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Mutual Unbiasedness in Coarse-Grained Continuous Variables.

Daniel S Tasca1, Piero Sánchez2, Stephen P Walborn3

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Physical Review Letters
|February 14, 2018
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Summary
This summary is machine-generated.

Standard coarse graining disrupts quantum measurement unbiasedness. Periodic coarse graining, demonstrated in an optics experiment, restores and confirms this crucial mutual unbiasedness for quantum continuous variables.

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Area of Science:

  • Quantum Information Science
  • Quantum Optics
  • Quantum Measurement Theory

Background:

  • Mutual unbiasedness is a key property for quantum measurements, particularly between conjugate variables.
  • Standard coarse-graining techniques in quantum continuous variable systems often fail to preserve mutual unbiasedness.
  • Understanding this property is crucial for advancing quantum information processing and quantum mechanics foundations.

Purpose of the Study:

  • To investigate the preservation of mutual unbiasedness under different coarse-graining procedures for quantum continuous variable systems.
  • To theoretically establish and experimentally verify conditions for maintaining mutual unbiasedness.
  • To explore the connection between discrete and continuous variable quantum mechanics through measurement properties.

Main Methods:

  • Theoretical analysis of mutual unbiasedness for coarse-grained measurements.
  • Development of the concept of periodic coarse graining.
  • Experimental implementation using Fraunhofer diffraction through a periodic grating in an optics setup.

Main Results:

  • Standard coarse graining was shown to break mutual unbiasedness between conjugate variables.
  • Periodic coarse graining was theoretically shown to establish and experimentally confirm mutual unbiasedness.
  • Experimental results demonstrated excellent agreement with the developed theoretical framework.

Conclusions:

  • Periodic coarse graining offers a viable method to maintain mutual unbiasedness in quantum continuous variable measurements.
  • The findings provide a pathway for connecting discrete and continuous variable quantum mechanics.
  • This work has implications for quantum information protocols relying on unbiased measurements.