Blindly Verifying Unknown Entanglement without State Tomography

TL;DR

This paper introduces a nonlinear entanglement witness method that verifies unknown quantum entanglement without requiring full state tomography, demonstrating robustness and applicability to various multipartite states.

Contribution

It develops a new nonlinear entanglement witness based on a GHZ-like paradox, enabling verification of unknown entanglement with partial information and noise robustness.

Findings

Verified bipartite entanglement with noise robustness

Generalized to multipartite entangled states including GHZ and cluster states

Applicable to quantum zero-knowledge proof scenarios

Abstract

Quantum entangled states have shown distinguished features beyond any classical state. Many methods like quantum state tomography have been presented to verify entanglement. In this work, we aim to identify unknown entanglements with partial information of the state space by developing a nonlinear entanglement witness. The witness consists of a generalized Greenberger-Horne-Zeilinger-like paradox expressed by Pauli observables, and a nonlinear inequality expressed by density matrix elements. First, we verify unknown bipartite entanglements and study the robustness of entanglement witnesses against the white noise. Second, we generalize such a verification to unknown multipartite entangled states, including the Greenberger-Horne-Zeilinger-type states and the cluster states under local channel operations. Third, we give a quantum-information application related to the quantum zero-knowledge proof. Our results provide a useful method in verifying universal quantum computation resources with robustness against white noises. Our work is applicable to detect unknown entanglement without the state tomography.