Evolution of Entanglement Witness of Dicke State under Noise and Error Mitigation

TL;DR

This paper derives and experimentally tests an entanglement witness for four-qubit Dicke states on IBM quantum computers, analyzing noise effects and error mitigation to enhance multipartite entanglement detection.

Contribution

It introduces a theoretical entanglement witness for four-qubit Dicke states and evaluates its performance on real quantum hardware under various noise conditions.

Findings

Maximum witness values of -0.178 and -0.169 on two IBM QPUs.

Noise channels significantly affect the entanglement detection.

Bound on T1 time necessary for successful Dicke state generation.

Abstract

The experimental verification of multipartite entangled states is essential for advancing quantum information processing. Entanglement witnesses (EWs) provide a widely used and experimentally accessible approach for detecting genuinely multipartite entangled states. In this work, we theoretically derive the entanglement witness for the four-qubit Dicke state and experimentally evaluate it on two distinct IBM 127-qubit Quantum Processing Units (QPUs), namely ibm\_sherbrook and ibm\_brisbane. A negative expectation value of the witness operator serves as a sufficient condition for confirming genuine multipartite entanglement. We report the maximum (negative) values of the witness achieved on these QPUs as $-0.178 \pm 0.009$ and $-0.169 \pm 0.002$, corresponding to two different state preparation protocols. Additionally, we theoretically investigate the effect of various noise channels on the genuine entanglement of a four-qubit Dicke state using the Qiskit Aer simulator. We show the behavior of the EW constructed under the assumption of Markovian and non-Markovian amplitude damping and depolarizing noises, bit-phase flip noise, and readout errors. We also investigate the effect of varying thermal relaxation time on the EW, depicting a bound on the $T_1$ time required for successful generation of a Dicke State on a superconducting QPU.