Deterministic All-Optical Continuous-Variable Quantum Telecloning

Quantum telecloning, a pivotal multiuser quantum communication protocol in the realm of quantum information science, facilitates the copy of a quantum state across $M$ distinct locations through teleportation technique. In the continuous-variable regime, the implementation of quantum telecloning necessitates the distribution of multipartite entanglement among the sender and $M$ receiver parties. Following this, the sender carries out optic-electro conversion and transmits information via classical channel to $M$ spatially separated receivers simultaneously. To successfully reconstruct the input state, electro-optic conversion needs to be employed by each receiver. However, due to these conversions, the bandwidth of the optical mode in this process is largely constrained. In this Letter, we present an all-optical version of the $1\to 2$ continuous-variable quantum telecloning scheme, wherein both optic-electro and electro-optic conversions are replaced by optical components. Our scheme allows the two receivers to achieve input state reconstruction solely by utilizing beam splitters, significantly simplifying its complexity. We experimentally demonstrate all-optical $1\to 2$ quantum telecloning of coherent state and achieve the fidelities of $58.6\%\pm 1.0\%$ and $58.6\%\pm 1.1\%$ for two clones, exceeding the corresponding classical limits ($51.9\%\pm 0.5\%$ and $51.9\%\pm 0.6\%$). Our results establish a platform for constructing a flexible all-optical multiuser quantum network and promote the field of all-optical quantum information processing.

Figure 1

Schematic of all-optical $1\to 2$ CV quantum telecloning. (a) The scheme of all-optical $1\to 2$ quantum telecloning protocol. EPR, Einstein-Podolsky-Rosen entangled source; PA, parametric amplifier; FWM, four-wave mixing; BS, beam splitter; ${\widehat{a}}_1$ and ${\widehat{b}}_1$, the annihilation operators associated with beams ${\mathrm{EPR}}_1$ and ${\mathrm{EPR}}_2$, respectively; ${\widehat{a}}_{\mathrm{in}}$, the annihilation operator associated with input state; ${\widehat{a}}_4$, the annihilation operator associated with amplified ${\widehat{a}}_{\mathrm{in}}$; ${\widehat{a}}_{{\text{clone}}_1}$ (${\widehat{a}}_{{\text{clone}}_2}$), the annihilation operator associated with the clone state; Alice, sender; Bob and Claire, receivers. (b) Energy level structure of the double-$\mathrm{\Lambda }$ FWM process in the $D1$ line of ${}^{85}\mathrm{Rb}$. $\mathrm{\Delta }$, one-photon detuning; $\delta$, two-photon detuning.

Figure 2

Detailed experimental setup for all-optical $1\to 2$ CV quantum telecloning protocol. HWP, half-wave plate; PBS, polarization beam splitter; FWM, four-wave mixing; ${}^{85}\mathrm{Rb}$, hot ${}^{85}\mathrm{Rb}$ vapor cell; BS, beam splitter; AOM, acousto-optic modulator; PZT, piezoelectric transducer; BHD, balanced homodyne detection; LO, local oscillator; OS, oscilloscope; SA, spectrum analyzer. The resolution bandwidth (RBW) of the SA is 1 MHz. The video bandwidth (VBW) of the SA is 100 Hz.

Figure 3

The typical results of all-optical $1\to 2$ CV quantum telecloning. (a)[(b)] The variances of amplitude quadrature (phase quadrature) of ${\text{clone}}_1$. (c)[(d)] The variances of amplitude quadrature (phase quadrature) of ${\text{clone}}_2$. The black solid traces represent the variances of amplitude quadrature (phase quadrature) of the input state. The blue solid traces represent the variances of amplitude quadrature (phase quadrature) of the corresponding classical limits. The red solid traces are noise power of the photocurrents output from BHD versus the scanning phase.

Figure 4

The experimental fidelities versus the sideband frequency. The fidelities of all-optical $1\to 2$ quantum telecloning [(a) ${\text{clone}}_1$ and (b) ${\text{clone}}_2$] and corresponding experimental classical limits are shown as the red traces and the blue traces, respectively. The error bars are obtained from the standard deviations of multiple repeated measurements.