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The uncertainty principle in the presence of quantum memory

Research output: Contribution to journalArticlepeer-review


  • Mario Berta
  • Matthias Christandl
  • Roger Colbeck
  • Joseph M. Renes
  • Renato Renner


Publication details

JournalNature Physics
DatePublished - 10 Sep 2010
Issue number9
Number of pages4
Pages (from-to)659-662
Original languageEnglish


The uncertainty principle, originally formulated by Heisenberg(1), clearly illustrates the difference between classical and quantum mechanics. The 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, a device that might be available in the not-too-distant future(2), it is possible to predict the outcomes for both measurement choices precisely. Here, we extend the uncertainty principle to incorporate this case, providing a lower bound on the uncertainties, which depends on the amount of entanglement between the particle and the quantum memory. We detail the application of our result to witnessing entanglement and to quantum key distribution.

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