Efficient verification of bipartite pure states
arXiv:1901.09783 · doi:10.1103/PhysRevA.100.032316
Abstract
We propose practical and efficient protocols for verifying bipartite pure states for any finite dimension, which can also be applied to fidelity estimation. Our protocols are based on adaptive local projective measurements with either one-way or two-way communications, which are very easy to implement in practice. They can extract the key information much more efficiently than known protocols based on tomography or direct fidelity estimation, and their efficiencies are comparable to the best protocols based on entangling measurements. These protocols highlight the significance of mutually unbiased bases (MUBs) and complex projective 2-designs in quantum state verification and fidelity estimation. Moreover, our protocols can be applied to the adversarial scenario, in which states are controlled by a malicious adversary. In this case, surprisingly, one of our protocols based on local measurements is even optimal among protocols without locality restriction.
arXiv comment5.5 pages, 1 figure; published in PRA
References in corpus (19)
- Quantum entanglement
- Scalable multi-particle entanglement of trapped ions
- Symmetric Informationally Complete Quantum Measurements
- On mutually unbiased bases
- Direct Fidelity Estimation from Few Pauli Measurements
- Tight informationally complete quantum measurements
- Verifiable measurement-only blind quantum computing with stabilizer testing
- Optimal verification of entangled states with local measurements
- Efficient Verification of Pure Quantum States in the Adversarial Scenario
- Verification of Many-Qubit States
- Weighted complex projective 2-designs from bases: optimal state determination by orthogonal measurements
- A study of LOCC-detection of a maximally entangled state using hypothesis testing
- General framework for verifying pure quantum states in the adversarial scenario
- Optimal Verification of Two-Qubit Pure States
- Optimal verification and fidelity estimation of maximally entangled states
- Optimal verification of general bipartite pure states
- Group theoretical study of LOCC-detection of maximally entangled state using hypothesis testing
- Mutually unbiased bases as minimal Clifford covariant 2-designs
- Discrete realization of group symmetric LOCC-detection of maximally entangled state
Cited by in corpus (39)
- Theory of quantum system certification: a tutorial
- Efficient Verification of Pure Quantum States in the Adversarial Scenario
- General framework for verifying pure quantum states in the adversarial scenario
- Nonstabilizerness determining the hardness of direct fidelity estimation
- Optimal Verification of Two-Qubit Pure States
- Statistical Methods for Quantum State Verification and Fidelity Estimation
- Optimal verification of general bipartite pure states
- Efficient verification of Dicke states
- Direct Fidelity Estimation of Quantum States using Machine Learning
- Optimal Verification of Greenberger-Horne-Zeilinger States
- Optimal verification of stabilizer states
- Towards the standardization of quantum state verification using optimal strategies
- Verification of phased Dicke states
- Efficient verification of quantum processes
- Efficient verification of quantum gates with local operations
- Robust and efficient verification of graph states in blind measurement-based quantum computation
- Quantum gate verification and its application in property testing
- Universally Optimal Verification of Entangled States with Nondemolition Measurements
- Dense Coding with Locality Restriction for Decoder: Quantum Encoders vs. Super-Quantum Encoders
- Efficient verification of Affleck-Kennedy-Lieb-Tasaki states
- Quantum Measurements in the Light of Quantum State Estimation
- Efficient verification of entangled continuous-variable quantum states with local measurements
- Efficient Verification of Ground States of Frustration-Free Hamiltonians
- Collective Operations Can Exponentially Enhance Quantum State Verification
- Efficient verification of arbitrary entangled states with homogeneous local measurements
- Experimental optimal verification of three-dimensional entanglement on a silicon chip
- Proof-of-principle experimental demonstration of quantum gate verification
- Adaptive State Fidelity Estimation for Higher Dimensional Bipartite Entanglement
- Nondestructive Verification of Entangled States via Fidelity Witnessing
- Scalable Experimental Bounds for Entangled Quantum State Fidelities
- Cyclic measurements and simplified quantum state tomography
- Verification of entangled states under noisy measurements
- Experimental Verification of Entangled States in the Adversarial Scenario
- Universal and Efficient Quantum State Verification via Schmidt Decomposition and Mutually Unbiased Bases
- Prescriptive preparation and verification of nonstabilizer states
- Efficient verification and fidelity estimation of discrete bipartite squeezed states
- Classical Communication Enhanced Quantum State Verification
- Optimal Verification of the Bell State and Greenberger-Horne-Zeilinger States in Untrusted Quantum Networks
- Beating the Optimal Verification of Entangled States via Collective Strategies