Macroscopic limit of nonclassical correlations

Abstract

We consider macroscopic correlations in a bipartite system consisting of 2N particles described by a generalised probabilistic theory. In particular, we discuss a case of N PR-boxes shared between two parties. We characterise macroscopic measurements as collective measurements of the same property on all the boxes in the same region. Such measurements are assumed to reveal only the average value of the measured collective property. We show that for two measurements per observer and N ≥ 2 there always exist a joint probability distribution explaining all observable data and therefore the system admits local hidden variables. Next, we generalise this result to include measurement of fluctuations and additional measurement settings. Finally, we discuss our result in the context of previous works in which contradictory results were presented.

Bipartite nonlocality with a many-body system

“…Since the CHSH inequality is a non-trivial Bell inequality with N=1 spin locally, we focus on the case with N=2 spins locally. We know from [15,16] that in this case, one needs at least 3 measurements settings locally to circumvent known local models and thus possibly violate a Bell inequality of the form (8) with collective measurements.…”

“…The aim of this section is to study bi-partite Bell inequalities using only first order moments of collective spin components. Before we start, it is worth mentioning the result presented in [15,16] stating that no such inequality can be violated in our context when the number of settings is less than the number of local spins. Even if this puts stringent requirements on experiments on many-body systems, we want to know if this result holds without restriction on the number of settings.…”

“…There are thus at least two reasons for looking for Bell inequalities of the form (2) despite the result from [15,16] stating that no such inequality can be violated in our setting when the number of settings is less than the number of local spins, i.e.  m N .…”

“…k is a vector having the 3 Pauli matrices as components and a  is a unit length vector with components α x , While entanglement witnesses have been intensively studied in this scenario with first order moments [12][13][14], few results are known with respect to Bell inequality violations. One noticeable exception is [15,16] where authors showed that bipartite correlations issued from first order collective measurements can be reproduced by a local model if the number of measurement settings is smaller or equal to n A for Alice and n B for Bob. In section 2, we give numerical arguments suggesting that such a bipartite Bell violation may not be possible when considering only first order moments, independently of the number of settings.…”

Nonlocal correlations in a macroscopic measurement scenario

“…In order to study macroscopic properties of a correlation, one must take a measurement scheme on many copies of the correlation where the identity of individual particles involved in the correlation should not be revealed [29]. A practically relevant scheme for studying such macroscopicity of correlations is to consider a case when the identity of the individual particles in the correlations gets lost during the distribution of the correlated state.…”