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 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 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.

AN EFFICIENT SEPARABILITY CRITERION FOR n-PARTITE ARBITRARILY DIMENSIONAL QUANTUM STATES

2011 ◽  
Vol 09 (04) ◽  
pp. 1101-1112
Author(s):  
YINXIANG LONG ◽  
DAOWEN QIU ◽  
DONGYANG LONG
Keyword(s):  
Hilbert Space ◽  
Quantum State ◽  
Pure State ◽  
Coefficient Matrix ◽  
Quantum States ◽  
Mixed States ◽  
Density Matrices ◽  
Separability Criterion ◽  
Dimensional Hilbert Space ◽  
Pure States

In this paper, we obtain an efficient separability criterion for bipartite quantum pure state systems, which is based on the two-order minors of the coefficient matrix corresponding to quantum state. Then, we generalize this criterion to multipartite arbitrarily dimensional pure states. Our criterion is directly built upon coefficient matrices, but not density matrices or observables, so it has the advantage of being computed easily. Indeed, to judge separability for an arbitrary n-partite pure state in a d-dimensional Hilbert space, it only needs at most O(d) times operations of multiplication and comparison. Our criterion can be extended to mixed states. Compared with Yu's criteria, our methods are faster, and can be applied to any quantum state.

SEPARABILITY: A NEW APPROACH FROM THE CONIC STRUCTURE OF POSITIVE OPERATORS

2011 ◽  
Vol 09 (supp01) ◽  
pp. 415-422
Author(s):  
D. SALGADO ◽  
J. L. SÁNCHEZ-GÓMEZ ◽  
M. FERRERO
Keyword(s):  
Pure State ◽  
Convex Combination ◽  
Quantum States ◽  
Necessary Condition ◽  
New Approach ◽  
Product Matrix ◽  
Separability Problem ◽  
Multipartite System ◽  
Arbitrary Dimensions ◽  
Bipartite Case

We exploit the cone structure of unnormalized quantum states to reformulate the separability problem. Firstly a convex combination of every quantum state ρ in terms of a state Cρ with the same rank and another one Eρ with lower rank is perfomed, with weights 1 − λρ and λρ, respectively. Secondly a scalar [Formula: see text] is computed. Then ρ is separable if, and only if, [Formula: see text]. The computation of [Formula: see text] has been undergone under the simplest choice for Cρ as a product matrix and Eρ being a pure state, valid for any bipartite and multipartite system in arbitrary dimensions. A necessary condition is also formulated when Eρ is not pure in the bipartite case.

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.

Probabilistic secret sharing through noise quantum channe

2012 ◽  
Vol 12 (3&4) ◽  
pp. 253-261
Author(s):  
Satyabrata Adhikari ◽  
Indranil Chakrabarty ◽  
Pankaj Agrawal
Keyword(s):  
Quantum Information ◽  
Secret Sharing ◽  
Mixed State ◽  
Pure State ◽  
Noisy Channel ◽  
Noisy Channels ◽  
Superdense Coding ◽  
Classical Information ◽  
Phase Damping ◽  
Realistic Situation

In a realistic situation, the secret sharing of classical or quantum information will involve the transmission of this information through noisy channels. We consider a three qubit pure state. This state becomes a mixed-state when the qubits are distributed over noisy channels. We focus on a specific noisy channel, the phase-damping channel. We propose a protocol for secret sharing of classical information with this and related noisy channels. This protocol can also be thought of as cooperative superdense coding. We also discuss other noisy channels to examine the possibility of secret sharing of classical information.

Decoherence of Driven Coupled Harmonic Oscillator

2016 ◽  
Vol 01 (01) ◽  
Author(s):  
Kenfack Sadem Christian ◽  
Nguimeya GP ◽  
Talla PK ◽  
Fotue AJ ◽  
Fobasso MFC ◽  
...  
Keyword(s):  
Harmonic Oscillator ◽  
Coupled Harmonic Oscillator

Centerofmass Quantum States Motion of Two Ions Drived by Feeble Field

2011 ◽  
Vol 40 (3) ◽  
pp. 453-457
Author(s):  
江敏 JIANG Min ◽  
邬云文 WU Yunwen ◽  
彭俊 PENG Jun ◽  
伊健 YI Jian ◽  
李小娟 LI Xiaojuan
Keyword(s):  
Center Of Mass ◽  
Quantum States
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