From no causal loop to absoluteness of cause: discarding the quantum NOT logic

TL;DR

This paper introduces the principle of absoluteness of cause in quantum theory, deriving a no-go result that rules out certain quantum devices and analyzing implications of violating this principle.

Contribution

It formulates the AC principle in quantum context, deriving a fundamental no-go theorem and exploring the consequences of its violation within generalized probability theories.

Findings

The AC principle restricts cause-effect relations in quantum systems.

A no-go theorem rules out universal quantum NOT devices under AC.

Violations of AC imply signaling or non-local tomography.

Abstract

The principle of `absoluteness of cause' (AC) assumes the cause-effect relation to be observer independent and is a distinct assertion than prohibiting occurrence of any causal loop. Here, we study implication of this novel principle to derive a fundamental no-go result in quantum world. AC principle restrains the `time order' of two spacelike separated events/processes to be a potential cause of another event in their common future, and in turn negates existence of a quantum device that transforms an arbitrary pure state to its orthogonal one. The present {\it no-go} result is quite general as its domain of applicability stretches out from the standard linear quantum theory to any of its generalizations allowing deterministic or stochastic nonlinear evolution. We also analyze different possibilities of violating the AC principle in generalized probability theory framework. A strong form of violation enables instantaneous signaling, whereas a weak form of violation forbids the theory to be locally tomographic. On the other hand, impossibility of an intermediate violation suffices to discard the universal quantum NOT logic.