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Physical Review A

Causal links between operationally independent events in quantum theory

Shubhayan Sarkar

Published Apr 11, 2024• 2 citations
Publisher

Abstract

The work challenges the concept of ``classical independence'' between physical systems by demonstrating that within quantum theory two systems can affect each other despite no observable changes, unveiling the interconnected nature of the quantum world. The findings also unveil potential applications for device-independent certification of quantum states and measurements.

DOI
10.1103/physreva.109.l040202

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The work challenges the concept of ``classical independence'' between physical systems by demonstrating that within quantum theory two systems can affect each other despite no observable changes, unveiling the interconnected nature of the quantum world. The findings also unveil potential applications for device-independent certification of quantum states and measurements.
A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it. – Max Planck, 1936 The only way quantum theory allows us to interact with quantum systems is via quantum processes. Thus, the only way we can extract information about the state of a quantum system is to apply some non-deterministic process and observe which of the branches happened. For that reason, many people refer to the act of applying certain quantum processes as measurement and sometimes even as observation . A consequence of this unfortunate terminology is that one of the most touted ‘strange’ features of quantum theory is often misleadingly described as follows: ‘The mere act of observing a quantum state changes it.’ ‘Misleading’, since the concept of measurement described in the previous paragraph is far from the passive concept of observation familiar from our macroscopic world, but is rather a non-trivial process that will almost always drastically affect the quantum state. So, the mysterious aspect of quantum theory is not that ‘observation’ alters the quantum state but, rather, that it is impossible, even in principle, to ‘observe’ a quantum system in the classical sense. Given this fundamental restriction on how we can extract information from a quantum system, what can we learn about that system by means of a quantum process? The answer is, in fact, very little! First, performing a particular measurement could, for the vast majority of quantum states, yield any outcome i with a non-zero probability. In that case, obtaining an outcome i doesn't tell us much about what the state of the system was. Second, we say ‘was’, because the measurement will moreover irreversibly change the state according to the outcome. So rather than revealing the state of a system, a quantum measurement typically erases that state from history! Nonetheless, these quantum measurements are crucial to quantum theory since they constitute the only interface between us, in our classical world, and the quantum world. The great insight of the quantum computing community is that the non-deterministic changes induced by these quantum measurements are not a nuisance, but rather an extremely useful resource.
In any known description of nature, two physical systems are considered independent of each other if any action on one of the systems does not change the other system. From our classical intuitions about the world, we further conclude that these two systems are not affecting each other in any possible way, and thus these two systems are causally disconnected or they do not influence each other. Building on this idea, we show that in quantum theory such a notion of classical independence is not satisfied, that is, two quantum systems can still influence each other even if any operation on one of the systems does not create an observable effect on the other. For our purpose, we consider the framework of quantum networks and construct a linear witness utilizing the Clauser-Horne-Shimony-Holt inequality. We also discuss one of the interesting applications resulting from the maximal violation of classical independence towards device-independent certification of quantum states and measurements.
Causality is one of the most fundamental notions in physics. Generalized probabilistic theories (GPTs) and the process matrix framework incorporate it in different forms. However, a direct connection between these frameworks remains unexplored. By demonstrating the duality between no-signaling principle and classical processes in tripartite classical systems, and extending some results to multipartite systems, we first establish a strong link between these two frameworks, which are two sides of the same coin. This provides an axiomatic approach to describe the measurement space within both box world and local theories. Furthermore, we describe a logically consistent 4-partite classical process acting as an extension of the quantum switch. By incorporating more than two control states, it allows both parallel and serial application of operations. We also provide a device-independent certification of its quantum variant in the form of an inequality.
The device-independent approach to physics is one where conclusions about physical systems (and hence of Nature) are drawn directly and solely from the observed correlations between measurement outcomes. This operational approach to physics arose as a byproduct of Bell's seminal work to distinguish, via a Bell experiment, quantum correlations from the set of correlations allowed by locally-causal theories. In practice, since one can only perform a finite number of experimental trials, deciding whether an empirical observation is compatible with some class of physical theories will have to be carried out via the task of hypothesis testing. In this paper, we demonstrate how the prediction-based-ratio method---initially developed for performing a hypothesis testing against locally-causal correlations---can be applied to test also other classes of physical theories, such as those constrained only by the nonsignaling principle, and those that are constrained to produce the so-called almost-quantum set of correlations. As an application, we demonstrate how this method allows us to unveil an apparent violation of the nonsignaling conditions in certain experimental data collected in a Bell test. This, in turn, highlights the importance of the randomization of measurement settings, as well as a consistency check of the nonsignaling conditions in a Bell test.