We analyze the security and feasibility of a protocol for Quantum Key Distribution (QKD), in a context where only one of the two parties trusts his measurement apparatus. This scenario lies naturally between standard QKD, where both parties trust their measurement apparatuses, and Device-Independent QKD (DI-QKD), where neither does, and can be a natural assumption in some practical situations. We show that the requirements for obtaining secure keys are much easier to meet than for DI-QKD, which opens promising experimental opportunities. We clarify the link between the security of this one-sided DI-QKD scenario and the demonstration of quantum steering, in analogy to the link between DI-QKD and the violation of Bell inequalities.

Our common understanding of the physical world deeply relies on the notion that events are ordered with respect to some time parameter, with past events serving as causes for future ones. Nonetheless, it was recently found that it is possible to formulate quantum mechanics without any reference to a global time or causal structure. The resulting framework includes new kinds of quantum resources that allow performing tasks-in particular, the violation of causal inequalities-which are impossible for events ordered according to a global causal order. However, no physical implementation of such resources is known. Here we show that a recently demonstrated resource for quantum computationthe quantum switch-is a genuine example of 'indefinite causal order'. We do this by introducing a new tool-the causal witness-which can detect the causal nonseparability of any quantum resource that is incompatible with a definite causal order. We show however that the quantum switch does not violate any causal inequality.

Entanglement swapping is a process by which two initially independent quantum systems can become entangled and generate nonlocal correlations. To characterize such correlations, we compare them to those predicted by bilocal models, where systems that are initially independent are described by uncorrelated states. We extend in this paper the analysis of bilocal correlations initiated in [Phys. Rev. Lett. 104, 170401 (2010)]. In particular, we derive new Bell-type inequalities based on the bilocality assumption in different scenarios, we study their possible quantum violations, and we analyze their resistance to experimental imperfections. The bilocality assumption, being stronger than Bell's standard local causality assumption, lowers the requirements for the demonstration of quantumness in entanglement-swapping experiments.

Quantum systems that have never interacted can become nonlocally correlated through a process called entanglement swapping. To characterize nonlocality in this context, we introduce local models where quantum systems that are initially uncorrelated are described by uncorrelated local variables. This additional assumption leads to stronger tests of nonlocality. We show, in particular, that an entangled pair generated through entanglement swapping will already violate a Bell-type inequality for visibilities as low as 50% under our assumption.

Correlations are generally described by one of two mechanisms: either a first event influences a second one by sending information encoded in bosons or other physical carriers, or the correlated events have some common causes in their shared history. Quantum physics predicts an entirely different kind of cause for some correlations, named entanglement. This reveals itself in correlations that violate Bell inequalities (implying that they cannot be described by common causes) between space-like separated events (implying that they cannot be described by classical communication). Many Bell tests have been performed, and loopholes related to locality and detection have been closed in several independent experiments. It is still possible that a first event could influence a second, but the speed of this hypothetical influence (Einstein's 'spooky action at a distance') would need to be defined in some universal privileged reference frame and be greater than the speed of light. Here we put stringent experimental bounds on the speed of all such hypothetical influences. We performed a Bell test over more than 24 hours between two villages separated by 18 km and approximately east-west oriented, with the source located precisely in the middle. We continuously observed two-photon interferences well above the Bell inequality threshold. Taking advantage of the Earth's rotation, the configuration of our experiment allowed us to determine, for any hypothetically privileged frame, a lower bound for the speed of the influence. For example, if such a privileged reference frame exists and is such that the Earth's speed in this frame is less than 10(-3) times that of the speed of light, then the speed of the influence would have to exceed that of light by at least four orders of magnitude.

