies in quantifying the mixedness and bounding the entanglement. We prove the existence of strict upper and lower bounds on the entanglement and the existence of extremally (maximally and minimally) entangled states at fixed global and marginal degrees of information. This results allow for a powerful, operative method to measure mixed-state entanglement without the full tomographic reconstruction of the state. Finally, we briefly discuss the ongoing extension of our analysis to the quantification of multipartite entanglement in highly symmetric Gaussian states of arbitrary 1 × N-mode partitions.

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