scholarly journals SPIN–MOMENTUM CORRELATION IN RELATIVISTIC SINGLE-PARTICLE QUANTUM STATES

2010 ◽  
Vol 08 (03) ◽  
pp. 517-528 ◽  
Author(s):  
M. A. JAFARIZADEH ◽  
M. MAHDIAN
Keyword(s):  
Single Particle ◽  
Inertial Frame ◽  
Quantum States ◽  
Moving Frame ◽  
Lorentz Transformations ◽  
Mixed States ◽  
Wigner Rotation ◽  
Lorentz Boost ◽  
Momentum Correlation ◽  
Spin Momentum

This paper is concerned with the spin–momentum correlation in single-particle quantum states, which is described by the mixed states under Lorentz transformations. For convenience, instead of using the superposition of momenta we use only two momentum eigenstates (p1 and p2) that are perpendicular to the Lorentz boost direction. Consequently, in 2D momentum subspace we show that the entanglement of spin and momentum in the moving frame depends on the angle between them. Therefore, when spin and momentum are perpendicular the measure of entanglement is not an observer-dependent quantity in the inertial frame. Likewise, we have calculated the measure of entanglement (by using the concurrence) and have shown that entanglement decreases with respect to the increase in observer velocity. Finally, we argue that Wigner rotation is induced by Lorentz transformations and can be realized as a controlling operator.

Helicity rotation induced by Lorentz boosts

2019 ◽  
Vol 17 (08) ◽  
pp. 1941005
Author(s):  
Massimo Blasone ◽  
Victor A. S. V. Bittencourt ◽  
Alex E. Bernardini
Keyword(s):  
Dirac Equation ◽  
Quantum Entanglement ◽  
Single Particle ◽  
Inertial Frame ◽  
Rotation Angle ◽  
Positive Energy ◽  
Wigner Rotation ◽  
Lorentz Boost ◽  
The One ◽  
Lorentz Boosts

In this paper, we calculate the helicity rotation angle induced by Lorentz boosts. This is relevant for the study of Lorentz boost effects on quantum entanglement encoded in pairs of massive fermions, which are described in terms of positive energy solutions of the Dirac equation with definite helicity. A Lorentz boost describing the change to an inertial frame moving at uniform speed will in general rotate the particle’s helicity. We obtain the coefficients of the helicity superposition in the boosted frame and specialize our results for a perpendicular boost geometry. We verify that the helicity rotation angle can be obtained in terms of the Wigner rotation angle for spin [Formula: see text] states, bridging the framework considered in our previous works to the one of the Wigner rotations. Finally, we calculate the boost-induced spin-parity entanglement for a single particle.

scholarly journals Comparative Study of the Volume Charge Density in Most General Lorentz Transformation and Quaternion Lorentz Transformation

2019 ◽  
Vol 11 (2) ◽  
pp. 165-171
Author(s):  
A. R. Baizid
Keyword(s):  
Comparative Study ◽  
Charge Density ◽  
Special Relativity ◽  
Lorentz Transformation ◽  
Inertial Frame ◽  
Numerical Data ◽  
Moving Frame ◽  
Lorentz Transformations ◽  
Volume Charge ◽  
Volume Charge Density

Lorentz transformation is the relation of space and time coordinates of one inertial frame relative to another inertial frame in special relativity. In this paper we have studied the volume charge density in most general and quaternion Lorentz transformations for different angles with different velocities of the moving frame.  We have also used numerical data to see the comparative situation.

scholarly journals Wigner Rotations of Different Types of Lorentz Transformations

2016 ◽  
Vol 8 (3) ◽  
pp. 249-258
Author(s):  
A. R. Baizid ◽  
M. S. Alam
Keyword(s):  
Inertial Frame ◽  
Simulated Data ◽  
The Other ◽  
Pion Decay ◽  
Lorentz Transformations ◽  
Arbitrary Direction ◽  
Wigner Rotation ◽  
Geometric Product ◽  
Different Types ◽  
Velocity Addition

We have studied Wigner rotations of different types of Lorenz Transformations according to the nature of movement of one inertial frame relative to the other inertial frame. When the motion is along any arbitrary direction then we can find the formulae for Wigner rotations using the velocity addition formulae for most general, mixed number, quaternion and geometric product Lorentz transformations. Finally we have used simulated data for applying the Wigner rotation formula in pion decay chainand concluded the result.

scholarly journals Entanglement Polytopes: Multiparticle Entanglement from Single-Particle Information

Science ◽  
2013 ◽  
Vol 340 (6137) ◽  
pp. 1205-1208 ◽  
Author(s):  
Michael Walter ◽  
Brent Doran ◽  
David Gross ◽  
Matthias Christandl
Keyword(s):  
Quantum Computing ◽  
Single Particle ◽  
Local Information ◽  
Geometric Object ◽  
Quantum States ◽  
Many Body ◽  
Arbitrary Size ◽  
Global Entanglement ◽  
Low Levels ◽  
Essential Resource

Entangled many-body states are an essential resource for quantum computing and interferometry. Determining the type of entanglement present in a system usually requires access to an exponential number of parameters. We show that in the case of pure, multiparticle quantum states, features of the global entanglement can already be extracted from local information alone. This is achieved by associating any given class of entanglement with an entanglement polytope—a geometric object that characterizes the single-particle states compatible with that class. Our results, applicable to systems of arbitrary size and statistics, give rise to local witnesses for global pure-state entanglement and can be generalized to states affected by low levels of noise.

