Measurement in control and discrimination of entangled pairs under self-distortion

TL;DR

This paper presents a method to reconstruct and discriminate entangled pairs affected by self-distortion due to Heisenberg interactions and magnetic fields, achieving high fidelity in state recovery and improved discrimination.

Contribution

It introduces a combined process of state reconstruction and discrimination that enhances quantum state fidelity without initial discrimination, applicable to entangled pairs under self-distortion.

Findings

Reconstruction without discrimination achieves fidelity close to 1.

Combined process improves discrimination and faithful re-preparation.

Fidelities surpass 0.9 with optimized measurement strategies.

Abstract

Quantum correlations and entanglement are fundamental resources for quantum information and quantum communication processes. Developments in these fields normally assume these resources stable and not susceptible of distortion. That is not always the case, Heisenberg interactions between qubits can produce distortion on entangled pairs generated for engineering purposes (e. g. for quantum computation or quantum cryptography). Experimental work shows how to produce entangled spin qubits in quantum dots and electron gases, so its identification and control are crucial for later applications. The presence of parasite magnetic fields modifies the expected properties and behavior for which the pair was intended. Quantum measurement and control help to discriminate the original state in order to correct it or, just to try of reconstruct it using some procedures which do not alter their quantum nature. Two different kinds of quantum entangled pairs driven by a Heisenberg Hamiltonian with an additional inhomogeneous magnetic field which becoming self-distorted, can be reconstructed without previous discrimination by adding an external magnetic field, with fidelity close to 1 (with respect to the original state, but without discrimination). After, each state can be more efficiently discriminated. The aim of this work is to show how combining both processes, first reconstruction without discrimination and after discrimination with adequate non-local measurements, it's possible a) improve the discrimination, and b) reprepare faithfully the original states. The complete process gives fidelities better than 0.9. In the meanwhile, some results about a class of equivalence for the required measurements were found. This property lets us select the adequate measurement in order to ease the repreparation after of discrimination, without loss of entanglement.