Measurement Disturbance Relation as a Principle for Multipartite Quantum Correlations

In this work, we find that generally the measurement disturbance relation (MDR) may be transformed into a constraint inequality of the multipartite correlations functions. In this scheme, the various forms of MDR give different bounds for the strength of particle correlations, which suggests that the MDR may stand as a underlying physical principle determining the multipartite non-locality. Hence, the validity of the different MDRs can be verified by measuring the correlation functions. Quantum non-locality and the Heisenberg’s uncertainty principle [1] are two essential concepts in quantum mechanics (QM). The nonclassical information shared among different parts forms the basis of quantum information and is responsible for many counterintuitive features of QM, e.g. quantum cryptography [2], quantum teleportation [3]. Principles from information theory have been proposed to specify the quantum correlations, including for example non-trivial communication complexity [4], information causality [5], entropic uncertainty relations [6], local orthogonality [7], and global exclusivity [8, 9]. These principles generally stem from information concepts, many of which explain only bipartite correlations. It has been shown that the determining of the quantum correlations requires principles of an intrinsically multipartite structure [10], and it is rather difficult to derive the Hilbert space structure of QM from information quantities alone. ∗corresponding author; qiaocf@ucas.ac.cn 1 Heisenberg’s uncertainty principle on the other hand plays a fundamental role in quantum measurement and solely concerning the MDR does it reflect the measurement precision and the disturbance of the quantum system. The well-known Heisenberg-Robertson uncertainty relation [11] ∆A∆B ≥ |〈C〉| , C = 1 2i [A,B] , (1) with the standard deviation ∆X = √ 〈ψ|X2|ψ〉 − 〈ψ|X|ψ〉2 for X = A, or B, however involves only the properties of two observables within an ensemble of a quantum state and is independent with specific measurement processes. At present, the MDR is an intensively studied subject both theoretically [12–16] and experimentally [17–20]. There are not only a divergent forms of MDR survived the experiments [19, 20], but also the doubts on their practical importance in quantum information science [21, 22]. As the uncertainty principle is the basis of QM, slight alteration of the MDR may result in grave consequences in QM, especially in quantum measurement [23]. A fundamental question then arises: What practical role would the MDR play in quantum physics? Here we present a general scheme where the MDR, as a fundamental measurement principle, may be transformed into constraint inequality on multipartite correlation functions. The range of the measurement precision and disturbance attainable by the MDR gives the supremum on the bipartite correlations in multipartite state. Thus, the strength of correlations in multipartite state may be considered as the physical consequences of the restriction on the measurement imposed by the MDR, and the variant forms of MDR have the physical meaning of predicting distinct types of correlations. The experimental verification of the validity of various MDRs also becomes straightforward by measuring the correlation functions with various physical systems where two such experiments involving twoand four-dimensional quantum systems are proposed.