Classical-to-quantum non-signalling boxes

Abstract

Here we introduce the concept of classical input - quantum output (C-Q) non-signalling boxes, a generalisation of the classical input - classical output (C-C) non-signalling boxes. We argue that studying such objects leads to a better understanding of the relation between quantum nonlocality and non-locality beyond quantum mechanics. The main issue discussed in the paper is whether there exist 'genuine' C-Q boxes or all C-Q boxes can be built from objects already known, namely C-C boxes acting on pre-shared entangled quantum particles. We show that large classes of C-Q boxes are non-genuine. In particular, we show that all bi-partite C-Q boxes with outputs that are pure states are non-genuine. We also present various strategies for addressing the general problem, i.e. for multi-partite C-Q boxes which output mixed states, whose answer is still open. Finally, we show that even some very simple non-genuine C-Q boxes require large amounts of C-C nonlocal correlations in order to simulate them.

14 pages, 3 figures, 1 table, accepted for publication in Quantum

References in corpus (18)

• Quantum Nonlocality without Entanglement
• Information Causality as a Physical Principle
• Exact and Approximate Unitary 2-Designs: Constructions and Applications
• Non-local correlations as an information theoretic resource
• Quantum Theory From Five Reasonable Axioms
• A limit on nonlocality in any world in which communication complexity is not trivial
• Spin flips and quantum information for anti-parallel spins
• A glance beyond the quantum model
• Local orthogonality as a multipartite principle for quantum correlations
• Causal and localizable quantum operations
• No quantum advantage for nonlocal computation
• General probabilistic theories: An introduction
• Emergence of Quantum Correlations from Non-Locality Swapping
• Strong nonlocality: A trade-off between states and measurements
• A channel-based framework for steering, non-locality and beyond
• Postquantum common-cause channels: the resource theory of local operations and shared entanglement
• A formalism for steering with local quantum measurements
• The resource theory of nonclassicality of channel assemblages