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Lorentzian Threads as Gatelines and Holographic Complexity.

Juan F Pedraza1,2, Andrea Russo1, Andrew Svesko1

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Summary
This summary is machine-generated.

This study reformulates the complexity=volume conjecture using Lorentzian flows, linking quantum complexity to geometric volume. It introduces a refined complexity measure based on tensor networks and holographic principles, proposing "spacetime complexity."

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Area of Science:

  • Quantum Gravity
  • High Energy Physics
  • Theoretical Physics

Background:

  • The
  • The concept of quantum complexity is central to understanding quantum systems, particularly in holographic contexts.
  • Relating quantum complexity to geometric quantities in a gravitational dual is a key challenge.

Purpose of the Study:

  • To reformulate the
  • To develop a new measure of quantum complexity that accounts for suboptimal constructions.
  • To explore the connection between quantum information and spacetime geometry.

Main Methods:

  • Utilizing the continuous min flow-max cut principle with Lorentzian flows.
  • Applying the nesting property to establish lower bounds on complexity rates.
  • Interpreting discretized flows as threads or gatelines for tensor network states.

Main Results:

  • Established an equivalence between minimum flux of Lorentzian flows and the volume of homologous bulk Cauchy slices.
  • Demonstrated that complexity rate is bounded below by conditional complexity, involving multistep optimization.
  • Proposed a refined complexity measure as an ensemble average, accounting for suboptimal tensor networks.

Conclusions:

  • The study advocates for a notion of
  • The findings suggest a deep connection between quantum information theory and the geometry of spacetime.
  • Linearized Einstein's equations are equivalent to the holographic first law of complexity.