Method for Generating Randomly Perturbed Density Operators Subject to Different Sets of Constraints

TL;DR

This paper introduces a versatile method for generating randomly perturbed quantum density operators under various constraints, useful for simulating noise effects in quantum systems and analyzing entanglement sensitivity.

Contribution

The paper presents a novel general approach for creating constrained, randomly perturbed density operators, applicable to bipartite qubit systems and experimental quantum device simulations.

Findings

Method effectively simulates noise in quantum states.

Perturbation impacts on entanglement measures are characterized.

Perturbed states match experimental Bell states on IBM quantum hardware.

Abstract

This paper presents a general method for producing randomly perturbed density operators subject to different sets of constraints. The perturbed density operators are a specified "distance" away from the state described by the original density operator. This approach is applied to a bipartite system of qubits and used to examine the sensitivity of various entanglement measures on the perturbation magnitude. The constraint sets used include constant energy, constant entropy, and both constant energy and entropy. The method is then applied to produce perturbed random quantum states that correspond with those obtained experimentally for Bell states on the IBM quantum device ibmq_manila. The results show that the methodology can be used to simulate the outcome of real quantum devices where noise, which is important both in theory and simulation, is present.