Uncertainty Relations for Entangled States
G. Rigolin
TL;DR
This paper derives a new uncertainty relation for entangled particles that generalizes Heisenberg's principle, incorporating correlations and potentially providing tighter bounds for position and momentum uncertainties.
Contribution
It introduces a symmetrization-based generalized uncertainty relation for entangled states, extending traditional bounds to include particle correlations.
Findings
New lower bounds for position-momentum uncertainty products in entangled states
Reduction to Heisenberg's relation in uncorrelated cases
Potential for tighter uncertainty bounds in quantum entanglement
Abstract
A generalized uncertainty relation for an entangled pair of particles is obtained if we impose a symmetrization rule for all operators that we should use when doing any calculation using the entangled wave function of the pair. This new relation reduces to Heisenberg's uncertainty relation when the particles have no correlation and suggests that we can have new lower bounds for the product of position and momentum dispersions.
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Taxonomy
TopicsQuantum Mechanics and Applications · Quantum Information and Cryptography · Cold Atom Physics and Bose-Einstein Condensates