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arXiv:1711.07739 · Physical Review A

Information-reality complementarity: The role of measurements and quantum reference frames

Pedro R. Dieguez, R. M. Angelo

Published Feb 16, 2018• 50 citations
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Abstract

Relations among the concepts of measurement, information, and physical reality are established with the quantification of the degree of reality of an observable for a given preparation. It is found that for pure states the entanglement with the apparatus precisely determines the amount by which the reality of the monitored observable increases.

DOI
10.1103/physreva.97.022107

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Relations among the concepts of measurement, information, and physical reality are established with the quantification of the degree of reality of an observable for a given preparation. It is found that for pure states the entanglement with the apparatus precisely determines the amount by which the reality of the monitored observable increases.
Consideration of the von Neumann measurement process underlying interference experiments shows that the uncertainty in the incoming wave, responsible for its interference, translates during measurement into an uncertainty at the measuring apparatus. However, subsequent measurement on the apparatus does not reveal any new information about the interfering wave. This observation, in the context of recent advances in quantum information, suggests an argument for an information theoretic interpretation of quantum mechanics.
Under the principle that quantum-mechanical observables are invariant under relevant symmetry transformations, we explore how the usual, non-invariant quantities may capture measurement statistics. Using a relativisation mapping, viewed as the incorporation of a quantum reference frame, we show that the usual quantum description approximates the relative one precisely when the reference system admits an appropriate localisable quantity and a localised state. From this follows a new perspective on the nature and reality of quantum superpositions and optical coherence.
The concept of information offers a more complete description of complementarity than the traditional approach based on observables. We present the first experimental test of information complementarity for two-qubit pure states, achieving close agreement with theory. We also explore the distribution of information in a comprehensive range of mixed states. Our results highlight the strange and subtle properties of even the simplest quantum systems; for example, entanglement can be increased by reducing the correlations between two subsystems.
Under the principle that quantum mechanical observables are invariant under relevant symmetry transformations, we explore how the usual, non-invariant quantities may capture measurement statistics. Using a relativisation mapping, viewed as the incorporation of a quantum reference frame, we show that the usual quantum description approximates the relative one precisely when the reference system admits an appropriate localisable quantity and a localised state. From this follows a new perspective on the nature and reality of quantum superpositions and optical coherence.
Measurements invariably determine the physical state of a given ``observed system'' with respect to an ``observer system.'' This implies an inescapable two-body relationality upon which physical theories must rely. There has been a growing effort to understand how quantum mechanics can accommodate the notion of reference frame in its substratum and whether such approach would respect general covariance. With regard to quantum resources, it has been shown that coherence and entanglement are not invariant upon changes of quantum reference frames. Here, we construct a theoretical framework within which a given combination of quantum resources, including not only coherence and entanglement, is shown to be a physical invariant. Under the premise of the universality of quantum phenomena, the proven covariance between quantum reference frames then implies that the total quantumness accessible to any observer in the universe is absolute.
Complex physical systems contain information which, under some well-defined processes can differentiate between local and nonlocal information. Both these fundamental aspects of information are defined operationally. Local information is locally accessible and allows one to perform processes, such as physical work, while nonlocal information allows one to perform processes such as teleportation. It is shown that these two kinds of information are complementary in the sense that two parties can either gain access to the nonlocal information or to the local information but not both. This complementarity has a form similar to that expressed by entropic uncertainty relations. For pure states, the entanglement plays the role of Planck's constant. We also find another class of complementarity relations which applies to operators and is induced when two parties can only perform local operations and communicate classical (LOCC). In particular, observables such as the parity and phase of two qubits commute but under LOCC, they are complementary observables. It is also found this complementarity is pure in the sense that it can be ``decoupled'' from the uncertainty principle. It is suggested that these complementarities represent an essential extension of Bohr's complementarity to complex (distributed) systems which are entangled.