Promoting quantum correlations in DQC1 model via post-selection

TL;DR

This paper demonstrates that applying post-selection to the DQC1 quantum computing model can generate entanglement and Bell nonlocality, potentially transforming it into a universal quantum computing model.

Contribution

Introducing a purification process via post-selection in DQC1 enhances quantum correlations, including entanglement and Bell nonlocality, which were absent in the standard model.

Findings

Small purification suffices to generate entanglement and Bell nonlocality.

Repeated purification yields 99% purity in the auxiliary qubit.

Almost maximally entangled states violate Bell's inequality significantly.

Abstract

The deterministic quantum computation with one qubit (DQC1) model is a restricted model of quantum computing able to calculate efficiently the normalized trace of a unitary matrix. In this work we analyse the quantum correlations named entanglement, Bell's nonlocality, quantum discord, and coherence generated by the DQC1 circuit considering only two qubits (auxiliary and control). For the standard DQC1 model only quantum discord and coherence appear. By introducing a filter in the circuit we purify the auxiliary qubit taking it out from the totally mixed state and consequently promoting other quantum correlations between the qubits, such as entanglement and Bell's nonlocality. Through the optimization of the purification process we conclude that even a small purification is enough to generate entanglement and Bell's nonlocality. We obtain, in average, that applying the purification process repeatedly by twelve times the auxiliary qubit becomes 99% pure. In this situation, almost maximally entangled states are achieved, which by its turn, almost maximally violate the Bell's inequality. This result suggests that with a simple modification the DQC1 model can be promoted to a universal model of quantum computing.