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Shadow Tomography from Emergent State Designs in Analog Quantum Simulators.

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This study presents a new quantum state tomography method using global control and ancilla entanglement. It efficiently infers quantum state properties, including nonlinear functions, suitable for analog quantum simulators.

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Area of Science:

  • Quantum Information Science
  • Quantum Many-Body Physics

Background:

  • Quantum state tomography is crucial for characterizing quantum systems.
  • Existing methods often require complex, qubit-selective operations.

Purpose of the Study:

  • To develop a novel quantum state tomography protocol using global control.
  • To enable efficient inference of both linear and nonlinear quantum state properties.

Main Methods:

  • Entangling the target quantum state with ancillas via a global unitary evolution.
  • Performing projective measurements on the ancillas.
  • Utilizing the emergent quantum state design phenomenon for property reconstruction.

Main Results:

  • A universal relationship between measurement statistics and quantum state properties is established.
  • The method reconstructs arbitrary observables with efficiency comparable to classical shadow tomography.
  • The protocol is implementable with global Hamiltonian evolution, avoiding qubit-selective gates.

Conclusions:

  • This global control approach simplifies quantum state tomography.
  • It is particularly advantageous for analog quantum simulators like ultracold atoms and Rydberg atom arrays.
  • The method facilitates the characterization of complex quantum states and nonlinear functions.