Is Post Selection Physical: A Device Independent Outlook

TL;DR

This paper investigates whether post-selection can be considered a valid physical process within a device-independent framework, revealing its potential to transform probability distributions and solve complex problems, but also highlighting its practical inefficiencies.

Contribution

The work models post-selection as a device-independent assumption, analyzes its effects on probability distributions, and demonstrates its implications for computational complexity and foundational principles.

Findings

Post-selection can turn no signaling distributions into signaling.

Solving NP problems becomes easier with post-selection, equating Post RP to NP.

Post-selection can violate the pigeonhole principle independently of underlying theories.

Abstract

The basic motivation behind this work is to raise the question that whether post selection can be considered a valid physical transformation (on probability space) or not. We study the consequences of both answers set in a device (theory) independent framework, based only on observed statistics. We start with taking up post-selection as an assumption and model the same using independent devices governed by Boolean functions. We establish analogy between the post selection functions and the general probabilistic games in a two party binary input-output scenario. As an observation, we categorize all possible post-selection functions based on the effect on a uniform input probability distribution. We find that post-selection can transform simple no signaling probability distributions to signaling. Similarly, solving NP complete problems is easy independent of classical or quantum computation (in particular we prove that Post RP = NP). Finally, we demonstrate an instance of the violation of the pigeon hole principle independent of underlying theory. As result of our theory independent modeling we conclude that post-selection as an assumption adds power to the underlying theory. In particular, quantum mechanics benefits more with the post-selection assumption, only because it admits a more general set of allowed probabilities as compared to the local hidden variable model. Without the assumption we associate a device independent efficiency factor to quantify the cost of post selection. Our study shows that in the real world post-selection is not efficient enough to be of any advantage. But from an adversarial perspective it is still of significance. As an application, we obtain robust bounds on faking the bell violation in terms of minimum efficiency required using post selection.