Genuine High-Order Einstein-Podolsky-Rosen Steering

Einstein-Podolsky-Rosen (EPR) steering demonstrates that two parties share entanglement even if the measurement devices of one party are untrusted. Here, going beyond this bipartite concept, we develop a novel formalism to explore a large class of EPR steering from generic multipartite quantum systems of arbitrarily high dimensionality and degrees of freedom, such as graph states and hyperentangled systems. All of these quantum characteristics of genuine high-order EPR steering can be efficiently certified with few measurement settings in experiments. We faithfully demonstrate for the first time such generality by experimentally showing genuine four-partite EPR steering and applications to universal one-way quantum computing. Our formalism provides a new insight into the intermediate type of genuine multipartite Bell nonlocality and potential applications to quantum information tasks and experiments in the presence of untrusted measurement devices.

Figure 1

Genuine multipartite EPR steerability and applications. Generic entanglement-based quantum protocols rely on both characterized measurement devices and genuine multipartite entanglement, such as one-way quantum computation [12, 13] and multiparty quantum communications [14]. Genuine multipartite EPR steerability enables them to perform quantum applications in the presence of untrusted measurement apparatus (a). Here, we develop quantum steering witnesses to ensure that an experimental state ${\rho }_{\text{expt}}$ of an $N$-partite quantum $d$-dimensional system ($N$ qudits) has such ability, for example, an experimental graph state [18, 19, 20, 21] used for one-way computing. To implement gate operations, such as circuits, composed of one-qubit ($d=2$) gate $\widehat{H}$ and two-qubit controlled-$Z$ (CZ) gates (b) and (c) for input states $|{\mathrm{In}}_{\beta }^{\alpha }⟩$, one needs to prepare chain-type (d), i.e., $|G_4⟩$, and box-type (e) cluster states, respectively. By performing measurements $B_2^{(\alpha )}$ and $B_3^{(\beta )}$ on qubits 2 and 3, respectively, the rest of the qubits 1,4 together with the outcomes of measurements on qubits 2, 3 would provide a readout of the gate operations. See the Supplemental Material for detailed discussions [21]. In addition to releasing the assumptions about the measurement devices, genuine multipartite steerability promises high-quality one-way computation (see Fig. 3).

Figure 2

Experimental setup. A pulse (5 ps) of UV light with a central wavelength of 355 nm and an average power of 200 mW at repetition rate of 80 MHz double passes a two-crystal structured BBO to produce polarization entangled photon pairs either in the forward direction or in the backward direction. To create desired entangled pairs in mode $R_A,R_B$ and in $L_A,L_B$, two quarter wave plates (QWPs) are properly tilted along their optic axis. Half wave plates (HWPs), polarizing beam splitters (PBSs), and eight single-photon detectors are used as polarization analyzers for the output states. Here 3-nm bandpass filters (IFs) with central wavelength 710 nm are placed in front of them.

Figure 3

Steerability and performance of quantum gates. Two kinds of gate operations are experimentally realized for the target quantum gates [Figs. 1, 1]. We measure the fidelities of the output states by inputting four orthogonal states into the experimental gates, $|mn⟩$ for $m,n=+,-$ [24]: (a) a mean fidelity $\sim 0.935\pm 0.004$ for the gate operation, Fig. 1, and (b) an average fidelity $\sim 0.960\pm 0.004$ for the target gate, Fig. 1. (c) From the estimate of the average computation fidelity $F_{\text{comp}}$ (5), we obtain the lower bounds of the quantum process fidelity $F_{\text{process}}$ ($\sim 0.9415\pm 0.0025$) and the average state fidelity $F_{\mathrm{av}}$ ($\sim 0.9532\pm 0.0020$), which indicate good qualities of our experimental gates, regardless of the input states [24]. Since both created gates are based on the same source, their estimations of the three different fidelities are identical [21]. The gate performance reveals genuine four-partite steerability by the steering witness $F_{\text{comp}}>W_{4C}/2\sim 0.8536$. The double-arrow dashed line shows the region where the source states are truly four-partite steerable.