Enhancing quantum teleportation efficacy with noiseless linear amplification

Abstract

Quantum teleportation constitutes a fundamental tool for various applications in quantum communication and computation. However, state-of-the-art continuous-variable quantum teleportation is restricted to moderate fidelities and short-distance configurations. This is due to unavoidable experimental imperfections resulting in thermal decoherence during the teleportation process. Here we present a heralded quantum teleporter able to overcome these limitations through noiseless linear amplification. As a result, we report a high fidelity of 92% for teleporting coherent states using a modest level of quantum entanglement. Our teleporter in principle allows nearly complete removal of loss induced onto the input states being transmitted through imperfect quantum channels. We further demonstrate the purification of a displaced thermal state, impossible via conventional deterministic amplification or teleportation approaches. The combination of high-fidelity coherent state teleportation alongside the purification of thermalized input states permits the transmission of quantum states over significantly long distances. These results are of both practical and fundamental significance; overcoming long-standing hurdles en route to highly-efficient continuous-variable quantum teleportation, while also shining new light on applying teleportation to purify quantum systems from thermal noise.

Fig. 1. Noise-reduced quantum teleportation.

a Schematic of the optical quantum teleporter. Two squeezed modes are combined to generate the EPR state, which is coupled to the input state. A dual homodyne joint measurement is performed to evaluate both conjugate quadratures. Noiseless amplification, embodied by the NLA Processing panel, is implemented by post-selecting the outcomes of the joint measurement according to an acceptance function f(α_m) (see Methods). The successful events are then amplified by ϕ_x/y and fedfoward to displace the transmitted EPR mode via a bright auxiliary beam. Lastly, a verification homodyne is employed to characterize the teleported state. b Conceptual diagram of the teleporter. The teleportation can be described as a two-step process. First, the electronic rescaling factors ϕ_x and ϕ_y are set to $\lambda \sqrt{2}$. The transformation is effectively equivalent to a beamsplititer with transmittivity of λ. Second, deterministic amplification with a gain of ϵ is applied that inevitably introduces some excess noise. The combined action of β and ϵ is effectively parametrized by ϕ_x(y), in (a) Noiseless amplification with a gain of g is then performed to fulfil the unity-gain condition. The additional noise can be made arbitrarily small by increasing g while reducing ϵ. Note that the teleported state has a significantly reduced noise compared to the optimal results of conventional teleportation schemes using the same entanglement resource, denoted by the Heisenberg limit. RNG random number generator, HL Heisenberg limit, CL classical limit, SQ squeezed beams, AM/PM electro-optic amplitude/phase modulators, LO local oscillator, AUX auxiliary beam.

Fig. 2. Enhancement in quantum teleportation fidelity.

a Amplitude noise vs mean of the teleported state (blue line), benchmarked against the optimal conventional quantum teleportation (pink dashed curve) and teleportaion without entanglement (brown dotted line). In contrast to the conventional approach, an increase in the output mean is possible with negligible increase in the variance, verifying that our teleporter has a built-in noiseless amplification feature. Error bars represented 1 s.d. of the variance in the amplitude quadrature. b Improvement in fidelity over conventional techniques as a function of the noiseless gain (blue). This enhancement comes at the price of finite success probability, as evidenced in the grey curve with labels on the right side. Error bars represented 1 s.d. of the output fidelity. c–e Histograms of the measured amplitude quadratures of the teleported states for a series of noiseless gains g = 1.0 − 1.6. Gaussian fits to the data are given by the blue curves, while the Heisenberg limit (pink dashed curve), and the input (green dash-dotted curve) are superimposed for comparison.

Fig. 3. Quantum teleportation of coherent states.

a, c Recorded fidelities for various coherent states that are displaced in amplitude and phase quadratures, respectively. Error bars represent 1 s.d. of the output fidelity. Bars refer to the theoretical expectations of the output fidelities (blue), together with the corresponding Heisenberg limit (pink) and classical limit (brown). b, d Teleported states depicted in phase space. Inner circle (green dashed) represents the input state, blue shaded region denotes the operational regime of our noise-reduced teleporter, whilst the pink and brown shaded regions show the accessible working spaces of the conventional and classical teleporters, respectively. Darker blue bands represent the uncertainties associated with the estimation of variances in output quadrature amplitudes. Contours: 1 s.d. width of the corresponding Wigner functions.

Fig. 4. Purification effect.

a Purification of a displaced thermal state that reduces the input noise while preserving the input displacement. In contrast, a conventional teleporter would introduce additional noise. b Wigner functions of the input and output (semi-transparent) together with the corresponding quadrature probability distributions (green for the input and blue for the output). Quadrature measurement histograms of the output state that are constructed from 5 × 10⁸ measurements are superimposed.