scholarly journals On the Separability of Unitarily Invariant Random Quantum States: The Unbalanced Regime

2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
Ion Nechita
Keyword(s):  
Probability Distribution ◽  
Spectral Distribution ◽  
Quantum States ◽  
The Other ◽  
Unitary Operators ◽  
Matrix Size ◽  
Limiting Spectral Distribution ◽  
Large Matrix ◽  
Random Quantum States ◽  
Invariant Quantum

We study entanglement-related properties of random quantum states which are unitarily invariant, in the sense that their distribution is left unchanged by conjugation with arbitrary unitary operators. In the large matrix size limit, the distribution of these random quantum states is characterized by their limiting spectrum, a compactly supported probability distribution. We prove several results characterizing entanglement and the PPT property of random bipartite unitarily invariant quantum states in terms of the limiting spectral distribution, in the unbalanced asymptotical regime where one of the two subsystems is fixed, while the other one grows in size.

NO EIGENVALUES OUTSIDE THE SUPPORT OF THE LIMITING SPECTRAL DISTRIBUTION OF INFORMATION-PLUS-NOISE TYPE MATRICES

2012 ◽  
Vol 01 (01) ◽  
pp. 1150004 ◽  
Author(s):  
ZHIDONG BAI ◽  
JACK W. SILVERSTEIN
Keyword(s):  
Probability Distribution ◽  
Spectral Distribution ◽  
Correlation Matrix ◽  
Closed Interval ◽  
Empirical Distribution ◽  
Limiting Distribution ◽  
Limiting Spectral Distribution ◽  
Noise Type ◽  
Sample Correlation ◽  
Class Of Matrices

We consider a class of matrices of the form Cn = (1/N)(Rn + σXn)(Rn + σXn)*, where Xn is an n × N matrix consisting of independent standardized complex entries, Rn is an n × N nonrandom matrix, and σ > 0. Among several applications, Cn can be viewed as a sample correlation matrix, where information is contained in [Formula: see text], but each column of Rn is contaminated by noise. As n → ∞, if n/N → c > 0, and the empirical distribution of the eigenvalues of [Formula: see text] converge to a proper probability distribution, then the empirical distribution of the eigenvalues of Cn converges a.s. to a nonrandom limit. In this paper we show that, under certain conditions on Rn, for any closed interval in ℝ+ outside the support of the limiting distribution, then, almost surely, no eigenvalues of Cn will appear in this interval for all n large.

High-Resolution Neutron Spectroscopy for the Investigation of Hydrogen Diffusion and Molecular Rotations in Solids

1993 ◽  
Vol 48 (1-2) ◽  
pp. 406-414
Author(s):  
T. Springer
Keyword(s):  
High Resolution ◽  
Hydrogen Diffusion ◽  
Quantum Effects ◽  
Quantum States ◽  
The Other ◽  
Neutron Spectroscopy ◽  
Impurity Atoms ◽  
Molecular Rotations ◽  
Rotational Motions ◽  
Diffusion Of Hydrogen

Abstract An introductory survey on applications of high-resolution neutron spectroscopy is presented, dealing with the motion of hydrogen in solids, namely concerning (i) random rotational motions or stationary tunneling states of NH+4-ions or CH3-groups, and (ii) diffusion of hydrogen in alloys. For the rotation of hydrogenous groups in solids, at higher temperatures rotational jumps can be found, whereas quantum states are observed by μeV-spectroscopy at temperatures below 50 K. On the other hand, hydrogen diffusion does not reveal pronounced evidence of quantum effects, except for hydrogen in a metal containing impurity atoms.

scholarly journals Multi-Bloch vector representation of the qutrit

2011 ◽  
Vol 11 (5&6) ◽  
pp. 361-373
Author(s):  
Pawel Kurzynski
Keyword(s):  
Quantum State ◽  
Quantum Systems ◽  
Quantum States ◽  
The Other ◽  
Two Dimensional ◽  
Bloch Vector ◽  
Vector Representation ◽  
Alternative Approach ◽  
Complete Set

An ability to describe quantum states directly by average values of measurement outcomes is provided by the Bloch vector. For an informationally complete set of measurements one can construct unique Bloch vector for any quantum state. However, not every Bloch vector corresponds to a quantum state. It seems that only for two-dimensional quantum systems it is easy to distinguish proper Bloch vectors from improper ones, i.e. the ones corresponding to quantum states from the other ones. I propose an alternative approach to the problem in which more than one vector is used. In particular, I show that a state of the qutrit can be described by the three qubit-like Bloch vectors.

