A visual representation of the properties of pre- and post- selected entangled systems

TL;DR

This paper introduces a visual framework for representing and analyzing entangled quantum systems with pre- and post-selected states, revealing equivalences between different quantum effects and enabling the realization of complex multi-qubit interactions.

Contribution

It presents a novel visual representation method for entangled quantum systems, demonstrating equivalences between experiments and generalizing multi-qubit interactions beyond pairwise interactions.

Findings

Equivalence between the quantum Cheshire cat and Hardy's paradox experiments.

Ability to realize multiwise interactions among qubits.

Weak values of product operators encode complete information about individual weak values.

Abstract

We introduce a visual representation for generating entangled-based quantum effects under pre- and post- selected states that allows us to reveal equivalence between seemingly different quantum effects. We show how to realize entangled quantum systems of an arbitrary number of qubits from a single or pre-specified number of physical particles. We then show that a variation of the quantum Cheshire cat experiment and Hardy's paradox are equivalent and propose a class of experiments that generalizes both experiments. We show that the weak values of the products of projection operators allow us to get the weak value of each projection operator, implying that the weak value of the product of projection operators includes the entire information about the weak values in the system. In nature, interactions can only be acted between a pair of particles. We show how to realize quantum systems of multiwise interacted qubits, i.e., interactions that come in groups of n>2 qubits. In this way, we are able to propose unique quantum systems that consist of interacted groups of entangled states. The proposed framework opens the door toward a new way to explore quantum systems of entangled particles and quantum phenomena that emerge from such a general setting.