Operational Quantum Reference Frame Transformations

Abstract

Quantum reference frames are needed in quantum theory for much the same reasons that reference frames are in classical theories: to manifest invariance in line with fundamental relativity principles and to provide a basis for the definition of observable quantities. Though around since the 1960s, and used in a wide range of applications, only recently has the means for transforming descriptions between different quantum reference frames been tackled in detail. In this work, we provide a general, operationally motivated framework for quantum reference frames and their transformations, holding for locally compact groups. The work is built around the notion of operational equivalence, in which quantum states that cannot be physically distinguished are identified. For example, we describe the collection of relative observables as a subspace of the algebra of invariants on the composite of system and frame, and from here the set of relative states is constructed through the identification of states which cannot be distinguished by relative observables. Through the notion of framed observables -- the formation of joint observables of system and frame -- of which the relative observables can be understood as examples, quantum reference frame transformations are then maps between equivalence classes of relative states which respect the framing. We give an explicit realisation in the setting that the initial frame admits a highly localized state with respect to the frame observable. The transformations are invertible exactly when the final frame also has such a localizability property. The procedure we present is in operational agreement with other recent inequivalent constructions on the domain of common applicability, but extends them in a number of ways, and weakens claims of entanglement generation through frame changes.

References in corpus (16)

• Reference frames, superselection rules, and quantum information
• An Algebra of Observables for de Sitter Space
• Gravity and the Crossed Product
• Generalized entropy for general subregions in quantum gravity
• Between classical and quantum
• Crossed product algebras and generalized entropy for subregions
• Quantum reference frames, measurement schemes and the type of local algebras in quantum field theory
• 'Measurement of Quantum Mechanical Operators' Revisited
• Relative Quantum Time
• Semifinite von Neumann algebras in gauge theory and gravity
• Algebras, Regions, and Observers
• Relative subsystems and quantum reference frame transformations
• Fluctuation theorems, quantum channels and gravitational algebras
• Operational Quantum Frames: An operational approach to quantum reference frames
• Crossed Products, Conditional Expectations and Constraint Quantization
• Relativization is naturally functorial

Cited by in corpus (14)

• Identification is Pointless: Quantum Coordinates, Localisation of Events, and the Quantum Hole Argument
• Gravitational entropy is observer-dependent
• Generalised second law beyond the semiclassical regime
• Crossed products and quantum reference frames: on the observer-dependence of gravitational entropy
• The sum of entanglement and subsystem coherence is invariant under quantum reference frame transformations
• Uncertainty Relations Relative to Phase-Space Quantum Reference Frames
• Searching for a physical description relative to a quantum system
• Quantum Galilei group as quantum reference frame transformations
• Towards a Quantum Erlangen Program
• What can we do in a symmetry-constrained perspective? The importance of the total charge's status in quantum reference frame frameworks
• Linearization (in)stabilities and crossed products
• Quantum Mechanics Relative to a Quantum Reference System: a Relative State Approach
• Einstein causality of quantum measurements in the Tomonaga-Schwinger picture
• Large effects from quantum reference frames