Experimental Demonstration of Remotely Creating Wigner Negativity via Quantum Steering

Non-Gaussian states with Wigner negativity are of particular interest in quantum technology due to their potential applications in quantum computing and quantum metrology. However, how to create such states at a remote location remains a challenge, which is important for efficiently distributing quantum resource between distant nodes in a network. Here, we experimentally prepare an optical non-Gaussian state with negative Wigner function at a remote node via local non-Gaussian operation and shared Gaussian entangled state existing quantum steering. By performing photon subtraction on one mode, Wigner negativity is created in the remote target mode. We show that the Wigner negativity is sensitive to loss on the target mode, but robust to loss on the mode performing photon subtraction. This experiment confirms the connection between the remotely created Wigner negativity and quantum steering. As an application, we present that the generated non-Gaussian state exhibits metrological power in quantum phase estimation.

Figure 1

The principle and experimental setup. (a) Schematic of the remote preparation of Wigner negativity. We first prepare a Gaussian EPR entangled state and then transmit two entangled optical fields to two distant nodes controlled by Alice and Bob, where the lossy channels are characterized by ${\eta }_A$ and ${\eta }_B$, respectively. Then once Alice successfully performs a single-photon subtraction from her mode, the remote Bob’s mode collapses to a Wigner-negative state. (b) Experimental setup. Two acousto-optic modulators (AOM) are used to chop the seed beam. The NOPA is composed of a type-II potassium titanyl phosphate crystal and a concave mirror with 50 mm radius. Lossy channel is simulated by the combination of a half wave plate and a PBS. The optical isolators are used to avoid the back scattered light to the NOPA cavity. LO: local oscillator, MC: mode cleaner, OI: optical isolator, LS: laser shutter, IF: interference filter.

Figure 2

The reconstructed Wigner function of Bob’s state remotely created by performing single-photon subtraction from Alice’s field with two sets of input squeezing levels, (a)–(c) $-1.74/+2.08\mathrm{dB}$ and (d)–(f) $-1.302/+1.407\mathrm{dB}$, under different transmission efficiencies of mode $B$: ${\eta }_B=0.7$, 0.8, 0.9. Note that in our experiment, 10% detection loss is caused by the limited homodyne detection efficiency including the quantum efficiency of the photo diode (98%), the mode matching efficiency (98%), and the clearance of homodyne detection (96%), which is corrected in the above plot.

Figure 3

The steerability ${\mathcal{G}}^{B\to A}$ of the initial Gaussian entangled states and the remotely created Wigner negativity in the steering mode $B$ after subtracting a single photon from the steered mode $A$ as functions of the transmission efficiency ${\eta }_B$ shown in (a),(b), or ${\eta }_A$ in (c),(d), respectively. In (a),(b), we also examine two sets of input squeezing levels, $-1.74/+2.08\mathrm{dB}$ (red lines) and $-1.302/+1.407\mathrm{dB}$ (blue lines). Error bars represent $\pm 1$ standard deviation and are obtained based on the statistics of the measured noise variances and density matrices.

Figure 4

The metrological power remotely created in mode $B$ after single-photon subtraction on mode $A$, varying with (a) transmission efficiency ${\eta }_B$ of Bob and (b) transmission efficiency ${\eta }_A$ of Alice. The squeezing levels are $-1/+1\mathrm{dB}$ (blue) and $-3/+3\mathrm{dB}$ (red).