### Observation of Genuine One-Way Einstein-Podolsky-Rosen Steering

**From Left to Right: Sabine Wollmann, Howard Wiseman, Geoff Pryde.**

**Authors:**

**Sabine Wollmann**

^{1}, Nathan Walk^{1,2}, Adam J. Bennet^{1}, Howard M. Wiseman^{1}, Geoff J. Pryde^{1}

**Affiliations:**

^{1}Centre for Quantum Computation and Communication Technology and Centre for Quantum Dynamics, Griffith University, Brisbane, Queensland, Australia.

^{2}Department 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 [1]. 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 [2].

**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. [3]. 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 [4]. However their experimental investigation was in a limited context: Gaussian measurements on Gaussian states. As we have shown [5] 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 [6]. 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 [7].

**Figure 2: Creation of a one-way steerable state (see text for details). One half of a Werner state ρ**

_{W}is sent directly to Alice, whose measurements are described by {M_{a|k}}, while the other is transmitted to Bob through a loss channel, which replaces a qubit with the vacuum state and is parametrized by probability p. Bob’s measurements are described by {M_{b|j}}. For differing values of p the final state is unsteerable by Bob for arbitrary projective measurements or arbitrary POVMs. For the same range of p values, Alice can explicitly demonstrate steering via a finite number of Pauli measurements on both sides. She does this by steering Bob’s measurement outcomes so that their shared correlations exceed the upper bound Cn allowed in an optimal local hidden state model.In our work, recently published in [5], we ask if we can extend the result in Ref. [6] 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

between our observers Alice and Bob. This is a probabilistic mixture of a maximally entangled singlet state with a symmetric noise state parametrised by the mixing probability, or Werner parameter, µ. Using the theorem of Quintino et al. [5] allowed us to construct a state

*p*of a vacuum state represents adding asymmetric loss in Bob’s arm. This state is one-way steerable for arbitrary measurements, if we can fulfil the condition

*p*.

**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 S

_{n}– which exceeds the classically allowed value. We observe that Alice’s steering parameter of S

_{16}= 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 S

_{16}= 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 S

_{16}= 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 S

_{16}= 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.[8]. While their result is restricted to two measurement settings, our experimental demonstration holds for an arbitrary number of measurements.

**References:**

**[1]**A. Einstein, B. Podolsky, N. Rosen, "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?", Physical Review, 47, 777 (1935). Abstract.

**[2]**John S. Bell, “On the Einstein Podolsky Rosen paradox”, Physics, 1, 195 (1964). Full Text.

**[3]**H. M. Wiseman, S. J. Jones, and A. C. Doherty, “Steering, entanglement, nonlocality, and the Einstein-Podolsky-Rosen paradox”, Physical Review Letters, 98, 140402 (2007). Abstract.

**[4]**Vitus Händchen, Tobias Eberle, Sebastian Steinlechner, Aiko Samblowski, Torsten Franz, Reinhard F. Werner, and Roman Schnabel, “Observation of one-way Einstein-Podolsky-Rosen steering”, Nature Photonics, 6, 596 (2012). Abstract.

**[5]**Sabine Wollmann, Nathan Walk, Adam J. Bennet, Howard M. Wiseman, and Geoff J. Pryde, "Observation of Genuine One-Way Einstein-Podolsky-Rosen Steering", Physical Review Letters, 116, 160403 (2016). Abstract.

**[6]**Marco Túlio Quintino, Tamás Vértesi, Daniel Cavalcanti, Remigiusz Augusiak, Maciej Demianowicz, Antonio Acín, Nicolas Brunner, "Inequivalence of entanglement, steering, and Bell nonlocality for general measurements", Physical Review A, 92, 032107 (2015). Abstract.

**[7]**D. A. Evans, H. M. Wiseman, "Optimal measurements for tests of Einstein-Podolsky-Rosen steering with no detection loophole using two-qubit Werner states", Physical Review A, 90, 012114 (2014). Abstract.

**[8]**Kai Sun, Xiang-Jun Ye, Jin-Shi Xu, Xiao-Ye Xu, Jian-Shun Tang, Yu-Chun Wu, Jing-Ling Chen, Chuan-Feng Li, and Guang-Can Guo, “Experimental quantification of asymmetric Einstein-Podolsky-Rosen steering”, Physical Review Letters, 116, 160404 (2016). Abstract. 2Physics Article.

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