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Gradient Echo Quantum Memory in Warm Atomic Vapor
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Union bound for quantum information processing.

Samad Khabbazi Oskouei1, Stefano Mancini2,3, Mark M Wilde4

  • 1Department of Mathematics, Islamic Azad University, Varamin-Pishva Branch, 33817-7489 Iran.

Proceedings. Mathematical, Physical, and Engineering Sciences
|February 15, 2019
PubMed
Summary
This summary is machine-generated.

Researchers developed a new quantum union bound for analyzing quantum measurements. This bound, useful in quantum information theory, simplifies proofs and has applications in quantum communication and algorithms.

Keywords:
quantum communicationquantum union boundsequential decoding

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Area of Science:

  • Quantum Information Theory
  • Quantum Measurement Theory

Background:

  • The Hayashi-Nagaoka inequality is crucial for analyzing error probabilities in quantum information theory, particularly for square-root measurements.
  • Existing methods for analyzing sequences of quantum measurements can be complex.

Purpose of the Study:

  • To introduce and prove a novel quantum union bound applicable to sequential binary-outcome quantum measurements.
  • To demonstrate the bound's utility and elementary proof method.

Main Methods:

  • The proof relies on fundamental concepts: properties of projectors, the Pythagorean theorem, and the Cauchy-Schwarz inequality.
  • A tunable parameter in the bound is optimized, analogous to parameters in existing inequalities.

Main Results:

  • A new quantum union bound is established, featuring an optimizable parameter.
  • The bound is applied to show that a sequential decoding strategy achieves a lower bound on a quantum channel's second-order coding rate.

Conclusions:

  • The derived quantum union bound offers an elementary and advantageous approach for analyzing quantum measurements.
  • The bound has potential applications in quantum communication, quantum algorithms, and quantum complexity theory, especially in the non-asymptotic regime.