# Quantifying entanglement of two relativistic particles using optimal entanglement witness

Quantifying entanglement of two relativistic particles using optimal entanglement witness In a recent paper, it was shown that the projections of a relativistic spin operator (RSO) massive spin- $${\frac{1}{2}}$$ particle on a world-vector which can be in timelike or null tetrad direction are proportional to the helicity or Bargman-Wigner (BW) qubit, respectively. Here we consider Lorentz transformations of two-particle states, which have been constructed both in helicity basis. For convenience, instead of using the superposition of momenta we use only two momentum eigenstates (p 1 and p 2) for each particle. Consequently, in 2D momentum subspace we describe the structure of one particle in terms of the four-qubit system. We present a new approach to quantification of relativistic entanglement based on entanglement witness (EW), which is obtained by a new method of convex optimization. In addition, Lorentz invariance of entanglement using BW qubit is also studied. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

# Quantifying entanglement of two relativistic particles using optimal entanglement witness

, Volume 10 (4) – Nov 24, 2010
18 pages

/lp/springer_journal/quantifying-entanglement-of-two-relativistic-particles-using-optimal-7ospZjXtyt
Publisher
Springer US
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-010-0206-x
Publisher site
See Article on Publisher Site

### Abstract

In a recent paper, it was shown that the projections of a relativistic spin operator (RSO) massive spin- $${\frac{1}{2}}$$ particle on a world-vector which can be in timelike or null tetrad direction are proportional to the helicity or Bargman-Wigner (BW) qubit, respectively. Here we consider Lorentz transformations of two-particle states, which have been constructed both in helicity basis. For convenience, instead of using the superposition of momenta we use only two momentum eigenstates (p 1 and p 2) for each particle. Consequently, in 2D momentum subspace we describe the structure of one particle in terms of the four-qubit system. We present a new approach to quantification of relativistic entanglement based on entanglement witness (EW), which is obtained by a new method of convex optimization. In addition, Lorentz invariance of entanglement using BW qubit is also studied.

### Journal

Quantum Information ProcessingSpringer Journals

Published: Nov 24, 2010

### References

• Can quantum-mechanical description of physical reality be considered complete?
Einstein, A.; Podolsky, B.; Rosen, N.
• Bell inequalities and the separability criterion
Terhal, B.M.

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