Classical causal models for Bell and Kochen-Specker inequality violations require fine-tuning

Nonlocality and contextuality are at the root of conceptual puzzles in quantum mechanics, and are key resources for quantum advantage in information-processing tasks. Bell nonlocality is best understood as the incompatibility between quantum correlations and the classical theory of causality, applied to relativistic causal structure. Contextuality, on the other hand, is on a more controversial foundation. In this work, I provide a common conceptual ground between nonlocality and contextuality as violations of classical causality. First, I show that Bell inequalities can be derived solely from the assumptions of no-signalling and no-fine-tuning of the causal model. This removes two extra assumptions from a recent result from Wood and Spekkens, and remarkably, does not require any assumption related to independence of measurement settings -- unlike all other derivations of Bell inequalities. I then introduce a formalism to represent contextuality scenarios within causal models and show that all classical causal models for violations of a Kochen-Specker inequality require fine-tuning. Thus the quantum violation of classical causality goes beyond the case of space-like separated systems, and manifests already in scenarios involving single systems.Comment: 9 pages, 14 figures. Modified title, discussion and presentatio

Weak values in a classical theory with an epistemic restriction

Weak measurement of a quantum system followed by postselection based on a subsequent strong measurement gives rise to a quantity called the weak value: a complex number for which the interpretation has long been debated. We analyse the procedure of weak measurement and postselection, and the interpretation of the associated weak value, using a theory of classical mechanics supplemented by an epistemic restriction that is known to be operationally equivalent to a subtheory of quantum mechanics. Both the real and imaginary components of the weak value appear as phase space displacements in the postselected expectation values of the measurement device's position and momentum distributions, and we recover the same displacements as in the quantum case by studying the corresponding evolution in the classical theory. By using this analogous classical theory, we gain insight into the appearance of the weak value as a result of the statistical effects of post selection, and this provides us with an operational interpretation of the weak value, both its real and imaginary parts. We find that the imaginary part of the weak value is a measure of how much postselection biases the mean phase space distribution for a given amount of measurement disturbance. All such biases proportional to the imaginary part of the weak value vanish in the limit where disturbance due to measurement goes to zero. Our analysis also offers intuitive insight into how measurement disturbance can be minimised and the limits of weak measurement.Comment: 9 pages, 2 figures, comments welcome; v2 added some references; v3 published versio

Causation, decision theory, and Bell's theorem: a quantum analogue of the Newcomb problem

I apply some of the lessons from quantum theory, in particular from Bell's theorem, to a debate on the foundations of decision theory and causation. By tracing a formal analogy between the basic assumptions of Causal Decision Theory (CDT)--which was developed partly in response to Newcomb's problem-- and those of a Local Hidden Variable (LHV) theory in the context of quantum mechanics, I show that an agent who acts according to CDT and gives any nonzero credence to some possible causal interpretations underlying quantum phenomena should bet against quantum mechanics in some feasible game scenarios involving entangled systems, no matter what evidence they acquire. As a consequence, either the most accepted version of decision theory is wrong, or it provides a practical distinction, in terms of the prescribed behaviour of rational agents, between some metaphysical hypotheses regarding the causal structure underlying quantum mechanics.Comment: Cross-posted in http://philsci-archive.pitt.edu/archive/00004872