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The concept of dimension is important because every mathematical equation linking physical quantities must be dimensionally consistent, implying that mathematical equations must meet the following two rules. The first rule is that, in an equation, the expressions on each side of the equal sign must have the same dimensions. This is fairly intuitive since we can only add or subtract quantities of the same type (dimension). The second rule states that, in an equation, the arguments of any of the...
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Evidence-Based Certification of Quantum Dimensions.

Y S Teo1, S U Shringarpure1, H Jeong1

  • 1Department of Physics and Astronomy, <a href="https://ror.org/04h9pn542">Seoul National University</a>, 08826 Seoul, South Korea.

Physical Review Letters
|August 19, 2024
PubMed
Summary
This summary is machine-generated.

We developed a new evidence-based protocol to determine the effective dimension of quantum states using relative belief. This method provides reliable error bars for quantum information processing experiments.

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Area of Science:

  • Quantum Information Science
  • Quantum Computing
  • Quantum State Characterization

Background:

  • Efficient quantum information processing requires accurately describing quantum states within a minimal Hilbert space.
  • Current methods often rely on assumptions beyond experimental data.
  • Determining the effective dimension of quantum states is a key challenge.

Purpose of the Study:

  • To introduce a general, evidence-based dimension-certification protocol for quantum states.
  • To utilize Bayesian relative belief for determining effective dimension without unjustified assumptions.
  • To provide a robust method for assessing evidence for or against specific dimensions.

Main Methods:

  • Developed a dimension-certification protocol applicable to both discrete and continuous variable systems.
  • Employed Bayesian relative belief to define effective dimension based on posterior and prior probabilities derived from data.
  • Utilized spectral-temporal and polarimetry measurement data for validation.

Main Results:

  • Demonstrated a fully evidence-based protocol relying solely on experimental data.
  • Showcased the assignment of Bayesian plausible error bars for effective dimensions.
  • Validated the protocol's effectiveness using real-world experimental data.

Conclusions:

  • Relative belief offers a conservative and user-friendly model-selection method for quantum experiments.
  • The protocol enhances the reliability of determining quantum state dimensions.
  • This approach facilitates more efficient and accurate quantum information processing.