The problem of demonstrating entanglement is central to quantum information processing applications. Resorting to standard entanglement witnesses requires one to perfectly trust the implementation of the measurements to be performed on the entangled state, which may be an unjustified assumption. Inspired by the recent work of F. Buscemi [Phys. Rev. Lett. 108, 200401 (2012)], we introduce the concept of Measurement-Device-Independent Entanglement Witnesses (MDI-EWs), which allow one to demonstrate entanglement of all entangled quantum states with untrusted measurement apparatuses. We show how to systematically obtain such MDI-EWs from standard entanglement witnesses. Our construction leads to MDI-EWs that are loss-tolerant, and can be implemented with current technology.Quantum entanglement [1] -an essential feature of quantum theory, describing nonclassical correlations between quantum systems -is the key resource that gives quantum information processing applications their advantage over classical computing [2]. Its characterization and verification, both from a theoretical and a practical point of view, are therefore crucial problems in quantum information science.Several criteria have been proposed to distinguish entangled quantum states from separable ones. A simple one is based on the concept of Entanglement Witnesses [3, 4]: for any entangled state ρ, there exists a Hermitian operator W such that tr[W ρ] < 0, while tr[W σ] ≥ 0 for all separable states σ. Such an operator W -called an Entanglement Witness (EW) -can thus be used to detect the entanglement of ρ. Experimentally testing an EW requires one to be able to estimate tr[W ρ]; this is typically done by decomposing W as a linear combination of product Hermitian operators, estimated independently from different local measurements on each subsystem of ρ. A drawback of this entanglement verification technique using standard EWs is, however, that it requires a perfect implementation of the measurements, so as to faithfully reconstruct tr[W ρ]. Imperfect measurements can indeed lead to an erroneous estimation of tr[W ρ], and possibly to the wrong conclusion about the presence of entanglement, even if ρ is separable [5][6][7][8][9][10].A way to get around this difficulty is to rely on the (loophole-free) violation of a Bell inequality [11]. Indeed, within quantum theory this can only be obtained when one performs measurements on an entangled state [12]. A violation therefore guarantees the presence of entanglement, independently of the measurements actually performed, of the functioning of any device used in the experiment, as well as of the dimension of the underlying shared quantum state. The price to pay when considering such Device-Independent Entanglement Witnesses (DI-EWs) [9] is that not all entangled states can be detected: there are indeed (mixed) entangled states that can only generate locally-causal correlations, which satisfy all Bell inequalities [12,13] when measured one copy at a time. While this problem can be circumvented to some extent whe...

Quantum steering allows two parties to verify shared entanglement even if one measurement device is untrusted. A conclusive demonstration of steering through the violation of a steering inequality is of considerable fundamental interest and opens up applications in quantum communication. To date, all experimental tests with single-photon states have relied on post selection, allowing untrusted devices to cheat by hiding unfavourable events in losses. Here we close this 'detection loophole' by combining a highly efficient source of entangled photon pairs with superconducting transition-edge sensors. We achieve an unprecedented ∼62% conditional detection efficiency of entangled photons and violate a steering inequality with the minimal number of measurement settings by 48 s.d.s. Our results provide a clear path to practical applications of steering and to a photonic loophole-free Bell test.

Quantum theory predicts and experiments confirm that nature can produce correlations between distant events that are nonlocal in the sense of violating a Bell inequality 1 . Nevertheless, Bell's strong sentence 'Correlations cry out for explanations' (ref. 2) remains relevant. The maturing of quantum information science and the discovery of the power of non-local correlations, for example for cryptographic key distribution beyond the standard quantum key distribution schemes 3-5 , strengthen Bell's wish and make it even more timely. In 2003, Leggett proposed an alternative model for non-local correlations 6 that he proved to be incompatible with quantum predictions. We present here a new approach to this model, along with new inequalities for testing it. These inequalities can be derived in a very simple way, assuming only the non-negativity of probability distributions; they are also stronger than previously published and experimentally tested Leggett-type inequalities 6-9 . The simplest of the new inequalities is experimentally violated. Then we go beyond Leggett's model, and show that we cannot ascribe even partially defined individual properties to the components of a maximally entangled pair.Formally, a correlation is a conditional probability distribution P(α, β|a, b), where α, β are the outcomes observed by two partners, Alice and Bob, when they make measurements labelled by a and b, respectively. On the abstract level, a and b are merely inputs, freely and independently chosen by Alice and Bob. On a more physical level, Alice and Bob hold two subsystems of a quantum state; in the simple case of qubits, the inputs are naturally characterized by vectors on the Poincaré sphere, hence the notation a,b.How should we understand non-local correlations, in particular those corresponding to entangled quantum states? A natural approach consists in decomposing P(α, β|a, b) into a statistical mixture of hopefully simpler correlations:Bell's locality assumption is P l (α, β|a, b) = P A l (α|a)P B l (β|b), admittedly the simplest choice, but an inadequate one as it turns out: quantum correlations violate Bell's locality 1 . Setting out to explore other choices, it is natural to require first that the P l fulfil the so-called no-signalling condition, that is, that none of the correlations P l results from a communication between Alice and Bob. This can be guaranteed by ensuring spacelike separation between Alice and Bob. Non-signalling correlations happen without any time ordering: there is not a first event, let us say on Alice's side, that causes the second event via some spooky action at a distance. We may phrase it differently: nonsignalling correlations happen from outside space-time, in the sense that there is no story in space-time that tells us how they happen. This is the case in orthodox quantum physics, or in some illuminating toy models such as the non-local box of Popescu and Rohrlich (PR box) 10 . Mathematically, the no-signalling condition reads P l (α|a,b) = P l (α|a) and P l (β|a,b) = P l (β|b): Alice'...