Minimum Uncertainty and Entanglement

Details Minimum Uncertainty and Entanglement Minimum Uncertainty and Entanglement

2011-07-29

arxiv.org/abs/1107.5929v4

Physics

Quantum Physics

4 pages, Revtex. Revised in the light of arXiv:1108.1106v2

Scientific paper

We address the question, does a system A being entangled with another system B, put any constraints on the Heisenberg uncertainty relation (or the Schrodinger-Robertson inequality)? We find that for position and momentum, the equality of the uncertainty relation cannot be reached for entangled states. It cannot be reached for any two noncommuting observables, for finite dimensional Hilbert spaces if the Schmidt rank of the entangled state is maximal, barring the trivial cases of uncertainties in both the observables being zero. As a consequence, the lower bound of the uncertainty relation can never be attained for any two observables for qubits, if the state is entangled.

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