Photon distinguishability is a fundamental property manifested in multiphoton interference and one of the main sources of noise in any photonic quantum information processing. In this work, rather than relying on first-quantization methods, we build on a generating-function framework based on the phase-space formalism to characterize the effects of partial distinguishability on the interference of single-mode squeezed states. Our approach goes beyond commonly used models that represent distinguishability via additional noninterfering modes and captures genuine multiphoton interference effects induced by the overlap of the internal state of the photons. This description provides a clear physical account of how distinguishability gives rise to effective noise in Gaussian boson sampling protocols while enabling a systematic investigation of phase effects arising from the overlap of the internal states.
Photon distinguishability is a fundamental property manifested in multiphoton interference and one of the main sources of noise in any photonic quantum information processing. In this work, rather than relying on first-quantization methods, we build on a generating-function framework based on the phase-space formalism to characterize the effects of partial distinguishability on the interference of single-mode squeezed states. Our approach goes beyond commonly used models that represent distinguishability via additional noninterfering modes and captures genuine multiphoton interference effects induced by the overlap of the internal state of the photons. This description provides a clear physical account of how distinguishability gives rise to effective noise in Gaussian boson sampling protocols while enabling a systematic investigation of phase effects arising from the overlap of the internal states.
This thesis explores the interference of nonclassical states of light, particularly Fock and Gaussian states, in noisy linear interferometers, with applications to quantum information and quantum sensing. Using the phase-space formalism, analytical tools based on generating functions are developed to describe quantum optical interference in a unified way. For multiphoton Fock states, new zero probability events (suppression laws) are identified beyond the previously derived symmetry permutation principle, revealing rich interference structures that is degraded with photon distinguishability. For Gaussian states, the Hafnian-based description of Gaussian Boson Sampling is extended to include partial distinguishability via the overlap matrix of the internal state of the photons. Finally, the link between these interference effects and quantum multiparameter estimation is examined for the simultaneous estimation of phase and loss. This study shows that while probe incompatibility can vanish for optimized non-Gaussian states and some two-mode Gaussian states, at high photon number, measurement incompatibility remains a fundamental constraint even in this limit.
Anomalous bunching is a paradoxical quantum interferometric phenomenon in which partially distinguishable photons exhibit a higher probability of bunching into two or more modes than fully indistinguishable photons [Nat. Photonics 17, 702 (2023)]. While this effect is directly linked to violations of certain conjectures on matrix permanents, the mechanism underlying the anomaly is not yet fully understood. Here, we show that boson bunching is governed not by internal indistinguishability alone, but by the total indistinguishability of the postselected output state. Total indistinguishability combines the internal degrees of freedom, such as polarization or arrival time, with the spatial degrees of freedom of their wave functions restricted to the measured output modes of the interferometer. This reformulation preserves the expected connection between boson bunching and total indistinguishability, while clarifying how anomalous bunching can arise. It also reveals several additional facets of the same phenomenon, which are captured within a unified framework. In particular, we exhibit situations in which adding an independent source of distinguishability, either internal or spatial, can enhance multimode or even single-mode bunching probabilities, offering new insights into the subtle role of distinguishability in multiphoton interference.
Distinguishability theory is developed for quantum interference of the squeezed vacuum states on unitary linear interferometers. It is found that the entanglement of photon pairs over the Schmidt modes is one of the sources of distinguishability. The distinguishability is quantified by the symmetric part of the internal state of n pairs of photons over the spectral Schmidt modes, whose normalization q2n is the probability that 2n photons interfere as indistinguishable. For two pairs of photons q4=(1+2P)/3, where P is the purity of the squeezed states (K=1/P is the Schmidt number). For a fixed purity P, the probability q2n decreases exponentially fast in n. For example, in the experimental Gaussian boson sampling of H.-S. Zhong et al., [Science 370, 1460 (2020)], the achieved purity $\mathbb{P}\ensuremath{\approx}0.938$ for the average number of photons $2n\ensuremath{\ge}43$ gives ${q}_{2n}\ensuremath{\lesssim}0.5$, i.e., close to the middle line between n indistinguishable and n distinguishable pairs of photons. In derivation of all the results, the first-order quantization representation based on the particle decomposition of the Hilbert space of identical bosons serves as an indispensable tool. The approach can be applied also to the generalized (non-Gaussian) squeezed states, such as those recently generated in the three-photon parametric down-conversion.
Photon distinguishability is a key factor limiting quantum interference in photonic devices, directly impacting the performance of protocols such as Boson Sampling and photonic quantum computing. We present a basis-independent framework for analyzing multi-photon interference, identifying a necessary and sufficient condition under which distinguishability behaves as a stochastic error process. This condition enables any multi-photon state to be uniquely expressed as a classical mixture of partition states -- discrete configurations representing different patterns of photon distinguishability. We introduce an experimentally implementable operation, analogous to Pauli twirling, that enforces this condition without compromising computational hardness. The resulting probability distribution over partition states defines the system's incoherent distinguishability spectrum, which we show can be fully characterized through a specific set of experiments. Building on this structure, we also demonstrate the existence of an error mitigation strategy. This framework clarifies key challenges in defining genuine multi-photon indistinguishability, links previous perspectives on partial distinguishability, and provides a rigorous foundation for robust photonic protocols.
The non-classical interference undergone by multiple photons in passive, linear optical networks gives rise to a surprising computational power of such quantum systems. This is prominently highlighted by boson sampling, a scheme for quantum computation which relies solely on such multiphoton interference and omits the usage of more sophisticated techniques such as entangling gates or feed-forward control. Despite these limitations, it still allows to efficiently solve a class of computational problems which is intractable for classical computers. In this thesis, several open challenges on the way to an experimental realization of boson sampling are addressed. To that end, the idealized model for boson sampling is extended to account, for example, for inner degrees of freedom of the single-photon pulses or the probabilistic nature of single-photon sources. It is shown that the difficulties arising from these real-world effects can be overcome by suitably adapting existing boson sampling schemes. Additionally, the extended model for such interference is applied to reveal its intricate dependence on input state, evolution inside the interferometer, and the detection process. Finally, a novel description of SPDC in terms of temporal Bogoliubov transformations is provided, revealing new, intuitive insights into the temporal structure of photon correlations for such sources.
The effects of optical loss and photon distinguishability on the heralded generation of entangled states based on Gaussian resources are quantitatively investigated. By incorporating mode-dependent loss and the statistical characteristics of partially distinguishable photons into a phase-space representation, an efficient numerical framework is established to optimize target-state fidelity and success probability, with a specific focus on the enhancement triggered by non-Gaussian operations such as photon addition and subtraction. The numerical optimization results indicate that a non-vacuum post-selection strategy within a dual-rail encoding framework, combined with the simultaneous tuning of squeezing parameters and the interferometer network, effectively suppresses vacuum noise, enabling the generation of high-fidelity Bell, GHZ, and W states under realistic experimental constraints. The results show that introducing non-Gaussian operations can successfully enhance the state generation performance under realistic imperfections analogous to the enhancements observed under ideal conditions. This study demonstrates that experimental imperfections primarily scale down the success probability rather than fundamentally compromising the state fidelity, providing practical design guidelines for scalable state engineering on integrated photonic platforms.