A note on the degree conjecture for separability of multipartite quantum states

2021 ◽  
pp. 2050048
Author(s):  
Zhen Wang ◽  
Ming-Jing Zhao ◽  
Zhi-Xi Wang
Keyword(s):  
Quantum States ◽  
Point Graph ◽  
Mixed States ◽  
Degree Condition ◽  
Graph Laplacians ◽  
Nearest Point ◽  
Necessary And Sufficient ◽  
Ppt Criterion ◽  
Math Phys ◽  
Degree Criterion

The degree conjecture for bipartite quantum states which are normalized graph Laplacians was first put forward by Braunstein et al. [Phys. Rev. A 73 (2006) 012320]. The degree criterion, which is equivalent to PPT criterion, is simpler and more efficient to detect the separability of quantum states associated with graphs. Hassan et al. settled the degree conjecture for the separability of multipartite quantum states in [J. Math. Phys. 49 (2008) 0121105]. It is proved that the conjecture is true for pure multipartite quantum states. However, the degree condition is only necessary for separability of a class of quantum mixed states. It does not apply to all mixed states. In this paper, we show that the degree conjecture holds for the mixed quantum states of nearest point graph. As a byproduct, the degree criterion is necessary and sufficient for multipartite separability of [Formula: see text]-qubit quantum states associated with graphs.

Thomas–Wigner rotation and Thomas precession in covariant ether theories: novel approach to experimental verification of special relativity

2015 ◽  
Vol 93 (5) ◽  
pp. 503-518 ◽  
Author(s):  
Alexander L. Kholmetskii ◽  
Tolga Yarman
Keyword(s):  
Inertial Frame ◽  
Empty Space ◽  
Special Theory ◽  
Theory Of Relativity ◽  
Thomas Precession ◽  
Wigner Rotation ◽  
Novel Approach ◽  
Inertial Frames ◽  
Crucial Test ◽  
Ether Theories

We continue the analysis of Thomas–Wigner rotation (TWR) and Thomas precession (TP) initiated in (Kholmetskii and Yarman. Can. J. Phys. 92, 1232 (2014). doi:10.1139/cjp-2014-0015 ; Kholmetskii et al. Can. J. Phys. 92, 1380 (2014). doi:10.1139/cjp-2014-0140 ), where a number of points of serious inconsistency have been found in the relativistic explanation of these effects. These findings motivated us to address covariant ether theories (CET), as suggested by the first author (Kholmetskii. Phys. Scr. 67, 381 (2003)) and to show that both TWR and TP find a perfect explanation in CET. We briefly reproduce the main points of CET, which are constructed on the basis of general symmetries of empty space–time, general relativity principles, and classical causality, instead of Einstein’s postulates of the special theory of relativity (STR). We demonstrate that with respect to all known relativistic experiments performed to date in all areas of physics, both theories, STR and CET, yield identical results. We further show that the only effect that differentiates STR and CET is the measurement of time-dependent TWR of two inertial frames, K1 and K2, related by the rotation-free Lorentz transformation with a third inertial frame, K0, in the situation, where the relative velocity between K1 and K2 remains fixed. We discuss the results obtained and suggest a novel experiment, which can be classified as a new crucial test of STR.

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.

MAGNETO-CONTROLLING QUANTUM STATES OF A SINGLE PARTICLE INTERACTING WITH A SQUARE BARRIER

2008 ◽  
Vol 22 (12) ◽  
pp. 1231-1241
Author(s):  
QIONG CHEN ◽  
KUO HAI ◽  
WENHUA HAI
Keyword(s):  
Theoretical Analysis ◽  
Single Particle ◽  
Quantum Wire ◽  
Lower Energy ◽  
Magnetic Trap ◽  
Quantum States ◽  
Series Solutions ◽  
One Dimensional ◽  
Barrier Region ◽  
D Values

We obtain the exact solutions of a single particle magneto-confined in a one-dimensional (1D) quantum wire with a single square barrier. Theoretical analysis and numerical computation show that for a set of fixed barrier height and width, the quantum levels and states of the system depend on the displacement d of the magnetic trap, and for a fixed d value the system occupies only one or two lower quantum levels of n ≤ 20 of a free harmonic oscillator. In the barrier region, the finite-sized effect implies that only for some discrete barrier parameters and d values, the system has the Hermitian polynomial solutions, otherwise it has the infinite series solutions. Therefore, one can manipulate the external motional states of the system and prepare some required lower energy states by adjusting the displacement of the magnetic trap experimentally.

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