All Linear Optical Quantum Memory Based on Quantum Error Correction

When photons are sent through a fiber as part of a quantum communication protocol, the error that is most difficult to correct is photon loss. Here we propose and analyze a two-to-four qubit encoding scheme, which can recover the loss of one qubit in the transmission. This device acts as a repeater, when it is placed in series to cover a distance larger than the attenuation length of the fiber, and it acts as an optical quantum memory, when it is inserted in a fiber loop. We call this dual-purpose device a “quantum transponder.”

Figure 1

A cyclic quantum memory using a quantum transponder (T) based on quantum error correction. Placed in series these devices act as simple quantum repeaters.

Figure 2

Two-to-four qubit encoding, which converts the input $|q_1,q_2⟩$ into a four-qubit state, as given in Eq. (1).

Figure 3

Quantum transponder that recovers photon loss (here, for example, in the lower-most qubit) using two ancilla photons. The QND box represents a single-photon quantum nondemolition measurement device, followed by a single-photon source depicted by the gun-shaped polygon. $H$ represents the Hadamard gate. Four CNOT (controlled by the first ancilla) and four CZ (controlled by the second ancilla) gates are followed by another Hadamard gate and measurement on the computational basis for each ancilla. The final one-qubit operations are for the channel where the loss has occurred, and depend on the measurement results; see Table .

Figure 4

A contour plot of $r={\alpha }^{\prime }(x,n)/2\alpha$, the relative absorption coefficient, as a function of $x$, the normalized distance, and the success probability of the transponder, $p_t$. Note that the minimum of the $r=1$ curve is at $p_t=3/4$.

Figure 5

The probability of transponder success $p_t$ as a function of the number of ancillae $n$. The top graph (a) is for detector efficiency $\eta =1$, and the descending graphs have detector efficiencies (b) $1–{10}^{-6}$, (c) $1–{10}^{-5}$, and (d) $1–{10}^{-4.5}$, respectively. A typical value that $p_t$ needs to exceed is 0.75 (dashed line).