Eric G. Cavalcanti

Colloquium: The Einstein-Podolsky-Rosen paradox: From concepts to applications

This Colloquium examines the field of the Einstein, Podolsky, and Rosen (EPR) gedanken experiment, from the original paper of Einstein, Podolsky, and Rosen, through to modern theoretical proposals of how to realize both the continuous-variable and discrete versions of the EPR paradox. The relationship with entanglement and Bells theorem are analyzed, and the progress to date towards experimental confirmation of the EPR paradox is summarized, with a detailed treatment of the continuous-variable paradox in laser-based experiments. Practical techniques covered include continuous-wave parametric amplifier and optical fiber quantum soliton experiments. Current proposals for extending EPR experiments to massive-particle systems are discussed, including spin squeezing, atomic position entanglement, and quadrature entanglement in ultracold atoms. Finally, applications of this technology to quantum key distribution, quantum teleportation, and entanglement swapping are examined.

One-sided device-independent quantum key distribution: Security, feasibility, and the connection with steering

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 do, 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.

Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox

We formally link the concept of steering (a concept created by Schrodinger but only recently formalized by Wiseman, Jones and Doherty Phys. Rev. Lett. 98 140402 (2007)]) and the criteria for demonstrations of Einstein-Podolsky-Rosen (EPR) paradox introduced by Reid Phys. Rev. A 40 913 (1989)]. We develop a general theory of experimental EPR-steering criteria, derive a number of criteria applicable to discrete as well as continuous-variable observables, and study their efficacy in detecting that form of nonlocality in some classes of quantum states. We show that previous versions of EPR-type criteria can be rederived within this formalism, thus unifying these efforts from a modern quantum-information perspective and clarifying their conceptual and formal origin. The theory follows in close analogy with criteria for other forms of quantum nonlocality (Bell nonlocality and entanglement), and because it is a hybrid of those two, it may lead to insights into the relationship between the different forms of nonlocality and the criteria that are able to detect them.

Arbitrarily loss-tolerant Einstein-Podolsky-Rosen steering allowing a demonstration over 1 km of optical fiber with no detection loophole

Demonstrating nonclassical effects over longer and longer distances is essential for both quantum technology and fundamental science. The main challenge is the loss of photons during propagation, because considering only those cases where photons are detected opens a ‘‘detection loophole’’ in security whenever parties or devices are untrusted. Einstein-Podolsky-Rosen steering is equivalent to an entanglement-verification task in which one party (device) is untrusted. We derive arbitrarily loss-tolerant tests, enabling us to perform a detection-loophole-free demonstration of Einstein-Podolsky-Rosen steering with parties separated by a coiled 1-km-long optical fiber, with a total loss of 8.9 dB (87%).

Measurements on the reality of the wavefunction

Quantum mechanics is an outstandingly successful description of nature, underpinning fields from biology through chemistry to physics. At its heart is the quantum wavefunction, the central tool for describing quantum systems. Yet it is still unclear what the wavefunction actually is: does it merely represent our limited knowledge of a system, or is it in direct correspondence to reality? Recent no-go theorems argued that if there was any objective reality, then the wavefunction must be real. However, that conclusion relied on debatable assumptions. Here we follow a different approach without these assumptions and experimentally bound the degree to which knowledge interpretations can explain quantum phenomena. Using single photons, we find that no knowledge interpretation can fully explain the limited distinguishability of non-orthogonal quantum states in three and four dimensions. Assuming that a notion of objective reality exists, our results thus strengthen the view that the wavefunction should directly correspond to this reality.

Einstein-Podolsky-Rosen steering inequalities from entropic uncertainty relations

We use entropic uncertainty relations to formulate inequalities that witness Einstein-PodolskyRosen (EPR) steering correlations in diverse quantum systems. We then use these inequalities to formulate symmetric EPR-steering inequalities using the mutual information. We explore the diering natures of the correlations captured by one-way and symmetric steering inequalities, and examine the possibility of exclusive one-way steerability in two-qubit states. Furthermore, we show that steering inequalities can be extended to generalized positive operator valued measures (POVMs), and we also derive hybrid-steering inequalities between alternate degrees of freedom.

No psi−epistemic model can fully explain the indistinguishability of quantum states

According to a recent no-go theorem [M. Pusey, J. Barrett and T. Rudolph, Nat. Phys. 8, 475 (2012)], models in which quantum states correspond to probability distributions over the values of some underlying physical variables must have the following feature: the distributions corresponding to distinct quantum states do not overlap. In such a model, it cannot coherently be maintained that the quantum state merely encodes information about underlying physical variables. The theorem, however, considers only models in which the physical variables corresponding to independently prepared systems are independent, and this has been used to challenge the conclusions of that work. Here we consider models that are defined for a single quantum system of dimension d, such that the independence condition does not arise, and derive an upper bound on the extent to which the probability distributions can overlap. In particular, models in which the quantum overlap between pure states is equal to the classical overlap between the corresponding probability distributions cannot reproduce the quantum predictions in any dimension d ≥ 3. Thus any ontological model for quantum theory must postulate some extra principle, such as a limitation on the measurability of physical variables, to explain the indistinguishability of quantum states. Moreover, we show that as d→∞, the ratio of classical and quantum overlaps goes to zero for a class of states. The result is noise tolerant, and an experiment is motivated to distinguish the class of models ruled out from quantum theory.

Bell Nonlocality, Signal Locality and Unpredictability (or What Bohr Could Have Told Einstein at Solvay Had He Known About Bell Experiments)

The 1964 theorem of John Bell shows that no model that reproduces the predictions of quantum mechanics can simultaneously satisfy the assumptions of locality and determinism. On the other hand, the assumptions of signal locality plus predictability are also sufficient to derive Bell inequalities. This simple theorem, previously noted but published only relatively recently by Masanes, Acin and Gisin, has fundamental implications not entirely appreciated. Firstly, nothing can be concluded about the ontological assumptions of locality or determinism independently of each other—it is possible to reproduce quantum mechanics with deterministic models that violate locality as well as indeterministic models that satisfy locality. On the other hand, the operational assumption of signal locality is an empirically testable (and well-tested) consequence of relativity. Thus Bell inequality violations imply that we can trust that some events are fundamentally unpredictable, even if we cannot trust that they are indeterministic. This result grounds the quantum-mechanical prohibition of arbitrarily accurate predictions on the assumption of no superluminal signalling, regardless of any postulates of quantum mechanics. It also sheds a new light on an early stage of the historical debate between Einstein and Bohr.

Signatures for generalized macroscopic superpositions

We develop criteria sufficient to enable detection of macroscopic coherence where there are not just two macroscopically distinct outcomes for a pointer measurement, but rather a spread of outcomes over a macroscopic range. The criteria provide a means to distinguish a macroscopic quantum description from a microscopic one based on mixtures of microscopic superpositions of pointer-measurement eigenstates. The criteria are applied to Gaussian-squeezed and spin-entangled states.

Unified criteria for multipartite quantum nonlocality

Wiseman and co-workers [H. M. Wiseman, S. J. Jones, and A. C. Doherty, Phys. Rev. Lett. 98, 140402, (2007)] proposed a distinction among the nonlocality classes of Bells nonlocality, Einstein-Podolsky-Rosen (EPR) paradox or steering, and entanglement based on whether or not an overseer trusts each party in a bipartite scenario where they are asked to demonstrate entanglement. Here we extend that concept to the multipartite case and derive inequalities that progressively test for those classes of nonlocality, with different thresholds for each level. This framework includes the three classes of nonlocality above in special cases and introduces a family of others.