Device-Independent Certification of Genuinely Entangled Subspaces

Abstract

Self-testing is a procedure for characterizing quantum resources with the minimal level of trust. Up to now it has been used as a device-independent certification tool for particular quantum measurements, channels, and pure entangled states. In this work we introduce the concept of self-testing more general entanglement structures. More precisely, we present the first self-tests of an entangled subspace - the five-qubit code and the toric code. We show that all quantum states maximally violating a suitably chosen Bell inequality must belong to the corresponding code subspace, which remarkably includes also mixed states.

arXiv comment14 pages (5 + appendices), 6 figures

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Cited by in corpus (23)

• Understanding the interplay of entanglement and nonlocality: motivating and developing a new branch of entanglement theory
• Quantum computational advantage with string order parameters of 1D symmetry-protected topological order
• Self-testing maximally-dimensional genuinely entangled subspaces within the stabilizer formalism
• Self-testing quantum states via nonmaximal violation in Hardy's test of nonlocality
• Universal construction of genuinely entangled subspaces of any size
• Simple sufficient condition for subspace to be completely or genuinely entangled
• Scalable Bell inequalities for graph states of arbitrary prime local dimension and self-testing
• Fully non-positive-partial-transpose genuinely entangled subspaces
• Deriving three-outcome permutationally invariant Bell inequalities
• Experimental self-testing for photonic graph states
• A universal scheme to self-test any quantum state or measurement
• Self-testing composite measurements and bound entangled state in a single quantum network
• Experimentally Certified Transmission of a Quantum Message through an Untrusted and Lossy Quantum Channel via Bell's Theorem
• Almost device-independent certification of GME states with minimal measurements
• All genuinely entangled stabilizer subspaces are multipartite fully nonlocal
• Guarantees on the structure of experimental quantum networks
• Counterexamples in self-testing
• Wigner's approach enabled detection of multipartite nonlocality using all different bipartitions
• Blindly Verifying Unknown Entanglement without State Tomography
• Coarse-grained self-testing
• GHZ-W Genuinely Entangled Subspace Verification with Adaptive Local Measurements
• Frustration graph formalism for qudit observables
• Exploring Bell nonlocality of quantum networks with stabilizing and logical operators