dorsal/arxiv
View SchemaWigner rotations, Bell states, and Lorentz invariance of entanglement and von Neumann entropy
| Authors | Chopin Soo, Cyrus C. Y. Lin |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0307107 |
| URL | https://arxiv.org/abs/quant-ph/0307107 |
| Journal | Int. J. Quantum Info. 2 (2004) 183-200 |
Abstract
We compute, for massive particles, the explicit Wigner rotations of one-particle states for arbitrary Lorentz transformations; and the explicit Hermitian generators of the infinite-dimensional unitary representation. For a pair of spin 1/2 particles, Einstein-Podolsky-Rosen-Bell entangled states and their behaviour under the Lorentz group are analysed in the context of quantum field theory. Group theoretical considerations suggest a convenient definition of the Bell states which is slightly different from the conventional assignment. The behaviour of Bell states under arbitrary Lorentz transformations can then be described succinctly. Reduced density matrices applicable to identical particles are defined through Yang's prescription. The von Neumann entropy of each of the reduced density matrix is Lorentz invariant; and its relevance as a measure of entanglement is discussed, and illustrated with an explicit example. A regularization of the entropy in terms of generalized zeta functions is also suggested.
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"abstract": "We compute, for massive particles, the explicit Wigner rotations of\none-particle states for arbitrary Lorentz transformations; and the explicit\nHermitian generators of the infinite-dimensional unitary representation. For a\npair of spin 1/2 particles, Einstein-Podolsky-Rosen-Bell entangled states and\ntheir behaviour under the Lorentz group are analysed in the context of quantum\nfield theory. Group theoretical considerations suggest a convenient definition\nof the Bell states which is slightly different from the conventional\nassignment. The behaviour of Bell states under arbitrary Lorentz\ntransformations can then be described succinctly. Reduced density matrices\napplicable to identical particles are defined through Yang\u0027s prescription. The\nvon Neumann entropy of each of the reduced density matrix is Lorentz invariant;\nand its relevance as a measure of entanglement is discussed, and illustrated\nwith an explicit example. A regularization of the entropy in terms of\ngeneralized zeta functions is also suggested.",
"arxiv_id": "quant-ph/0307107",
"authors": [
"Chopin Soo",
"Cyrus C. Y. Lin"
],
"categories": [
"quant-ph",
"gr-qc",
"hep-th"
],
"journal_ref": "Int. J. Quantum Info. 2 (2004) 183-200",
"title": "Wigner rotations, Bell states, and Lorentz invariance of entanglement and von Neumann entropy",
"url": "https://arxiv.org/abs/quant-ph/0307107"
},
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