Uncertainty principle guarantees genuine source of intrinsic randomness

  • Authors:

  • Trina Chakraborty;Manik Banik;Pinaki Patra

  • Affiliations:

  • Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata, India 700108;Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata, India 700108;Department of Physics, University of Kalyani, Kalyani, India 741235

  • Venue:
  • Quantum Information Processing
  • Year:
  • 2014

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Abstract

The Born's rule introduces intrinsic randomness to the outcomes of a measurement performed on a quantum mechanical system. But, if the system is prepared in the eigenstate of an observable, then the measurement outcome of that observable is completely predictable, and hence, there is no intrinsic randomness. On the other hand, if two incompatible observables are measured (either sequentially on a particle or simultaneously on two identical copies of the particle), then uncertainty principle guarantees intrinsic randomness in the subsequent outcomes independent of the preparation state of the system. In this article, we show that this is true not only in quantum mechanics but for any no-signaling probabilistic theory. Also the minimum amount of intrinsic randomness that can be guaranteed for arbitrarily prepared state of the system is quantified by the amount of (un)certainty.