Optimal verification of general bipartite pure states

Xiao-Dong Yu,Otfried Gühne,Jiangwei Shang

doi:10.1038/s41534-019-0226-z

Abstract

The efficient and reliable verification of quantum states plays a crucial role in various quantum information processing tasks. We consider the task of verifying entangled states using one-way and two-way classical communication and completely characterize the optimal strategies via convex optimization. We solve these optimization problems using both analytical and numerical methods, and the optimal strategies can be constructed for any bipartite pure state. Compared with the nonadaptive approach, our adaptive strategies significantly improve the efficiency of quantum state verification. Moreover, these strategies are experimentally feasible, as only few local projective measurements are required.

Highlights

A basic yet important step in most quantum information processing tasks is to efficiently and reliably characterize a quantum state
Full tomographic information is often not required, and a lot of effort has been devoted to characterizing quantum states with nontomographic methods.[5,6,7,8]
Quantum state verification is a procedure for gaining confidence that the output of some quantum device is a particular state by employing local measurements.[9]

Summary

Introduction

A basic yet important step in most quantum information processing tasks is to efficiently and reliably characterize a quantum state. For each state σk the verifier may apply a different measurement with verification strategy some predefined can be expressed apsroΩba1⁄4biP lityni1⁄4. To achieve an optimal strategy, we need to maximize vðΩÞ over all accessible measurements. To the best of our knowledge, the only optimal strategy reported is the verification of two-qubit pure states with local projective measurements (PMs).[9]

Results

Conclusion