Arun Kumar Pati, A. R. Usha Devi, A. K. Rajagopal, Sudha
Uncertainty relations capture the essence of our inevitable ignorance associated with incompatible measurements of two non-commuting observables. Recently, it has been shown that the lower bound on the uncertainties of the measurement outcomes depends on the amount of entanglement between the observed system and the observer who holds a quantum memory. If the system is maximally entangled with its memory the outcomes of two incompatible measurements made on the system can be predicted precisely. Here, we prove a new bound on the conditioned uncertainties in the presence of quantum memory and show that even classical correlations between system and quantum memory can beat the uncertainties down towards precision. On application side, we show that our new inequality can be used to provide bounds on the distillable common randomness and entanglement of formation of bipartite quantum states.
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http://arxiv.org/abs/1204.3803
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