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Published on: June 8, 2018
Extending Noether's theorem by quantifying the asymmetry of quantum states
Iman Marvian1, Robert W Spekkens2
11] Perimeter Institute for Theoretical Physics, 31 Caroline St. N, Waterloo, Ontario, Canada N2L 2Y5 [2] Institute for Quantum Computing, University of Waterloo, 200 University Ave. W, Waterloo, Ontario, Canada N2L 3G1 [3] Center for Quantum Information Science and Technology, Department of Physics and Astronomy, University of Southern California, Los Angeles, California 90089, USA.
This study introduces new measures of symmetry breaking in quantum states, extending Noether's theorem. These measures reveal novel constraints on system dynamics and have applications in quantum information science.
Area of Science:
- Physics
- Quantum Information Theory
Background:
- Noether's theorem connects symmetry to conservation laws but has limitations for mixed quantum states and open systems.
- Existing conservation laws do not fully capture consequences of symmetries in mixed quantum states.
Purpose of the Study:
- To address limitations of Noether's theorem for mixed quantum states and open systems.
- To introduce quantifiable measures of symmetry breaking in quantum states.
Main Methods:
- Developing measures for the extent to which a quantum state breaks a symmetry.
- Utilizing quantum information theory tools to find non-trivial asymmetry measures.
Main Results:
- Introduced novel measures of symmetry breaking for quantum states.
- Established constraints on state transitions: asymmetry cannot increase in non-isolated systems and is conserved in isolated systems.
Conclusions:
- The developed asymmetry measures provide a more comprehensive understanding of symmetries in quantum dynamics.
- Applications include bounding quantum noise and assessing metrology schemes.
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