Demonstration of Multisetting One-Way Einstein-Podolsky-Rosen Steering in Two-Qubit Systems

Einstein-Podolsky-Rosen (EPR) steering describes the ability of one party to remotely affect another’s state through local measurements. One of the most distinguishable properties of EPR steering is its asymmetric aspect. Steering can work in one direction but fail in the opposite direction. This type of one-way steering, which is different from the symmetry concepts of entanglement and Bell nonlocality, has garnered much interest. However, an experimental demonstration of genuine one-way EPR steering in the simplest scenario, i.e., one that employs two-qubit systems, is still lacking. In this Letter, we experimentally demonstrate one-way EPR steering with multimeasurement settings for a class of two-qubit states, which are still one-way steerable even with infinite settings. The steerability is quantified by the steering radius, which represents a necessary and sufficient steering criterion. The demonstrated one-way steering in the simplest bipartite quantum system is of fundamental interest and may provide potential applications in one-way quantum information tasks.

Figure 1

Illustration of the EPR-steering scenario with three-measurement settings. The steps in the task are as follows. (1) Alice sends a qubit to Bob, who is not sure whether the state is from a steerable state (${\rho }_{AB}$, channel $a$) or from a local hidden state model (LHSM, channel $b$). (2) Alice measures her qubit along one of the directions $\{{\overrightarrow{n}}_1,{\overrightarrow{n}}_2,{\overrightarrow{n}}_3\}$ required by Bob through classical communication. (3) Alice sends her measurement results $\{0|{\overrightarrow{n}}_1,1|{\overrightarrow{n}}_1,0|{\overrightarrow{n}}_2,1|{\overrightarrow{n}}_2,0|{\overrightarrow{n}}_3,1|{\overrightarrow{n}}_3\}$ to Bob. Six corresponding conditional states are obtained by Bob, which are denoted as ${\tilde{\rho }}_{a|\overrightarrow{n}}$, with $a\in \{0,1\}$ and $\overrightarrow{n}\in \{{\overrightarrow{n}}_1,{\overrightarrow{n}}_2,{\overrightarrow{n}}_3\}$. (4) Bob analyzes the results to calculate the steering radius $R_{A\to B}$. If $R_{A\to B}>1$, Alice successfully steers Bob’s state. The qubit received by Bob is confirmed to be from channel $a$.

Figure 2

Experimental setup. (a) State preparation. A pair of photons in a state $|\psi (\theta )⟩$ is generated via the spontaneous parametric down-conversion process by pumping a type-II cut PPKTP crystal located in a Sagnac interferometer with an ultraviolet laser ($L$) at 404 nm. The parameter $\theta$ is controlled by the half-wave plate (HWP) in front of the laser. These two photons are filtered by interference filters (IFs). One of the photons passes through an unbalanced interferometer (UI) for state preparation and is sent to Alice. The other photon is sent to Bob. (b) Measurement settings. The polarization analyzer consisting of a quarter-wave plate (QWP), a HWP, and a polarization beam splitter (PBS) on both sides of Alice and Bob is used for measurement settings. The photons are detected by single-photon detectors (SPDs), and the signals are sent for coincidence. (c) The unbalanced interferometer (UI). The state of path $i_1$ remains unchanged. HWPs set at 22.5° and two sufficiently long birefringent crystals (PCs) along paths $i_2$ and $i_3$ introduce a sufficiently large time delay between $|H⟩$ and $|V⟩$ components, which can completely destroy the coherence. By combining these three paths into one, arbitrary two-qubit states ${\rho }_{AB}(p,\theta )$ can be prepared. The parameter $p$ can be controlled conveniently by employing removable shutters (RSs).

Figure 3

Distribution of experimental states and the value of $S_n-C_n$. (a) The distribution of experimental states. In the case of three-measurement settings, the light blue region represents the states for which the steering task fails in both directions. The light red region represents the case of one-way steering; i.e., Alice can steer Bob’s state, but Bob cannot steer Alice’s state. The light brown region represents the case for which Alice and Bob can steer each other. The blue dots, red triangles, and brown squares in the corresponding regions are the experimental states. The area between the two dashed black curves corresponds to the one-way steerable states in the case of two-measurement settings. States below the solid red curve are one-way steerable for infinite-measurement settings. (b) The results of $S_n-C_n$ of the four one-way steerable states are shown in the black pane in (a). All of the $S_n$’s are smaller than the $C_n$’s. Error bars are due to the Poissonian counting statistics, which are small, i.e., within the sizes of the symbols.

Figure 4

The values of $R_{A\to B}$ and $R_{B\to A}$. Different steering situations are clearly distinguished by the values of $R_{A\to B}$ and $R_{B\to A}$, i.e., two-way steerable ($A\leftrightarrow B$, brown squares), one-way steerable ($A\to B$, red triangles), and unsteerable ($A\nleftrightarrow B$, blue dots). (Inset) Enlargement of the corresponding region in the red pane. The error bars are due to the Poissonian counting statistics.