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Reconstructing quantum states from local data.

Brian Swingle1, Isaac H Kim2

  • 1Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA.

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Summary
This summary is machine-generated.

We can reconstruct global quantum states from local data using maximum entropy methods. This approach accurately recovers ground states and approximates others, offering insights into quantum information and emergent geometry.

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Area of Science:

  • Quantum Information Theory
  • Statistical Mechanics
  • Condensed Matter Physics

Background:

  • Reconstructing global quantum states from limited local measurements is a fundamental challenge.
  • General reconstruction methods often yield non-unique solutions, necessitating a principled approach to select the most likely state.

Purpose of the Study:

  • To develop a method for reconstructing global quantum states from local data.
  • To investigate the properties of maximum entropy states consistent with local information.
  • To explore the relationship between reconstruction entropy and emergent geometry in holographic duality.

Main Methods:

  • Employing the principle of maximum global entropy to select a unique state consistent with local measurements.
  • Analyzing the reconstruction of ground states of local Hamiltonians, including degenerate cases.
  • Investigating the reconstruction of thermal states of local Hamiltonians.
  • Developing a certification procedure to verify the accuracy of the reconstructed state.

Main Results:

  • Unique ground states of local Hamiltonians are exactly reconstructed as maximal entropy states.
  • For degenerate ground states, the maximal entropy state approximates the ground state projector.
  • Local reconstruction is demonstrated to be feasible for thermal states of local Hamiltonians.
  • A method for certifying the proximity of the reconstructed state to the true global state is presented.

Conclusions:

  • Maximum entropy reconstruction provides a robust method for inferring global quantum states from local data.
  • The 'reconstruction entropy' offers a quantifiable measure related to emergent geometric properties in holographic contexts.
  • This work bridges quantum information, statistical mechanics, and theoretical physics, with implications for understanding complex quantum systems.