Switching Quantum Reference Frames for Quantum Measurement

Jianhao M Yang

doi:10.22331/q-2020-06-18-283

Abstract

Physical observation is made relative to a reference frame. A reference frame is essentially a quantum system given the universal validity of quantum mechanics. Thus, a quantum system must be described relative to a quantum reference frame (QRF). Further requirements on QRF include using only relational observables and not assuming the existence of external reference frame. To address these requirements, two approaches are proposed in the literature. The first one is an operational approach (F. Giacomini, et al, Nat. Comm. 10:494, 2019) which focuses on the quantization of transformation between QRFs. The second approach attempts to derive the quantum transformation between QRFs from first principles (A. Vanrietvelde, et al,Quantum4:225, 2020). Such first principle approach describes physical systems as symmetry induced constrained Hamiltonian systems. The Dirac quantization of such systems before removing redundancy is interpreted as perspective-neutral description. Then, a systematic redundancy reduction procedure is introduced to derive description from perspective of a QRF. The first principle approach recovers some of the results from the operational approach, but not yet include an important part of a quantum theory - the measurement theory. This paper is intended to bridge the gap. We show that the von Neumann quantum measurement theory can be embedded into the perspective-neutral framework. This allows us to successfully recover the results found in the operational approach, with the advantage that the transformation operator can be derived from the first principle. In addition, the formulation presented here reveals several interesting conceptual insights. For instance, the projection operation in measurement needs to be performed after redundancy reduction, and the projection operator must be transformed accordingly when switching QRFs. These results represent one step forward in understanding how quantum measurement should be formulated when the reference frame is also a quantum system.

Highlights

The idea that a physical system or a physical phenomenon must be described relative to a reference frame is a well-accepted principle in the relativity theory
Process 1 is perspective and in general needs to be implemented after a quantum reference frame (QRF) is chosen, except in the special case where the pointer variable is invariant in the symmetry reduction procedure. 2.) At the methodology level, we show how the symmetry reduction procedure can be embedded in the unitary formulation of Process 2, and consistently integrated with projective operation in the reduced Hilbert space
Inspired by the novel approach of switching QRFs via a perspective-neutral framework [26], this paper extends the approach to the quantum measurement process

Summary

Introduction

The idea that a physical system or a physical phenomenon must be described relative to a reference frame is a well-accepted principle in the relativity theory. Abandoning the concept of absolute spacetime is a foundation of the general relativity where the laws of physics are invariant when changing reference systems. A reference frame essentially is a quantum system, if we agree that quantum mechanics is universally valid. A physical system or a physical phenomenon must be described relative to another quantum system This statement is applied to describe a relativity event, and applicable to descriptions of all quantum phenomena. The implication here is that a more fundamental theory should describe a physical system relative to a quantum reference frame (QRF), and address how such descriptions are transformed from one to another when switching the QRFs

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Discussion

Conclusion