Abstract In recent years, quantum nonlocality sharing has attracted widespread research attention. Nevertheless, all existing investigations are built upon the measurement independence assumption. The freedom‑of‑choice loophole originates when measurement settings and hidden variables cannot be guaranteed independent, which corresponds to the regime where the measurement independence assumption no longer holds. This paper pioneers the exploration of quantum nonlocality sharing under measurement-dependent scenarios. By integrating the inherent characteristics of measurement dependence with the optimization of measurement strategies for nonlocality sharing, and quantifying the performance of sequential-measurement-based nonlocality sharing via the experimental occurrence frequency of measurement dependence, we demonstrate that maintaining a certain degree of partial measurement independence is critical to achieving valid nonlocality sharing. Moreover, we analyze the correlation constraints imposed by measurement-dependent local models and clarify the physical boundary between correlations explainable by classical hidden-variable descriptions and those that cannot be reproduced by such models.
Abstract In recent years, quantum nonlocality sharing has attracted widespread research attention. Nevertheless, all existing investigations are built upon the measurement independence assumption. The freedom‑of‑choice loophole originates when measurement settings and hidden variables cannot be guaranteed independent, which corresponds to the regime where the measurement independence assumption no longer holds. This paper pioneers the exploration of quantum nonlocality sharing under measurement-dependent scenarios. By integrating the inherent characteristics of measurement dependence with the optimization of measurement strategies for nonlocality sharing, and quantifying the performance of sequential-measurement-based nonlocality sharing via the experimental occurrence frequency of measurement dependence, we demonstrate that maintaining a certain degree of partial measurement independence is critical to achieving valid nonlocality sharing. Moreover, we analyze the correlation constraints imposed by measurement-dependent local models and clarify the physical boundary between correlations explainable by classical hidden-variable descriptions and those that cannot be reproduced by such models.
It was showed in [Phys. Rev. Lett. 125 090401 (2020)] that there exist unbounded number of independent Bobs who can share quantum nonlocality with a single Alice by performing sequentially measurements on the Bob’s half of the maximally entangled pure two-qubit state. However, from practical perspectives, errors in entanglement generation and noises in quantum measurements will result in the decay of nonlocality in the scenario. In this paper, we analyze the persistency and termination of sharing nonlocality in the noisy scenario. We first obtain the two sufficient conditions under which there exist n independent Bobs who can share nonlocality with a single Alice under noisy measurements and the noisy initial two qubit entangled state. Analyzing the two conditions, we find that the influences on persistency under different kinds of noises can cancel each other out. Furthermore, we describe the change patterns of the maximal nonlocality-sharing number under the influence of different noises. Finally, we extend our investigation to the case of arbitrary finite-dimensional systems.
The work in this thesis focuses on the subject of quantum nonlocality. The fact that the principle of locality is violated in nature is among the most counter-intuitive revelations of the past century. The original proof of the nonlocal nature of quantum mechanics relies on the so-called measurement independence assumption. This assumption has come under scrutiny in recent years, mostly because nonlocality and its implications have found their way into the realm of potential applications. In this thesis, the measurement independence assumption is relaxed and replaced by a form of limited measurement dependence. The resulting set is analyzed and it is shown that the nonlocal features of quantum mechanics resist arbitrary lack of free choice. Additionally, a new perspective on how to deal with the so-called detection loophole is provided by the definition of limited detection locality. Finally, work on applications of quantum nonlocality, specifically entanglement certification and quantification is presented.
The demonstration and use of Bell-nonlocality, a concept that is fundamentally striking and is at the core of applications in device independent quantum information processing, relies heavily on the assumption of measurement independence, also called the assumption of free choice. The latter cannot be verified or guaranteed. In this paper, we consider a relaxation of the measurement independence assumption. We briefly review the results of Phys. Rev. Lett. 113, 190402 (2014), which show that with our relaxation, the set of so-called measurement dependent local (MDL) correlations is a polytope, i.e. it can be fully described using a finite set of linear inequalities. Here we analyze this polytope, first in the simplest case of 2 parties with binary inputs and outputs, for which we give a full characterization. We show that partially entangled states are preferable to the maximally entangled state when dealing with measurement dependence in this scenario. We further present a method which transforms any Bell-inequality into an MDL inequality and give valid inequalities for the case of arbitrary number of parties as well as one for arbitrary number of inputs. We introduce the assumption of independent sources in the measurement dependence scenario and give a full analysis for the bipartite scenario with binary inputs and outputs. Finally, we establish a link between measurement dependence and another strong hindrance in certifying nonlocal correlations: nondetection events.
It is well known that the effect of quantum nonlocality, as witnessed by violation of a Bell inequality, can be observed even when relaxing the assumption of measurement independence, i.e., allowing for the source to be partially correlated with the choices of measurement settings; however, what is the minimal amount of measurement independence needed to observe quantum nonlocality? Here we explore this question and consider models with strong measurement-dependent locality, where measurement choices can be perfectly determined in almost all rounds of the Bell test. Nevertheless, we show that quantum nonlocality can still be observed in this scenario, which we conjecture is minimal within the framework we use. We also discuss potential applications in randomness amplification.
In a recent note, Hance and Hossenfelder (arXiv:2211.01331) recall that "locally causal completions of quantum mechanics are possible, if they violate the assumption [called statistical independence or measurement independence] that the hidden variables do not in any way depend on measurement settings" and that, consequently, the experimental violations of Bell inequalities "show that maintaining local causality requires violating statistical independence". However, Hance and Hossenfelder also argue that "we should (...) look for independent experimental evidence that can distinguish the two different options: non-locality and statistical independence, or locality and violations of statistical independence" and that "the unwillingness to consider theories without statistical independence may be the reason we do not yet have a locally causal theory for the foundations of physics that is consistent with general relativity". Here, we recall that there is a third option, namely, rejecting that measurement outcomes are governed in any way by hidden variables. Moreover, we argue that some recent results in the search for principles singling out the sets of quantum correlations for Bell and Kochen-Specker contextuality scenarios point out that this third option is scientifically more plausible and answers the question of why and how nature produces quantum nonlocality.
This review offers a comprehensive exploration and synthesis of recent advancements in the domain of quantum correlation sharing facilitated through sequential measurements. We initiate our inquiry by delving into the interpretation of the joint probability, laying the foundation for an examination of quantum correlations within the context of specific measurement methods. The subsequent section meticulously explores nonlocal sharing under diverse measurement strategies and scenarios, with a specific focus on investigating the impact of these strategies on the dissemination of quantum nonlocality. Key perspectives such as "asymmetry" and "weak value" are scrutinized through detailed analyses across various scenarios, allowing us to evaluate the potential of nonlocality sharing. We also provide a retrospective overview of experimental endeavors associated with this phenomenon. The third part of our exploration presents research findings on steering sharing, offering clarity on the feasibility of steering sharing and summarizing the distinctive properties of quantum steering sharing in different scenarios. Continuing our journey, the fourth section delves into discussions on the sharing of diverse quantum correlations, encompassing network nonlocality, quantum entanglement, and quantum contextuality. Moving forward, the fifth section conducts a comprehensive review of the progress in the application of quantum correlation sharing, specifically based on sequential measurement strategies. Applications such as quantum random access coding, random number generation, and self-testing tasks are highlighted. Finally, we discuss and list some of the key unresolved issues in this research field, and conclude the entire article.