scholarly journals Quantum Physical Unclonable Functions: Possibilities and Impossibilities

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 475
Author(s):  
Myrto Arapinis ◽  
Mahshid Delavar ◽  
Mina Doosti ◽  
Elham Kashefi
Keyword(s):  
Large Family ◽  
Quantum States ◽  
The Other ◽  
Quantum Game ◽  
Physical Unclonable Function ◽  
Physical Unclonable Functions ◽  
Quantum Analogue ◽  
Universal Quantum ◽  
Different Levels ◽  
Comprehensive Study

A Physical Unclonable Function (PUF) is a device with unique behaviour that is hard to clone hence providing a secure fingerprint. A variety of PUF structures and PUF-based applications have been explored theoretically as well as being implemented in practical settings. Recently, the inherent unclonability of quantum states has been exploited to derive the quantum analogue of PUF as well as new proposals for the implementation of PUF. We present the first comprehensive study of quantum Physical Unclonable Functions (qPUFs) with quantum cryptographic tools. We formally define qPUFs, encapsulating all requirements of classical PUFs as well as introducing a new testability feature inherent to the quantum setting only. We use a quantum game-based framework to define different levels of security for qPUFs: quantum exponential unforgeability, quantum existential unforgeability and quantum selective unforgeability. We introduce a new quantum attack technique based on the universal quantum emulator algorithm of Marvin and Lloyd to prove no qPUF can provide quantum existential unforgeability. On the other hand, we prove that a large family of qPUFs (called unitary PUFs) can provide quantum selective unforgeability which is the desired level of security for most PUF-based applications.

Symmetry vs. Duality in Logic

2014 ◽  
Vol 8 (4) ◽  
pp. 83-97 ◽  
Author(s):  
Giulia Battilotti
Keyword(s):  
Sequent Calculus ◽  
Logical Consequence ◽  
Quantum States ◽  
The Other ◽  
Human Reasoning ◽  
Symmetric Mode ◽  
The Unconscious ◽  
Structural Rules ◽  
Model Based ◽  
Long Time

The author discusses the problem of symmetry, namely of the orientation of the logical consequence. The author shows that the problem is surprisingly entangled with the problem of “being infinite”. The author presents a model based on quantum states and shows that it features satisfy the requirements of the symmetric mode of Bi-logic, a logic introduced in the '70s by the psychoanalyst I. Matte Blanco to describe the logic of the unconscious. The author discusess symmetry, in the model, to include correlations, in order to obtain a possible approach to displacement. In this setting, the author finds a possible reading of the structural rules of sequent calculus, whose role in computation, on one side, and in the representation of human reasoning, on the other, has been debated for a long time.

scholarly journals Brown measure and asymptotic freeness of elliptic and related matrices

2019 ◽  
Vol 08 (02) ◽  
pp. 1950007
Author(s):  
Kartick Adhikari ◽  
Arup Bose
Keyword(s):  
Spectral Distribution ◽  
Limiting Spectral Distribution

We show that independent elliptic matrices converge to freely independent elliptic elements. Moreover, the elliptic matrices are asymptotically free with deterministic matrices under appropriate conditions. We compute the Brown measure of the product of elliptic elements. It turns out that this Brown measure is same as the limiting spectral distribution.

scholarly journals The Evolutionary Status of the Secondaries of Cataclysmic Binaries

1983 ◽  
Vol 72 ◽  
pp. 257-262
Author(s):  
H. Ritter
Keyword(s):  
Probability Distribution ◽  
Main Sequence ◽  
The Other ◽  
Initial Mass ◽  
Evolutionary Status ◽  
Mass Ratio ◽  
Main Sequence Stars ◽  
Cataclysmic Binaries ◽  
Low Mass ◽  
Orbital Periods

ABSTRACTIt is shown that the secondary components of cataclysmic binaries with orbital periods of less than ~10 hours are indistinguishable from ordinary low-mass main-sequence stars and that, therefore, they are essentially unevolved. On the other hand, it is shown that, depending on the mass ratio of the progenitor system, the secondary of a cataclysmic binary could be significantly evolved. The fact that nevertheless most of the observed secondaries are essentially unevolved can be accounted for by assuming that the probability distribution for the initial mass ratio is not strongly peaked towards unity mass ratio.

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