de Finetti reductions for correlations

Abstract

When analysing quantum information processing protocols one has to deal with large entangled systems, each consisting of many subsystems. To make this analysis feasible, it is often necessary to identify some additional structure. de Finetti theorems provide such a structure for the case where certain symmetries hold. More precisely, they relate states that are invariant under permutations of subsystems to states in which the subsystems are independent of each other. This relation plays an important role in various areas, e.g., in quantum cryptography or state tomography, where permutation invariant systems are ubiquitous. The known de Finetti theorems usually refer to the internal quantum state of a system and depend on its dimension. Here we prove a different de Finetti theorem where systems are modelled in terms of their statistics under measurements. This is necessary for a large class of applications widely considered today, such as device independent protocols, where the underlying systems and the dimensions are unknown and the entire analysis is based on the observed correlations.

5+13 pages; second version closer to the published one; new title

References in corpus (6)

• Bell nonlocality
• Device-independent quantum key distribution secure against collective attacks
• Post-selection technique for quantum channels with applications to quantum cryptography
• Limits of privacy amplification against non-signalling memory attacks
• Finite de Finetti theorem for conditional probability distributions describing physical theories
• Non-signalling parallel repetition using de Finetti reductions

Cited by in corpus (12)

• Simple and tight device-independent security proofs
• Entropy accumulation
• Experimental robust self-testing of the state generated by a quantum network
• Semidefinite programming hierarchies for constrained bilinear optimization
• Parallel repetition and concentration for (sub-)no-signalling games via a flexible constrained de Finetti reduction
• Postselection technique for optical Quantum Key Distribution with improved de Finetti reductions
• The black hole information puzzle and the quantum de Finetti theorem
• Reductions to IID in Device-independent Quantum Information Processing
• Optimising the relative entropy under semidefinite constraints
• A de Finetti theorem for quantum causal structures
• De Finetti Theorems for Quantum Conditional Probability Distributions with Symmetry
• de Finetti reductions for partially exchangeable probability distributions