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arXiv:2012.11189 · Quantum Reports

The ABC of Deutsch–Hayden Descriptors

Charles Alexandre Bédard

Published Apr 27, 2021• 14 citations
arXivHTMLPDF

Abstract

It has been more than 20 years since Deutsch and Hayden proved the locality of quantum theory, using the Heisenberg picture of quantum computational networks. Of course, locality holds even in the face of entanglement and Bell’s theorem. Today, most researchers in quantum foundations are still convinced not only that a local description of quantum systems has not yet been provided, but that it cannot exist. The main goal of this paper is to address this misconception by re-explaining the descriptor formalism in a hopefully accessible and self-contained way. It is a step-by-step guide to how and why descriptors work. Finally, superdense coding is revisited in the light of descriptors.

DOI
10.3390/quantum3020017

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It has been more than 20 years since Deutsch and Hayden proved the locality of quantum theory, using the Heisenberg picture of quantum computational networks. Of course, locality holds even in the face of entanglement and Bell’s theorem. Today, most researchers in quantum foundations are still convinced not only that a local description of quantum systems has not yet been provided, but that it cannot exist. The main goal of this paper is to address this misconception by re-explaining the descriptor formalism in a hopefully accessible and self-contained way. It is a step-by-step guide to how and why descriptors work. Finally, superdense coding is revisited in the light of descriptors.
Bell's theorem establishes that a local and spatially separable physical theory with no superdeterminism or retrocausality must be a theory of many local worlds. The local many worlds formalism of quantum mechanics is a transparent separable physical theory in spacetime with a Lorentz covariant causal structure. Unlike the Everett many worlds interpretation, there is no nonseparable universal wavefunction in configuration space, but like Everett, there is only local unitary evolution which conserves probability (fluid) current, and no wavefunction collapse. Each event in spacetime has its own local wavefunction which is built up using only the local wavefunctions and local unitary evolution operators within its past light cone, and which is entirely disconnected from spacelike separated local wavefunctions. We call this the local Schrödinger picture. Local many worlds can also be described in the Heisenberg picture by ascribing Deutsch-Hayden (DH) descriptors to each individual system, each of which evolves under local unitary operations. Both the local wavefunctions and DH descriptors contain records of past interactions, and while the local wavefunctions provide a clear and intuitive physical narrative, the descriptors contain all of the same information in a much more compact form. Unfortunately, the compact form is also somewhat cryptic, which has made the local Heisenberg picture relatively inaccessible. The purpose of this article is to show that the local wavefunctions for any NNN-qubit system can always be constructed directly from the DH descriptors, allowing us to combine the benefits of both pictures.
A growing body of literature supports Deutsch and Hayden’s (2000) claim that in the Heisenberg picture, quantum entanglement can be characterised locally using objects they call descriptors. I argue that their notion of locality rests, in part, on a qualified version of the principle of separability that I call spatial separability. I show that spatial separability is not sufficient for separability simpliciter, and that the more general version, spatiotemporal separability, reveals that their claim is false. Deutsch and Hayden’s approach also has a novel implication: if descriptors represent actual physical properties, they are non-qualitative properties, which are profoundly different from the qualitative properties we have come to expect from other branches of physics.
Local realism has been the subject of much discussion in modern physics, partly because our deepest theories of physics appear to contradict one another in regard to whether reality is local. According to general relativity, it is, as physical quantities (perceptible or not) in two spacelike separated regions cannot affect one another. Yet, in quantum theory, it has traditionally been thought that local realism cannot hold and that such effects do occur. This apparent discrepancy between the two theories is resolved by Everettian quantum theory, as first proven by Deutsch & Hayden (2000). In this paper, I will explain how local realism is respected in quantum theory and review the advances in our understanding of locality since Deutsch & Hayden's work, including the concept of local branching and the more general analysis by Raymond-Robichaud (2021)
In a previous paper, Hayden and I ( Deutsch & Hayden 2000 Proc. R. Soc. Lond. A 456 , 1759–1774. ( doi:10.1098/rspa.2000.0585 )) proved, using the Heisenberg picture, that quantum physics satisfies Einstein's criterion of locality. Wallace and Timpson ( Wallace & Timpson 2007 Found. Phys. 37 , 951–955. ( doi:10.1007/s10701-007-9135-7 )) have argued that certain transformations of the Heisenberg-picture description of a quantum system must be regarded as leaving invariant the factual situation being described, and that taking this into account reveals that Einstein's criterion is violated after all. Here, I vindicate the proof and explain some misconceptions that have led to this and other criticisms of it.
It has been more than 20 years since Deutsch and Hayden demonstrated that quantum systems can be completely described locally-notwithstanding Bell's theorem. More recently, Raymond-Robichaud proposed two other approaches to the same conclusion. In this paper, all these means of describing quantum systems locally are proved formally equivalent. The cost of such descriptions is then quantified by the dimensionality of their underlining space. The number of degrees of freedom of a single qubit's local description is shown to grow exponentially with the total number of qubits considered as a global system. This apparently unreasonable cost to describe such a small system in a large Universe is nonetheless shown to be expected. Finally, structures that supplement the universal wave function are investigated.