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Hidden Tensor Structures.

Marek Czachor1

  • 1Instytut Fizyki i Informatyki Stosowanej, Politechnika Gdańska, 80-233 Gdańsk, Poland.

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|February 23, 2024
PubMed
Summary
This summary is machine-generated.

All quantum and classical systems possess hidden structures, enabling quantum computation and explaining classical emulation of quantum devices. These hidden degrees of freedom offer new insights into fundamental physics and signal analysis.

Keywords:
Bell inequalityBell theoremBrandt-Greenberg representationFock spacesclassical emulation of quantum computationmodular observablesquantum logic gatestensor product structures

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Area of Science:

  • Theoretical Physics
  • Quantum Mechanics
  • Classical Field Theory
  • Signal Analysis

Background:

  • Separable Hilbert spaces, fundamental to quantum mechanics, inherently contain numerous hidden tensor-like structures.
  • These structures are not limited to quantum systems but also apply to classical field theories and signal analysis.

Purpose of the Study:

  • To demonstrate the ubiquitous nature of hidden tensor structures in systems described by separable Hilbert spaces.
  • To explore the implications of these hidden structures for quantum computation, Bell's inequalities, and classical emulation of quantum systems.

Main Methods:

  • Decomposition of systems (e.g., harmonic oscillator, potential well, classical signals) into arbitrary subsystems.
  • Analysis of hidden degrees of freedom, including hidden position and spin, and their analogy to modular variables.
  • Investigation of the connection between hidden structures and established theoretical constructs like the Brandt-Greenberg representation.

Main Results:

  • Systems as simple as a one-dimensional harmonic oscillator possess rich hidden structures.
  • These structures are sufficient for quantum computation, violation of Bell's inequalities, and universal quantum gates.
  • Hidden structures explain the classical emulation of quantum computers using analog circuits and relate to higher-order squeezing.

Conclusions:

  • Hidden tensor structures are a fundamental, yet often overlooked, aspect of systems described by separable Hilbert spaces.
  • Understanding these hidden degrees of freedom provides novel applications in quantum information science and classical signal processing.
  • The research bridges quantum and classical physics by revealing shared underlying structural properties.