Optimal Verification of the Bell State and Greenberger-Horne-Zeilinger States in Untrusted Quantum Networks
arXiv:2111.02800 · doi:10.1038/s41534-021-00499-8
Abstract
Bipartite and multipartite entangled states are basic ingredients for constructing quantum networks and their accurate verification is crucial to the functioning of the networks, especially for untrusted networks. Here we propose a simple approach for verifying the Bell state in an untrusted quantum network in which one party is not honest. Only local projective measurements are required for the honest party. It turns out each verification protocol is tied to a probability distribution on the Bloch sphere and its performance has an intuitive geometric meaning. This geometric picture enables us to construct the optimal and simplest verification protocols, which are also very useful to detecting entanglement in the untrusted network. Moreover, we show that our verification protocols can achieve almost the same sample efficiencies as protocols tailored to standard quantum state verification. Furthermore, we establish an intimate connection between the verification of Greenberger-Horne-Zeilinger states and the verification of the Bell state. By virtue of this connection we construct the optimal protocol for verifying Greenberger-Horne-Zeilinger states and for detecting genuine multipartite entanglement.
arXiv comment8+21 pages, 4+2 figures, and 1 table; published in npj Quantum Information
References in corpus (50)
- Quantum entanglement
- Entanglement of Formation of an Arbitrary State of Two Qubits
- The Quantum Internet
- Experimental quantum teleportation
- Quantum secret sharing
- Bell nonlocality
- Entanglement detection
- Device-independent security of quantum cryptography against collective attacks
- Steering, Entanglement, Nonlocality, and the EPR Paradox
- Multi-party entanglement in graph states
- The Uncertainty Principle in the Presence of Quantum Memory
- One-sided Device-Independent Quantum Key Distribution: Security, feasibility, and the connection with steering
- Quantum Steering
- Experimental Demonstration of Five-photon Entanglement and Open-destination Teleportation
- Direct Fidelity Estimation from Few Pauli Measurements
- Experimental EPR-Steering of Bell-local States
- Self-testing of quantum systems: a review
- Quantum certification and benchmarking
- Certified randomness in quantum physics
- Robust Self Testing of the Singlet
- Long-Distance Measurement-Device-Independent Multiparty Quantum Communication
- Detection of entanglement in asymmetric quantum networks and multipartite quantum steering
- Quantum Steering Ellipsoids
- Experimental demonstration of graph-state quantum secret sharing
- Analytic and nearly optimal self-testing bounds for the Clauser-Horne-Shimony-Holt and Mermin inequalities
- Robust and versatile black-box certification of quantum devices
- Experimental Verification of Multipartite Entanglement in Quantum Networks
- Optimal verification of entangled states with local measurements
- On the fidelity of mixed states of two qubits
- Efficient Verification of Pure Quantum States in the Adversarial Scenario
- Multipartite entanglement verification resistant against dishonest parties
- Rigidity of quantum steering and one-sided device-independent verifiable quantum computation
- Anonymity for practical quantum networks
- A study of LOCC-detection of a maximally entangled state using hypothesis testing
- General framework for verifying pure quantum states in the adversarial scenario
- Self-testing through EPR-steering
- Anonymous Quantum Conference Key Agreement
- Optimal Verification of Two-Qubit Pure States
- Optimal verification and fidelity estimation of maximally entangled states
- Self-guaranteed measurement-based quantum computation
- Efficient verification of bipartite pure states
- Optimal verification of general bipartite pure states
- Experimental validation of quantum steering ellipsoids and tests of volume monogamy relations
- Group theoretical study of LOCC-detection of maximally entangled state using hypothesis testing
- Optimal Verification of Greenberger-Horne-Zeilinger States
- Optimal verification of stabilizer states
- Phase-Matching Quantum Cryptographic Conferencing
- Self-testing of a single quantum device under computational assumptions
- Counting Classical Nodes in Quantum Networks
- Zero Uncertainty States in the Presence of Quantum Memory