Article

Extending Noether’s theorem by quantifying the asymmetry of quantum states

  • Nature Communications 5, Article number: 3821 (2014)
  • doi:10.1038/ncomms4821
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Abstract

Noether’s theorem is a fundamental result in physics stating that every symmetry of the dynamics implies a conservation law. It is, however, deficient in several respects: for one, it is not applicable to dynamics wherein the system interacts with an environment; furthermore, even in the case where the system is isolated, if the quantum state is mixed then the Noether conservation laws do not capture all of the consequences of the symmetries. Here we address these deficiencies by introducing measures of the extent to which a quantum state breaks a symmetry. Such measures yield novel constraints on state transitions: for nonisolated systems they cannot increase, whereas for isolated systems they are conserved. We demonstrate that the problem of finding non-trivial asymmetry measures can be solved using the tools of quantum information theory. Applications include deriving model-independent bounds on the quantum noise in amplifiers and assessing quantum schemes for achieving high-precision metrology.

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Acknowledgements

Research at Perimeter Institute is supported in part by the Government of Canada through NSERC and by the Province of Ontario through MRI. I.M. acknowledges support from NSERC grant RGPIN-387068-2010, a Mike and Ophelia Lazaridis fellowship, and ARO MURI grant W911NF-11-1-0268.

Author information

Affiliations

  1. Perimeter Institute for Theoretical Physics, 31 Caroline St. N, Waterloo, Ontario, Canada N2L 2Y5

    • Iman Marvian
    •  & Robert W Spekkens
  2. Institute for Quantum Computing, University of Waterloo, 200 University Ave. W, Waterloo, Ontario, Canada N2L 3G1

    • Iman Marvian
  3. Center for Quantum Information Science and Technology, Department of Physics and Astronomy, University of Southern California, Los Angeles, California 90089, USA

    • Iman Marvian

Authors

  1. Search for Iman Marvian in:

  2. Search for Robert W Spekkens in:

Contributions

I.M. and R.W.S. contributed equally to this work.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Iman Marvian.

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