Interference requires that it is impossible to distinguish between alternative ways in which an event can occur. This principle has been convincingly demonstrated in the context of single-photon interference in 1991 [1]. In this experiment it was shown that path information can be eliminated by overlapping the paths of photons emitted by two separate sources. The resulting interference can be directly observed, e.g. as a fringe pattern on a camera. No coincidence or heralded detection is necessary in this case. This effect is often referred to as induced coherence by indistinguishability and cannot be explained classically.

We use this effect to study the relationship between information and coherence of photons both at a fundamental level as well as with respect to possible applications. Based on the above phenomenon, we developed a quantum-imaging scheme, in which photons that pass through the object do not need to be detected [2]. Recently, we demonstrated a method to access information about the momentum correlation between two photons by detecting only one of them, given two identical sources are available [3]. We also showed that the concept of overlapping photon paths from different sources can be used to manipulate the polarization of photons [4] and to generate multipartite and high-dimensional entangled states [5].

[1] X. Y. Zou, L. J. Wang, and L. Mandel, "Induced coherence and indistinguishability in optical interference," Phys. Rev. Lett. **67**, 318 (1991).

[2] G. B. Lemos, V. Borish, G. D. Cole, S. Ramelow, R. Lapkiewicz, A. Zeilinger, "Quantum Imaging with Undetected Photons", Nature, **512**, 409–412 (2014).

[3] A. Hochrainer, M. Lahiri, R. Lapkiewicz, G. B. Lemos, A. Zeilinger., “Quantifying the Momentum Correlation between Two Light Beams by Detecting One”, arXiv:1610.05529 (2016).

[4] M. Lahiri, A. Hochrainer, R. Lapkiewicz, G. B. Lemos, A. Zeilinger, "Partial Polarization by Quantum Distinguishability", arXiv:1510.04192 (2015).

[5] M. Krenn, A. Hochrainer, M. Lahiri, A. Zeilinger, "Entanglement by Path Identity", arXiv:1610.00642 (2016).

**Further reading:**

A. Hochrainer, M. Lahiri, R. Lapkiewicz, G. B. Lemos, A. Zeilinger., “Interference Fringes Controlled by Non-Interfering Photons”, Optica 4(3), 341-344 (2017).

M. Lahiri, A. Hochrainer, R. Lapkiewicz, G. B. Lemos, A. Zeilinger, “Twin Photon Correlations in Single-Photon Interference”, arXiv:1610.04298 (2016).

M. Lahiri, R. Lapkiewicz, G. B. Lemos, A. Zeilinger, "Theory of Quantum Imaging with Undetected Photons", Phys. Rev. A **92**, 013832, (2015).

M. Lahiri, A. Hochrainer, R. Lapkiewicz, G. B. Lemos, A. Zeilinger. Can Induced Coherence without Induced Emission be Non-Quantum? arXiv:1709.09974 (2017).

## Zeilinger Group

#### Anton Zeilinger

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#### Eugenia Benech Charbonnier

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#### Xinhe Jiang

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#### Michael Keller

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#### Robert Kindler

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#### Jaroslav Kysela

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#### Amin Babazadeh

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