Faithful Qubit Distribution Assisted by One Additional Qubit against Collective Noise

We propose a distribution scheme of polarization states of a single photon over a collective-noise channel. By adding one extra photon with a fixed polarization, we can protect the state against collective noise via a parity-check measurement and postselection. While the scheme succeeds only probabilistically, it is simpler and more flexible than the schemes utilizing decoherence-free subspace. An application to the Bennett-Brassard 1984 protocol through a collective-noise channel, which is robust to the Trojan horse attack, is also given.

Figure 1

The schematic diagram of the proposed distribution scheme. The photons for the reference $\mathrm{r}$ and the signal $\mathrm{s}$, which are temporally separated by $\Delta t$, are split into two spatial modes by a PBS on Alice’s side. These photons in the polarizations $|H{⟩}_{\mathrm{r},\mathrm{s}}$ and $|V{⟩}_{\mathrm{r},\mathrm{s}}$ are distributed to Bob passing through the quantum channels 1 and 2, respectively. After reaching Bob, these photons are mixed by a PBS. Bob then extracts the signal state from the received two photons.

Figure 2

A decoder for the present scheme. The received photons are split into two optical paths by a BS, and then mixed by a PBS. ${\mathrm{HWP}}_L$ rotates the polarization by 90°. The detector ${\mathrm{D}}_X$ consists of ${\mathrm{HWP}}_X$, which rotates the polarization by 45°, a PBS, and photon detectors D, as shown in the dashed box. The polarization state of the photon in the mode $X$ is projected onto the diagonal basis $\{|D{⟩}_X,|\overline{D}{⟩}_X\}$. The optical path difference between short path $S$ and long path $L$ is adjusted to compensate the temporal difference $\Delta t$ between the reference and signal photons. The detector ${\mathrm{D}}_Y$ can be used to postselect the successful event by the twofold coincidence detection as described in the text.

Figure 3

The schematics of generation of signal and reference photons. Two photons are collinearly generated by PDC from a type II phase-matched $\beta$-barium borate (BBO) crystal. One is in $|H⟩$ and the other is in $|V⟩$. They are split into two optical paths by a PBS, and then mixed by BS. They are separated by $\Delta t$, which corresponds to the path difference between the short and long path. ${\mathrm{HWP}}_{\mathrm{r}}$ rotates the polarization by 45°, while ${\mathrm{HWP}}_{\mathrm{s}}$ and phase shifter (${\mathrm{PS}}_{\mathrm{s}}$) are used to transform the state $|V⟩$ into the desired signal state. Two photons in one output port of BS are in the state (1).