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This paper reviews the progress that has been made in our knowledge ofquantum correlations at the mesoscopic and macroscopic level. We begin bysummarizing the Einstein-Podolsky-Rosen (EPR) argument and the Bellcorrelations that cannot be explained by local hidden variable theories. It wasoriginally an open question as to whether (and how) such quantum correlationscould occur on a macroscopic scale, since this would seem to counter thecorrespondence principle. The purpose of this review is to examine how thisquestion has been answered over the decades since the original papers of EPRand Bell. We first review work relating to higher spin measurements whichrevealed that macroscopic quantum states could exhibit Bell correlations. Thiscovers higher dimensional, multi-particle and continuous-variable EPR and Bellstates where measurements on a single system give a spectrum of outcomes, andalso multipartite states where measurements are made at multiple separatedsites. It appeared that the macroscopic quantum observations were for anincreasingly limited span of measurement settings and required a fineresolution of outcomes. Motivated by this, we next review correlations formacroscopic superposition states, and examine predictions for the violation ofLeggett-Garg inequalities for dynamical quantum systems. These results revealBell correlations for coarse-grained measurements which need only distinguishbetween macroscopically distinct states, thus bringing into question thevalidity of certain forms of macroscopic realism. Finally, we review progressfor massive systems, including Bose-Einstein condensates and optomechanicaloscillators, where EPR-type correlations have been observed between massivesystems. Experiments are summarized, which support the predictions of quantummechanics in mesoscopic regimes.

Mesoscopic and macroscopic quantum correlations in photonic, atomic and optomechanical systems