Bell Nonlocality in Classical Systems Coexisting with Other System Types

The realistic interpretation of classical theory assumes that every classical system has well-defined properties, which may be unknown to the observer but are nevertheless part of reality and can, in principle, be revealed by measurements. Here we show that this interpretation can, in principle, be falsified if classical systems coexist with other types of physical systems. To make this point, we construct a toy theory that (i) includes classical theory as a subtheory and (ii) allows classical systems to be entangled with another type of system, called anticlassical. We show that our toy theory allows for the violation of Bell inequalities in two-party scenarios where one of the settings corresponds to a local measurement performed on a classical system alone. Building on this fact, we show that measurement outcomes in classical theory cannot, in general, be regarded as predetermined by the state of an underlying reality.

Figure 1

In a universe described by our toy theory, an observer who has access only to classical systems (represented by red disks on the left) would see a world described by classical theory. The same situation applies to an observer with access only to anticlassical systems (blue disks on the right). In contrast, observers with access to both types of systems can observe Bell nonlocality and other nonclassical features.

Figure 2

Activation of Bell nonlocality with bit-antibit entangled pairs. Alice (left) and Bob (right) perform local measurements on two copies of an entangled state of a bit-antibit pair. The first copy (top) involves bit $B_1$ and antibit $A_1$, while the second copy (bottom) involves bit $B_2$ and antibit $A_2$. Alice’s and Bob’s laboratories (represented by dotted boxes) contain systems $B_1{A}_2$ and $A_2{B}_1$, respectively. Their measurements have settings $x$ and $y$, respectively, and produce outcomes $a$ and $b$, respectively.