## Abstract

The year 2015 marks 80 years since Einstein, Podolsky, and Rosen argued for the incompleteness of quantum mechanics, in the process describing one of the most counterintuitive characteristics of quantum mechanics: distant measurements can influence the character of local quantum states. This led to reactions from Schrödinger, Bohr, and John Bell. This issue shows that these developments are still well under way, with new foundational insights on the history of steering and Bell-nonlocality, new directions in the mathematical characterization of EPR-steering, demonstrations in quantum optical experiments, and further connections with quantum information processing.

© 2015 Optical Society of America

The year 2015 marks 80 years since Einstein, Podolsky, and Rosen (EPR) [1] penned their letter arguing for the incompleteness of quantum mechanics, and in the process describing one of the most counterintuitive characteristics of quantum mechanics, that distant measurements can influence the character of local quantum states. In reaction, and in the same year, Schrödinger [2] generalized their notion and introduced the term “steering” to describe it. The EPR paper prompted a vigorous response from Bohr [3], and the debate eventually lead to the work of John Bell [4], which established quantitative methods for testing possible completions to quantum mechanics.

Experimental criteria and tests for demonstration of the EPR “paradox” were proposed by Reid in 1989 [5] and have been subject to several experimental tests [6]. In 2007, the phenomenon now called EPR-steering was formalized in modern quantum-information language [7], and identified as a type of quantum nonlocality intermediate between Bell nonlocality and entanglement. Following this, the notion of EPR-steering inequalities was introduced [8] and shown to include the original Reid criteria as a special case. These developments have led to important fundamental results, including loophole-free experiments [9–11], and applications in quantum cryptography [12].

The present issue shows that these developments are still well under way, with new foundational insights on the history of steering and Bell-nonlocality, new directions in the mathematical characterization of EPR-steering, demonstrations in quantum optical experiments, and further connections with quantum information processing.

Jevtic and Rudolph prove remarkable new theorems that show what a short step it could have been from steering, as formulated by Schrödinger in 1935, to Bell-nonlocality, which in fact had to wait a whole generation.

Kiesewetter *et al.* provide a review of stochastic simulation techniques for modeling EPR-correlations, from the early origins of the modern proposals using continuous variables to current developments, including the behavior of parametric downconversion near the critical point, the simulation of parametric Bell violations, quantum entanglement, and correlations in optomechanics, as well as extensions to quantum field systems with planar interferometers.

The decoherence of EPR-steering correlations between two parties when each of the systems are independently coupled to a reservoir is studied by Rosales-Zárate *et al.* They show that if system B is coupled to a reservoir, then the decoherence of the steering of A by B is particularly marked, to the extent that there is a sudden death of steering after a finite time. They also study the decoherence of the steering of a “Schrödinger-cat” state, modeled as the entangled state of a spin and harmonic oscillator, when the macroscopic system (the cat) is coupled to a reservoir.

Piani establishes the connection between the study of EPR-steering for bipartite states and quantum channels, and uses this connection to give specific criteria for ruling out the possibility of hidden channels, unknown to both sender and receiver in a two-party setup.

The original discussion of EPR-steering is of a phenomenon between two distant parties. In this issue, the articles of Karthik *et al.* and of Pusey explore temporal analogues of EPR-steering, considering one party performing preparations and the other measurements on a single system. Karthik *et al.* extend a recently developed relation between joint measurability and EPR-steering to the setting of temporal steering. Pusey demonstrates how information gained from an untrusted measurement device (but trusted preparation device) can be used to certify whether or not a quantum channel is not entanglement breaking. The condition for certification is shown to be formally equivalent to that for witnessing EPR-steering up to a formal translation between states and channels. Pusey applies this connection to propose a resource theory of measurement incompatibility and to shed new light on security analyses of quantum key distribution protocols.

Though the last decade has seen numerous new tests for EPR-steering, the most basic question of precisely which two-qubit states are EPR-steerable remains unanswered. Jevtic *et al.* provide a partial answer to this question for a broad class of two-qubit states called T-states—two-qubit states that are maximally mixed when either qubit is considered independently. In this mathematical tour de force, Jevtic *et al.* establish a condition that is necessary, and likely to be sufficient, for T-states to be EPR-steerable.

While sufficient conditions for EPR-steering have been developed since the work of Margaret Reid in 1989 [5], a condition that is both necessary and sufficient for a given set of correlations to demonstrate EPR-steering has remained an open question. Cavalcanti *et al.* solve this problem by deriving a necessary and sufficient criterion in the simple setup of two dichotomic measurements per party, similar to the CHSH inequality for witnessing Bell nonlocality. Consequently, their result can be applied directly to any experiment in which a CHSH inequality is tested. As a particular example, Cavalcanti *et al.* conclusively test whether a recent experiment reporting entanglement of a single photon shared by two parties also demonstrated EPR-steering.

Wang *et al.* propose an asymmetric multi-user access optical network with hierarchical structure in terms of steering ability. By construction, a “superior” user in the network possesses higher steering ability than any one of the remaining N-1 “subordinate” users. They show that, with this setup, the superior user can send a secret message to certain subordinates without trustworthy assumptions about them and their apparatus.

As a method for hedging against experimental limitations including finite detector sizes, dead space between pixels, etc., Schneeloch *et al.* develop a modified Fano inequality that can be used to demonstrate continuous-variable EPR-steering without needing to characterize entire measurement probability distributions.

Kogias and Adesso introduce a steering measure for two-mode continuous variable systems that is valid for arbitrary states, based on the violation of an optimized variance test, generalizing well-known EPR-steering criteria. They show that Gaussian states are extremal with respect to this measure, minimizing it among all continuous variable states with fixed second moments, and provide an operational interpretation in terms of a guaranteed key rate in semi-device independent quantum key distribution.

Olsen analyzes the EPR-steering properties of a three-well Bose–Hubbard model under the mechanism of coherent transport of atomic population. He shows that this system displays a basic asymmetry with respect to the EPR-steering inequality under study: for part of the evolution, Alice can steer Bob but not vice versa; after the midpoint of the population transfer, this situation reverses.

These contributions, and many others since the publication of the seminal EPR paper 80 years ago, help demystify nature’s “spookiest” feature.

## References

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