Entanglement-assisted scheme for nondemolition detection of the presence of a single photon

In this paper, we propose a resource-optimal linear-optical scheme for quantum nondemolition detection of single-photon presence. By measuring the state of ancillary photons, the presence of a photon in signal mode is revealed with a success probability of 1/2 without any disturbance to its state. We also show how to tune the setup to perform quantum nondemolition measurement of the signal photon state, and we provide a tradeoff between the extracted information and the signal state disturbance. Moreover, the optimality of resources and methods by which to increase the success probability are discussed.

Figure 1

Proposed setup for linear-optical quantum nondemolition measurement of single photon: PBS, polarizing beam splitter; HWP, half-wave plate (all rotated by 45 deg with respect to horizontal polarization direction); s, signal photon mode; a${}_1$, a${}_2$, ancillary photon modes; D${}_1$, D${}_2$, standard polarization analysis (for reference see [30]).

Figure 2

Output state fidelity $F$ depicted as a function of (a) coherent information $I_C$ and (b) mutual information $I$ between probe and signal, both for three different input states with parameters $\alpha$ and $\beta$. Note that the maxima in all cases coincide with the maximum physically obtainable information (Holevo bound, depicted by black crosses).

Figure 3

Output state fidelity $F$ vs correlation coefficient $T_{zz}$ (correlation between signal and probe measurements in the $H$,$V$ polarization basis) depicted for three different input states with parameters $\alpha$ and $\beta$.

Figure 4

Quantum-logical circuit explaining the operation of the nonperturbing measurement: $O_1$, vacuum; $H_i$ ($V_i$), single $H$-polarized photon in $i$th spatial mode, where $i=1$ denotes the analyzed photon and $i=2$ stands for the ancillary photon. Note that implementing the cnot gate with linear optics without using measurement-induced nonlinearity is impossible; hence, each such gate requires at least one measurement, where the last measurement could correspond to ${\sigma }_z$ of the ancillary qubit.