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The uncertainty principle in the presence of quantum memory

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The uncertainty principle bounds the uncertainties about the outcomes of two incompatible measurements, such as position and momentum, on a particle. It implies that one cannot predict the outcomes for both possible choices of measurement to arbitrary precision, even if information about the preparation of the particle is available in a classical memory. However, if the particle is prepared entangled with a quantum memory, it is possible to predict the outcomes for both measurement choices precisely. I will explain a recent extension of the uncertainty principle to incorporate this case. The new relation gives a lower bound on the uncertainties, which depends on the amount of entanglement between the particle and the quantum memory. If time permits, I will also outline a couple of applications.