Abstract
We show that sharing a quantum reference frame requires sharing measurement operators that identify the reference frame in addition to operators that measure its state. Observers restricted to finite resources cannot, in general, operationally determine that they share such operators. Uncertainty about whether system-identification operators are shared induces decoherence.
Highlights
Bartlett, Rudolph and Spekkens [1] define nonfungible quantum information as information that Alice and Bob can share only by exchanging a quantum system
This is in contradistinction to fungible information that Alice can communicate to Bob by sending a string of classical bits, e.g., a bit string that describes a system or encodes a measurement outcome
We show that the physical implementations of these observables encode nonfungible information
Summary
Rudolph and Spekkens [1] define nonfungible quantum information as information that Alice and Bob can share only by exchanging a quantum (i.e., physical) system This is in contradistinction to fungible information that Alice can communicate to Bob by sending a string of classical bits, e.g., a bit string that describes a system or encodes a measurement outcome. Pointer state outcomes specifying the relative states of QRFs, which as shown in [1] can be inferred without physically sharing the QRFs, are defined only with respect to such nonfungible, measurement-operator encoded information. The nonfungible information encoded by the physical implementations of QRF-identifying observables must already be shared either to exchange a QRF or to infer the relative states of non-shared QRFs. Whether Alice and Bob implement the same observables cannot be determined operationally with finite resources, either by Alice and Bob or by a third party. We suggest that the shared “classical reality” of the laboratory emphasized by Bohr [5] can be attributed to this unavoidable uncertainty about shared observables
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