The resource theory of steering

We present an operational framework for Einstein-Podolsky-Rosen steering as a physical resource. To begin with, we characterize the set of steering non-increasing operations (SNIOs) --i.e., those that do not create steering-- on arbitrary-dimensional bipartite systems composed of a quantum subsystem and a black-box device. Next, we introduce the notion of convex steering monotones as the fundamental axiomatic quantifiers of steering. As a convenient example thereof, we present the relative entropy of steering. In addition, we prove that two previously proposed quantifiers, the steerable weight and the robustness of steering, are also convex steering monotones. To end up with, for minimal-dimensional systems, we establish, on the one hand, necessary and sufficient conditions for pure-state steering conversions under stochastic SNIOs and prove, on the other hand, the non-existence of steering bits, i.e., measure-independent maximally steerable states from which all states can be obtained by means of the free operations. Our findings reveal unexpected aspects of steering and lay foundations for further resource-theory approaches, with potential implications in Bell non-locality.Comment: Presentation and structure improve

Causal hierarchy of multipartite Bell nonlocality

As with entanglement, different forms of Bell nonlocality arise in the multipartite scenario. These can be defined in terms of relaxations of the causal assumptions in local hidden-variable theories. However, a characterisation of all the forms of multipartite nonlocality has until now been out of reach, mainly due to the complexity of generic multipartite causal models. Here, we employ the formalism of Bayesian networks to reveal connections among different causal structures that make a both practical and physically meaningful classification possible. Our framework holds for arbitrarily many parties. We apply it to study the tripartite scenario in detail, where we fully characterize all the nonlocality classes. Remarkably, we identify new highly nonlocal causal structures that cannot reproduce all quantum correlations. This shows, to our knowledge, the strongest form of quantum multipartite nonlocality known to date. Finally, as a by-product result, we derive a non-trivial Bell-type inequality with no quantum violation. Our findings constitute a significant step forward in the understanding of multipartite Bell nonlocality and open several venues for future research.Comment: 6 pages + appendix, 3 figures, 3 tables. Minor errors corrected, discovery of strongest form of quantum multipartite non-locality known so far added. v3: text improved. v4: Accepted by Quantu

Scalable experimental estimation of multipartite entanglement

We present an efficient experimental estimation of the multipartite entanglement of mixed quantum states in terms of simple parity measurements.Comment: Three pages, three figure

Nonlocality free wirings and the distinguishability between Bell boxes

Bell nonlocality can be formulated in terms of a resource theory with local-hidden variable models as resourceless objects. Two such theories are known, one built upon local operations assisted by shared randomness (LOSRs) and the other one allowing, in addition, for prior-to-input classical communication. We show that prior communication, although unable to create nonlocality, leads to wirings not only beyond LOSRs but also not contained in a much broader class of (nonlocality-generating) global wirings. Technically, this is shown by proving that it can improve the statistical distinguishability between Bell correlations optimized over all fixed measurement choices. This has implications in nonlocality quantification, and leads us to a natural universal definition of Bell nonlocality measures. To end up with, we also consider the statistical strength of nonlocality proofs. We point out some issues of its standard definition in the resource-theoretic operational framework, and suggest simple fixes for them. Our findings reveal nontrivial features of the geometry of the set of wirings and may have implications in the operational distinguishability of nonlocal behaviors

Gapped Two-Body Hamiltonian for continuous-variable quantum computation

We introduce a family of Hamiltonian systems for measurement-based quantum computation with continuous variables. The Hamiltonians (i) are quadratic, and therefore two body, (ii) are of short range, (iii) are frustration-free, and (iv) possess a constant energy gap proportional to the squared inverse of the squeezing. Their ground states are the celebrated Gaussian graph states, which are universal resources for quantum computation in the limit of infinite squeezing. These Hamiltonians constitute the basic ingredient for the adiabatic preparation of graph states and thus open new venues for the physical realization of continuous-variable quantum computing beyond the standard optical approaches. We characterize the correlations in these systems at thermal equilibrium. In particular, we prove that the correlations across any multipartition are contained exactly in its boundary, automatically yielding a correlation area law.Comment: 4 pages, one figure. New version: typos corrected, one reference added. To appear in PR

Robust-fidelity atom-photon entangling gates in the weak-coupling regime

We describe a simple entangling principle based on the scattering of photons off single emitters in one-dimensional waveguides (or extremely-lossy cavities). The scheme can be applied to photonic qubits encoded in polarization or time-bin, and features a filtering mechanism that works effectively as a built-in error-correction directive. This automatically maps imperfections from weak couplings, atomic decay into undesired modes, frequency mismatches, or finite bandwidths of the incident photonic pulses, into heralded losses instead of infidelities. The scheme is thus adequate for high-fidelity maximally entangling gates even in the weak-coupling regime. These, in turn, can be directly applied to store and retrieve photonic-qubit states, thereby completing an atom-photon interface toolbox, or to sequential measurement-based quantum computations with atomic memories.Comment: 5 pages, 2 figure