Quantum networks self-test all entangled states

Abstract

Certifying quantum properties with minimal assumptions is a fundamental problem in quantum information science. Self-testing is a method to infer the underlying physics of a quantum experiment only from the measured statistics. While all bipartite pure entangled states can be self-tested, little is known about how to self-test quantum states of an arbitrary number of systems. Here, we introduce a framework for network-assisted self-testing and use it to self-test any pure entangled quantum state of an arbitrary number of systems. The scheme requires the preparation of a number of singlets that scales linearly with the number of systems, and the implementation of standard projective and Bell measurements, all feasible with current technology. When all the network constraints are exploited, the obtained self-testing certification is stronger than what is achievable in any Bell-type scenario. Our work does not only solve an open question in the field, but also shows how properly designed networks offer new opportunities for the certification of quantum phenomena.

30 pages (24 pages of appendices), 6 figures, 1 table

References in corpus (12)

• Device-independent security of quantum cryptography against collective attacks
• Device-independent quantum key distribution secure against collective attacks
• Optimal Remote State Preparation
• Quantum theory based on real numbers can be experimentally falsified
• Bell nonlocality in networks
• Measurement-Device-Independent Entanglement Witnesses for All Entangled Quantum States
• Robust and versatile black-box certification of quantum devices
• Robust self testing of the 3-qubit $W$ state
• Device-independent tomography of multipartite quantum states
• Quantum nonlocality in networks can be demonstrated with an arbitrarily small level of independence between the sources
• Sample-efficient device-independent quantum state verification and certification
• Quantum verification and estimation with few copies

Cited by in corpus (24)

• Proofs of network quantum nonlocality in continuous families of distributions
• Custom Bell inequalities from formal sums of squares
• Certification of the maximally entangled state using non-projective measurements
• Network quantum steering enables randomness certification without seed randomness
• All Real Projective Measurements Can be Self-tested
• Symmetric quantum states: a review of recent progress
• Model-independent inference of quantum interaction from statistics
• Two convergent NPA-like hierarchies for the quantum bilocal scenario
• $(n,m,p)$-type quantum network configuration and its nonlocality
• A universal scheme to self-test any quantum state or measurement
• Operationally independent events can influence each other in quantum theory
• Constant-sized self-tests for maximally entangled states and single projective measurements
• Cost of Locally Approximating High-Dimensional Ground States of Contextual Quantum Models
• Experimental genuine quantum nonlocality in the triangle network
• Translating Bell Non-Locality to Prepare-and-Measure Scenarios under Dimensional Constraints
• Topologically noise robust network steering without inputs
• Neural networks with quantum states of light
• The genuinely multipartite nonlocality of graph states is model-dependent
• Expanding bipartite Bell inequalities for maximum multi-partite randomness
• Parallel remote state preparation for fully device-independent verifiable blind quantum computation
• Robust self-testing and certified randomness based on chained Bell inequality
• Device-independent quantum state discrimination
• Certifying classes of $d$-outcome measurements with quantum steering
• Any gate of a quantum computer can be certified device-independently