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Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

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Published on: June 8, 2018

The operator tensor formulation of quantum theory.

Lucien Hardy1

  • 1Perimeter Institute, Waterloo, Ontario, Canada. lhardy@perimeterinstitute.ca

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|June 20, 2012
PubMed
Summary
This summary is machine-generated.

This paper introduces a covariant framework for discrete quantum theory, representing experiments as circuits of operations. Probabilities are calculated using operator tensors, ensuring physical constraints are met.

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Area of Science:

  • Quantum Information Theory
  • Foundations of Quantum Mechanics
  • Mathematical Physics

Background:

  • Quantum experiments involve apparatuses and systems.
  • Operations are defined by apparatus use and outcomes.
  • Circuits wire operations, representing experimental outcomes.

Purpose of the Study:

  • To present a manifestly covariant formulation of discrete quantum theory.
  • To establish a framework for calculating probabilities in quantum circuits.
  • To define physical constraints for operator tensors.

Main Methods:

  • Representing quantum experiments as circuits of operations.
  • Utilizing operator tensors to correspond to quantum operations.
  • Calculating circuit probabilities by replacing operations with operator tensors.
  • Applying partial trace over repeated labels to account for system interactions.

Main Results:

  • A manifestly covariant presentation of discrete quantum theory is provided.
  • A method for calculating probabilities in quantum circuits using operator tensors is detailed.
  • The requirement for physical operator tensors (positive input transpose and normalization) is highlighted.

Conclusions:

  • The proposed framework offers a covariant approach to discrete quantum theory.
  • The operator tensor formulation provides a calculable method for quantum circuit probabilities.
  • Ensuring operator tensors are physical is crucial for valid quantum theory representations.