What is Multi-photon indistinguishability?
The realization of a CNOT gate or other entangling operation in a photonic platform is based on photonic circuits when multiple photonic qubits and ancillary photons interfere at the same time.
It is impossible to generate entanglement with photons that are not perfectly identical and thus, in order to successfully execute a multi-photon entangling operation, the state of all the photons involved must be the same. As realistic gates are performed on photons that have imperfect internal states, multi-photon indistinguishability emerges as the property that quantifies how collectively equal the internal state of all $n$ photons is. It is an important metric in the assessment of large photonic schemes, because it accurately predicts the probability of not observing any errors in the computation.
The range of effects that are observed when considering more than 2 photons includes phenomena that are both of a quantum and classical nature. An example is the classical correlation in the internal state of the photons, which follows the features of the toy problem of extracting $n$ colored balls from $n$ distinct urns. A characterization of multi-photon distinguishability would then be able to correctly reconstruct the probability of obtaining each one of the possible color configurations. A second part of multi-photon distinguishability instead involves the genuinely quantum effects of coherence and entanglement between the internal state of each photon, linked to parameters known as geometric phases.
Frequently Asked Questions about Multi-photon indistinguishability
- Is Hong-Ou-Mandel interference enough to characterize multi-photon indistinguishability? No, while HOM interference provides a valuable tool for the characterization of photonic states it can’t access the collective properties which are characteristic of multi-photon indistinguishability, since it probes at most 2 photons at a time. This issue has a classical analogy: in the problem of extracting $n$ colored balls from $n$ distinct urns, it is impossible to predict how often they will all have the same color if the only information available is how often pairs of balls of the same color are extracted. Even restricting the problem to pure photons, one is required to interfere at least 3 photons at the same time in order to probe multi-photon distinguishability effects.
- How can I measure multi-photon indistinguishability? Measurement of multi-photon indistinguishability is an active area of research. A first scheme was proposed in 2022 by M. Pont and collaborators, which relies on a multi-photon generalization of the Mach-Zender interferometer. Recent work at Quandela shows that it is possible to determine genuine multi-photon indistinguishability exponentially more efficiently, using a different protocol based on a Fourier multiport interferometer.