Observation of Genuine One-Way Einstein-Podolsky-Rosen Steering
Sabine Wollmann1, Nathan Walk1,2, Adam J. Bennet1, Howard M. Wiseman1, Geoff J. Pryde1
1Centre for Quantum Computation and Communication Technology and Centre for Quantum Dynamics, Griffith University, Brisbane, Queensland, Australia.
2Department of Computer Science, University of Oxford, United Kingdom.
Quantum entanglement, a nonlocal phenomenon, is a key resource for foundational quantum information and communication tasks, such as teleportation, entanglement swapping and quantum key distribution. The idea of this widely investigated feature was first discussed by Albert Einstein, Boris Podolsky and Nathan Rosen (EPR) in 1935 . In their famous thought experiment they consider a maximally-entangled state shared between two observers, Alice and Bob. Alice makes a measurement on her system and controls Bob’s measurement outcomes by her choice of measurement setting. They concluded from this counterintuitive effect, which Einstein later called ‘spooky action at a distance’, that quantum theory must be incomplete and an underlying hidden variable model must exist. It took another 29 years until it was proven by Bell that there exist predictions of quantum mechanics for which no possible local hidden variable model could account for .
Figure 1: Illustration of one-way EPR steering. Alice and Bob share a state which only allows Alice to demonstrate steering.
It was not until recently that the class of nonlocality described by EPR, being intermediate to entanglement witness tests and Bell inequality violations, was formalized by Wiseman et al. . While the previous classes are a symmetric feature - in the sense that, the effects persist under exchange of the parties - this does not necessarily hold for EPR steering. The asymmetry arises because one of the parties is trusted (i.e. their measurements are assumed to be faithfully described by quantum mechanics) and the other is not. In this distinctive class of nonlocality we usually consider a shared state between the two parties Alice and Bob. The question which arises is whether sharing an asymmetric state can result in one-way EPR steering, where Alice can steer Bob, for example, but not the other way around.
This foundational question was first experimentally addressed by Haendchen et al. in 2012, who demonstrated experimentally Gaussian one-way EPR steering with two-mode squeezed states . However their experimental investigation was in a limited context: Gaussian measurements on Gaussian states. As we have shown  there exist explicit examples of supposedly one-way steerable Gaussian states actually being two-way steerable for a broader class of measurements. So one could ask, do states exist which are one-way steerable for arbitrary measurements? And the answer is yes. Two independent groups, Nicolas Brunner’s in Geneva and Howard Wiseman’s in Brisbane, proved the existence of such states. Brunner’s approach holds for arbitrary measurements with infinite settings, so called infinite-setting positive-operator-valued measures (POVM), with the cost of using an exotic family of states to demonstrate the effect over an extremely small parameter range, which is unsuitable for experimental observation . David Evans and Howard Wiseman showed one-way steerability exists for projective measurements of more practical, singlet states with symmetric noise - so called Werner states – and loss .
In our work, recently published in , we ask if we can extend the result in Ref.  to find a simple state which is steerable in one direction but cannot be steered in the other direction even for the case of arbitrary measurements and infinite settings. For that we consider a shared Werner state
Figure 3: In the experimental scheme, Alice and Bob are represented by black and green boxes, respectively. Both are in control of their line and their detectors. The party that is steering is additionally in control of the source. Entangled photon pairs at 820 nm were produced via SPDC in a Sagnac interferometer. Different measurement settings are realized by rotating half- and quarter-wave plates (HWP and QWP) relative to the polarizing beam splitters. A gradient neutral density (ND) filter is mounted in front of Bob’s line to control the fraction of photon qubits passing through. Long pass (LP) filters remove 410 nm pump photons copropagating with the 820 nm photons before the latter are coupled into single-mode fibers and detected by single photon counting modules and counting electronics.
In our experiment we generate an one-way steerable state for projective measurements with a fidelity of (99.6±0.01)% with a Werner state of µ = 0.991±0.003 and insert a filter into Bob’s line to generate the loss p = (87±3)%. To demonstrate that Alice remains able to steer Bob’s state, it is necessary to violate the EPR steering inequality. That means measuring a correlation function – the so called steering parameter Sn – which exceeds the classically allowed value. We observe that Alice’s steering parameter of S16 = 0.970±0.004 is 7.3 standard deviations above the classical bound at an heralding efficiency of η = (17.11±0.07)%. The loss of information in Bob’s arm makes him unable to steer the other party. We observe a steering parameter of S16 = 0.963±0.006. In this case, this S value would not have violated a steering inequality even with an infinite number of measurements.
The second one-way steerable regime which we investigate, does still allow Alice to steer Bob’s state but he remains unable to steer hers even by using POVMs. To demonstrate this case, we produce a state with a fidelity of (99.1±0.3)% with a Werner state of µ = 0.978±0.008 and applied a loss p =(99.5±0.3)%. Alice remains able to steer Bob with a steering parameter S16 = 0.951±0.005, being 6.6 standard deviations above the classical bound, at an heralding efficiency of η = (17.17±0.04)%. Bob’s steering parameter S16 = 0.951±0.006 does not violate the inequality and there is no kind of measurement he could choose, even in principle, to be able to steer Alice. We note that the shared state is not exactly a Werner state, but the extremely high fidelities imply, with low probability of error, that the state is only one-way steerable.
Thus, we observe genuine one-way EPR steering for the first time. We note that an independent demonstration was realised in Ref.. While their result is restricted to two measurement settings, our experimental demonstration holds for an arbitrary number of measurements.
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