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arXiv:1805.12237 · Annalen der Physik

Objective Realism and Joint Measurability in Quantum Many Copies

Adam Bednorz

Published May 30, 2018• 6 citations
arXivHTMLPDF

Abstract

Abstract In the standard quantum theory, one can measure precisely only a subset of the incompatible observables. It results in lack of a formal joint probability defining objective realism even if we accept nonlocal or certain faster‐than‐light interactions. Here, a construction of such realism extending the usual single‐copy description to many copies, partially analogous to familiar many worlds, is proposed. Failure of the standard single copy can be easily looked for experimentally. The copies should interact weakly at the macroscopic level, leading to effective collapse to a single identical pointer state. Experimental evidence for this conjecture could be obtained by detecting incomplete collapse in sequential measurements or finding deviations from the single‐copy Born rule when observing simple quantum systems.

DOI
10.1002/andp.201800002

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Cover Picture: Objective Realism and Joint Measurability in Quantum Many Copies (Ann. Phys. 7/2018)

Adam Bednorz

Quantum Many Copies In quantum theory, Schrödinger's cat exists only when one looks – there is no objective realism. The problem can be resolved assuming many copies of the cat. The cat-copies undergo the same dynamics and do not interact. When observed, the copies collapse to the same state, dead or alive, although with a finite probability. In article 1800002, Adam Bednorz discusses quantum objective realism for incompatible observables consistent with experiments, which can be defined assuming the existence of weakly interacting many copies of the same system.

Annalen der Physik•Jul 1, 2018•0 citations
Abstract In the standard quantum theory, one can measure precisely only a subset of the incompatible observables. It results in lack of a formal joint probability defining objective realism even if we accept nonlocal or certain faster‐than‐light interactions. Here, a construction of such realism extending the usual single‐copy description to many copies, partially analogous to familiar many worlds, is proposed. Failure of the standard single copy can be easily looked for experimentally. The copies should interact weakly at the macroscopic level, leading to effective collapse to a single identical pointer state. Experimental evidence for this conjecture could be obtained by detecting incomplete collapse in sequential measurements or finding deviations from the single‐copy Born rule when observing simple quantum systems.
The question of whether quantum measurements reflect some underlying objective reality has no generally accepted answer.We show that a description of such reality is possible under natural conditions such as linearity and causality, although in terms of moments and cumulants of finite order and without relativistic invariance.The proposed construction of observations' probability distribution originates from weak, noninvasive measurements, with detection error replaced by some external finite noise.The noise allows us to construct microscopic objective reality, but remains dynamically decoupled and hence unobservable at the macroscopic level.
We show that it is not possible to ascribe an objective reality to a property of a quantum system even if the system is in an eigenstate of the corresponding observable and a measurement of the property is certain to result in a particular value. This kind of incompatibility between realism and quantum mechanics is theoretically demonstrated with a simple example where sequential angular momentum measurements are performed on a quantum system. We discuss the relation of this result with other investigations about realism and quantum mechanics. In particular, we show that the Einstein-Podolsky-Rosen criterion for physical reality is incompatible with the quantum theory.
Fundamental principle of classical physics -- local realism, means that freely chosen observations can be explained by a local (slower than light) real process. It is apparently violated in quantum mechanics as shown by Bell theorem. Despite extreme efforts experiments have not conclusively confirmed this violation due to loopholes. We propose a new postulate that the description of quantum processes must be consistent with local realism, It also assumes existence of many worlds/copies of the same system, interacting weakly microscopically but strongly macroscopically, whose number can be estimated experimentally.Bell theorem will never address a real experiment because its assumptions cannot be strictly fulfilled. By an appropriate generalization of quantum framework and measurement postulates, in particular taking into account freedom of choice, local realism agrees with quantum mechanics and the performed experiments, also involving single qubit coherence and a weaker version of the Bell test, Einstein-Podolsky-Rosen steering.
We demonstrate violation of objective realism in quantum world using unconstrained weak measurements. Instead of limited Leggett-Garg approach with artificial bounds on the observed values, we assume two identical and indepenent weak detectors and final conditioning. The experimental verification has been performed on public quantum computers, IBM and IonQ. Thanks to sufficiently large statistics, the violation is observed at the level of 10 standard deviations. The tests confirmed also high quality of parametric two-qubit gates offered by main quantum hardware providers.
The measurement problem is the issue of explaining how the objective classical world emerges from a quantum one. Here we take a different approach. We assume that there is an objective classical system, and then ask that the standard rules of probability theory apply to it when it interacts with a quantum system. Under mild assumptions, we recover the unitary dynamics, collapse and Born rule postulates from quantum theory. Nonetheless, there is no decoherence, because the quantum state remains pure conditioned on the classical trajectory. This results in one world, rather than many-worlds. Our main technical tool is to exploit a change of measure on the space of classical paths, the functional form of which is shown to characterise the quantum dynamics and Born rules of a class of quantum-like theories.
Quantum Many Copies In quantum theory, Schrödinger's cat exists only when one looks – there is no objective realism. The problem can be resolved assuming many copies of the cat. The cat-copies undergo the same dynamics and do not interact. When observed, the copies collapse to the same state, dead or alive, although with a finite probability. In article 1800002, Adam Bednorz discusses quantum objective realism for incompatible observables consistent with experiments, which can be defined assuming the existence of weakly interacting many copies of the same system.