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What can we do in a symmetry-constrained perspective? The importance of the total charge's status in quantum reference frame frameworks

Guilhem Doat, Augustin Vanrietvelde

Abstract

The study of quantum reference frames has received renewed interest over the last years, leading to the parallel development of non-equivalent frameworks by different communities. We clarify the differences between these frameworks. At the mathematical level, they mainly differ in the kind of symmetry (either weak or strong) employed to constrain the system. We show that this mathematical difference corresponds to a fundamental physical question: whether the global charge associated to the symmetry group is accessible to symmetry-constrained observers. In this context, we formulate a definition of a perspective in terms of operational capacities, or lack thereof. Turning to consequences of adopting either approach, we discuss how adopting the weak approach induces an ambiguity in the momenta included in each perspective and bars from defining reversible QRF transformations. We then review and analyze the existing arguments motivating each approach, and show how they bear upon the problem of charge accessibility. Finally, we introduce a simple operational scenario in which upholding two reasonable physical postulates leads to the conclusion that internal observers could measure the global charge by 1/ performing a relativized interference measurement and 2/ classically communicating.

What can we do in a symmetry-constrained perspective? The importance of the total charge's status in quantum reference frame frameworks

Abstract

The study of quantum reference frames has received renewed interest over the last years, leading to the parallel development of non-equivalent frameworks by different communities. We clarify the differences between these frameworks. At the mathematical level, they mainly differ in the kind of symmetry (either weak or strong) employed to constrain the system. We show that this mathematical difference corresponds to a fundamental physical question: whether the global charge associated to the symmetry group is accessible to symmetry-constrained observers. In this context, we formulate a definition of a perspective in terms of operational capacities, or lack thereof. Turning to consequences of adopting either approach, we discuss how adopting the weak approach induces an ambiguity in the momenta included in each perspective and bars from defining reversible QRF transformations. We then review and analyze the existing arguments motivating each approach, and show how they bear upon the problem of charge accessibility. Finally, we introduce a simple operational scenario in which upholding two reasonable physical postulates leads to the conclusion that internal observers could measure the global charge by 1/ performing a relativized interference measurement and 2/ classically communicating.
Paper Structure (23 sections, 2 theorems, 35 equations, 6 figures, 1 table)

This paper contains 23 sections, 2 theorems, 35 equations, 6 figures, 1 table.

Table of Contents

  1. Introduction
  2. The two ways of imposing symmetry
  3. Weak and Strong symmetry
  4. Mathematical features of the two approaches: factoriality and non-factoriality
  5. Perspectives in the weak and strong approaches
  6. What is a perspective?
  7. Global and collaborative perspectives
  8. Perspectives in the weak approach
  9. Perspectives in the strong approach
  10. A review of arguments motivating each approach
  11. Pro-strong approach arguments
  12. Pro-weak approach arguments
  13. An operational proposal and how it leads to the weak approach
  14. Goal and strategy
  15. Scenario : Setting the scene
  16. ...and 8 more sections

Key Result

Theorem 2.1

(Wedderburn-Artin) Given a finite dimensional C* algebra $\mathcal{A}$, there exists a list of finite-dimensional Hilbert spaces $(\mathcal{H}_l)_{k\in L}$, indexed from 1 to L, such that

Figures (6)

  • Figure 1: Experimental set-up from Eve's perspective
  • Figure 2: Experimental set-up from Alice's perspective
  • Figure 3: Postulate 1: Alice's measurement of Bob's momentum in her own perspective
  • Figure 4: Alice performing a beam splitter on Bob's position as seen by different agents.
  • Figure 5: Alice's measurement of Bob's momentum in Eve's description
  • ...and 1 more figures

Theorems & Definitions (8)

  • Example 1
  • Example 2
  • Definition 2.1
  • Theorem 2.1
  • Definition 3.1
  • Example 3
  • Example 4
  • Theorem 5.1