Collective Operations Can Exponentially Enhance Quantum State Verification

Abstract

Maximally entangled states are a key resource in many quantum communication and computation tasks, and their certification is a crucial element to guarantee the desired functionality. We introduce collective strategies for the efficient, local verification of ensembles of Bell pairs that make use of an initial information and noise transfer to few copies prior to their measurement. In this way the number of entangled pairs that need to be measured and hence destroyed is significantly reduced as compared to previous, even optimal, approaches that operate on individual copies. Moreover the remaining states are directly certified. We show that our tools can be extended to other problems and larger classes of multipartite states.

arXiv comment5 pages, 2 figures

References in corpus (30)

• The Quantum Internet
• Quantum cryptography: Public key distribution and coin tossing
• Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels
• Efficient quantum state tomography
• Distributed Quantum Computation over Noisy Channels
• Direct Fidelity Estimation from Few Pauli Measurements
• Quantum certification and benchmarking
• Classification of multi-qubit mixed states: separability and distillability properties
• Multiparticle entanglement purification for graph states
• Verifiable measurement-only blind quantum computing with stabilizer testing
• Verification of quantum computation: An overview of existing approaches
• A quantum network stack and protocols for reliable entanglement-based networks
• Optimal verification of entangled states with local measurements
• Towards Large-Scale Quantum Networks
• Modular architectures for quantum networks
• Distributing Graph States Over Arbitrary Quantum Networks
• Efficient bipartite quantum state purification in arbitrary dimensional Hilbert spaces
• Tools for quantum network design
• Entanglement purification protocols for all graph states
• Quantum gates on hybrid qudits
• Opportunistic Entanglement Distribution for the Quantum Internet
• Optimal Verification of Two-Qubit Pure States
• Optimal verification and fidelity estimation of maximally entangled states
• Statistical Methods for Quantum State Verification and Fidelity Estimation
• Entanglement-assisted entanglement purification
• Efficient verification of bipartite pure states
• Experimental Optimal Verification of Entangled States using Local Measurements
• Efficient entanglement purification protocols for d-level systems
• Entanglement purification by counting and locating errors with entangling measurements
• Quantum verification and estimation with few copies

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