The uncertainty principle in the presence of quantum memory

          @misc{ pirsa_PIRSA:10090102,
            doi = {10.48660/10090102},
            url = {https://pirsa.org/10090102},
            author = {Colbeck, Roger},
            keywords = {Quantum Foundations},
            language = {en},
            title = {The uncertainty principle in the presence of quantum memory},
            publisher = {Perimeter Institute},
            year = {2010},
            month = {sep},
            note = {PIRSA:10090102 see, \url{https://pirsa.org}}
          }
          

Abstract

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.