Observation of one-way Einstein–Podolsky–Rosen steering

Abstract

The distinctive non-classical features of quantum physics were first discussed in the seminal paper 1 by A. Einstein, B. Podolsky and N. Rosen (EPR) in 1935. In his immediate response 2 , E. Schrödinger introduced the notion of entanglement, now seen as the essential resource in quantum information 3-5 as well as in quantum metrology [6][7][8] . Furthermore, he showed that at the core of the EPR argument is a phenomenon that he called steering. In contrast to entanglement and violations of Bell's inequalities, steering implies a direction between the parties involved. Recent theoretical works have precisely defined this property, but the question arose as to whether there are bipartite states showing steering only in one direction 9,10 . Here, we present an experimental realization of two entangled Gaussian modes of light that in fact shows the steering effect in one direction but not in the other. The generated one-way steering gives a new insight into quantum physics and may open a new field of applications in quantum information.The steering effect can be described by considering two remote observers, Alice and Bob, who share a bipartite quantum state. Their local systems are in a mixed state and therefore permit a decomposition into pure states. Schrödinger found that within quantum mechanics certain states do not allow such a decomposition locally. Depending on the observable Alice chooses to measure, Bob's local state is decomposed into incompatible mixtures of conditional states. So, if pure states were a local complete description of Bob's system, this would require some interaction from Alice to Bob. This is what Schrödinger named steering and Einstein later called the 'spooky action at a distance'. The first experimental demonstration of this effect was achieved by Ou et al.11 , and was followed by a great number of experiments [12][13][14][15] .Steering is strictly stronger than entanglement and strictly weaker than the violation of a Bell inequality; that is, steering does not imply the violation of any Bell inequality, while the violation of at least one Bell inequality immediately implies steering in both directions 16 , as shown in Fig. 1. In contrast to entanglement and Bell tests, Alice and Bob have certain roles in the steering scenario that are not interchangeable. This intrinsic asymmetry raises the question 9 of whether there are physical states certifying steering only in one direction for arbitrary observables. This one-way steering would lead to the peculiar situation that two experimenters measuring the same observables on their subsystems would describe the same shared state in qualitatively different ways. Whereas, in general, this question cannot as yet be answered, in the Gaussian regime (that is, for Gaussian state preparation and Gaussian measurements) the answer is yes. In a pioneering paper by H.-A. Bachor and co-workers, two-way steering with an asymmetry in the steering strengths was observed 17 . Their theoretical analysis proposes a possible extension of their set-up with a v...

Steering criteria via covariance matrices of local observables in arbitrary-dimensional quantum systems

“…(12) is vi- This means that if a given quantum state ρ AB violates the inequality in Eq. (12), there must exist the sets  k , B k for which the given state violates the inequality in Eq. (6) and then ρ AB is steerable.…”

“…P LHS is obviously a subset of P LHV as seen from its construction, which makes EPR steering more accessible in experiment than nonlocality [9]. There have been other remarkable works on quantum steering including its connection to measurement incompatibility [10] and the phenomenon of one-way steering [11,12], etc.. However, we need to have a more comprehensive set of steering criteria readily testable particularly for higher-dimensional systems, which may bring us a deeper understanding of quantum correlation.…”

Temporal steering inequality

“…Motivated by the advance of quantum information science, quantum nonlocality as a resource has been further studied in the form of entanglement and entanglement measures. Recently, an inequality to delineate quantum steering from other non-local properties was proposed [4][5][6] and tested in a range of experiments [6,7]. Steerability has since then been further investigated with all-versus-nothing measures [8], and has been utilized as a way to characterize and visualize the state-space of two-qubit systems [9].…”

A gravitational wave detector operating beyond the quantum shot-noise limit: Squeezed light in application

“…Squeezed vacuum states of light injected into the signal port (being close to a dark fringe) of the interferometer allow a reduction of the relative shot-noise without increasing the light power inside the interferometer [5]. The squeezed states split at the interferometer's beam splitter and result in entanglement between the high power light fields in the arms as previously verified in table-top experiments [13,14]. If a frequencydependent phase space rotation is applied to the squeezed field by filter cavities [11] (not shown) radiation pressure noise can be simultaneously squeezed as shown in case a further increase of light power fundamentally is of limited use.…”