Nonlocal quantum gate on quantum continuous variables with minimal resources

We experimentally demonstrate, with an all-optical setup, a nonlocal deterministic quantum nondemolition interaction gate applicable to quantum states at nodes separated by a physical distance and connected by classical communication channels. The gate implementation, based on entangled states shared in advance, local operations, and classical communication, runs completely in parallel fashion at both of the local nodes, requiring minimum resources. The nondemolition character of the gate up to the local unitary squeezing is verified by the analysis using several coherent states. A genuine quantum nature of the gate is confirmed by the capability of deterministically producing an entangled state at the output from two separable input states. The all-optical nonlocal gate operation can be potentially incorporated into distributed quantum computing with atomic or solid-state systems as a cross-processor unitary operation.

Figure 1

Abstract illustrations of some nonlocal gates. (a) Quantum teleportation from Alice to Bob. (b) Nonlocal entangling gate with sequential scheme by means of two quantum teleporters and one local entangling gate. (c) Optimal parallel nonlocal entangling gate. meas.: measurement; local U.: local unitary operation; EPR: entanglement resource; ${\widehat{E}}_{AB}$: entangling operation for two input states.

Figure 2

A schematic of our experimental setup. OPO: optical parametric oscillator; LO: local oscillator for homodyne measurement; EOM: electro-optical modulator; HD: homodyne detection; 50:50 (99:1): 50 (99)% reflectivity beam splitter.

Figure 3

(a) Powers at the outputs for vacuum inputs. The black and red traces show the shot noise and experimental output quadratures, respectively. The green dashed lines show the theoretical predictions without resource squeezing, while the cyan lines show the theoretical predictions for an ideal gate. (b)–(e) Powers at the outputs for coherent inputs where ($\langle {\widehat{x}}_A\rangle ,\langle {\widehat{p}}_A\rangle ,\langle {\widehat{x}}_B\rangle ,\langle {\widehat{p}}_B\rangle$) corresponds to $(a,0,0,0)$, $(0,a,0,0)$, $(0,0,b,0)$, and $(0,0,0,b)$, respectively. The coherent amplitudes $a$ and $b$ correspond to 11.0 and 12.5 dB above the shot-noise level, respectively. The blue lines show the theoretical predictions based on the experimental results of (a). vac.: vacuum state; coh.: coherent state.

Figure 4

A covariance matrix of output states for vacuum inputs. Measured values of the covariance matrix are shown in Eq. (13).