Quantum imaging as an ancilla-assisted process tomography

We show how a recent experiment of quantum imaging with undetected photons can basically be described as an (a partial) ancilla-assisted process tomography in which the object is described by an amplitude-damping quantum channel. We propose a simplified quantum circuit version of this scenario, which also enables one to recast quantum imaging in quantum computation language. Our analogy and analysis may help us to better understand the role of classical and/or quantum correlations in imaging experiments.

Figure 1

Experimental setup of the QI scenario in Ref. [12].

Figure 2

Quantum logical circuit of the imaging setup of Fig. 1. Here $H$ is the Hadamard gate and $Z$ is the $z$-Pauli gate.

Figure 3

An AAPT scheme with unmeasured particles (discarded). Here $\mathcal{M}$ denotes measurement on two of the ancillas.

Figure 4

A circuitlike version of the QI process of Fig. 1. Here parts $\mathbf{A}$ and $\mathbf{B}$ show the state preparation and measurement parts of the corresponding AAPT. Note that Fig. 1 does not include the phase shifter $\varphi$ (in the measurement part). The role of this extra device is to enable full tomography of the object operation—see Sec. 4c.

Figure 5

Probability of detecting a photon in path $\mathbf{h}$ as a function of the phase parameter $\varphi$. This plot shows that by varying $\varphi$ one can read both $T$ and $\gamma$.

Figure 6

The object—simulated as a beam splitter—transmits the incident beam with probability ${cos}^2\theta$ and reflects it otherwise.