Quantum information holds enormous potential to achieve communication and computational tasks that are impossible using classical systems. Many quantum information processing tasks can be implemented by exploiting the passive interference of photons. In this thesis, we reports advances towards the analysis, simulation, characterization, and design of passive interferometry experiments for quantum information processing applications. First, we develop a theory of passive optical interferometry experiments that relates coincidence rates at the output of an interferometer to the permutational symmetries of partially distinguishable photons. In our formalism, coincidence rates are elegantly expressed in terms of immanants, which are matrix functions that exhibit permutational symmetries, and the immanants appearing in our coincidence-rate expressions share permutational symmetries with the input state. Our formalism thus provides an intuitive qualitative understanding of how the permutational symmetries of distinguishable photons determine their interference. Our approach can be used to better understand the effect of partial distinguishability in modeling passive interferometry experiments aiming to perform quantum information tasks such as linear optical quantum computing and BosonSampling. By exploiting symmetries, we can also reduce some calculational tasks and provide additional insights into relations between the coincidence rates in various situations. Second, we tackle the problem of characterizing passive interferometers, essential for modelling any passive interferometry experiment. We develop a characterization procedure that uses only one- and two-photon coincidence data, and makes a number of advancements over existing procedures. We estimate the errors in the characterization via bootstrapping, a statistical technique with the advantage of not assuming any particular error model on the experimental data. We also introduce a scattershot approach to reduce the experimental data collection time quadratically in the number of modes of the interferometer. Third, we study a relativistic quantum information task called quantum summoning. We cast quantum summoning as an interactive protocol between a verifier and a possibly dishonest prover. For the prover, we present a protocol and quantum codes to summon in any valid configuration of causal diamonds, and design the encoding and decoding circuits for our code. Our protocol decreases the space complexity for encoding by a factor of two compared to the previous best result and reduces the gate complexity from scaling as the cube to the square of the number of causal diamonds. Within our interactive protocol framework, we construct an operational definition of quantum summoning, and use this definition to present a verification test. We prove that our verification test is sound and complete, thereby showing that quantum summoning can be verified by a resource-limited verifier in an adversarial setting. Our protocol and verification procedures are amenable to implementation by passive interferometry, thereby extending the reach of passive interferometry in the field of relativistic quantum information processing.
Quantum information holds enormous potential to achieve communication and computational tasks that are impossible using classical systems. Many quantum information processing tasks can be implemented by exploiting the passive interference of photons. In this thesis, we reports advances towards the analysis, simulation, characterization, and design of passive interferometry experiments for quantum information processing applications. First, we develop a theory of passive optical interferometry experiments that relates coincidence rates at the output of an interferometer to the permutational symmetries of partially distinguishable photons. In our formalism, coincidence rates are elegantly expressed in terms of immanants, which are matrix functions that exhibit permutational symmetries, and the immanants appearing in our coincidence-rate expressions share permutational symmetries with the input state. Our formalism thus provides an intuitive qualitative understanding of how the permutational symmetries of distinguishable photons determine their interference. Our approach can be used to better understand the effect of partial distinguishability in modeling passive interferometry experiments aiming to perform quantum information tasks such as linear optical quantum computing and BosonSampling. By exploiting symmetries, we can also reduce some calculational tasks and provide additional insights into relations between the coincidence rates in various situations. Second, we tackle the problem of characterizing passive interferometers, essential for modelling any passive interferometry experiment. We develop a characterization procedure that uses only one- and two-photon coincidence data, and makes a number of advancements over existing procedures. We estimate the errors in the characterization via bootstrapping, a statistical technique with the advantage of not assuming any particular error model on the experimental data. We also introduce a scattershot approach to reduce the experimental data collection time quadratically in the number of modes of the interferometer. Third, we study a relativistic quantum information task called quantum summoning. We cast quantum summoning as an interactive protocol between a verifier and a possibly dishonest prover. For the prover, we present a protocol and quantum codes to summon in any valid configuration of causal diamonds, and design the encoding and decoding circuits for our code. Our protocol decreases the space complexity for encoding by a factor of two compared to the previous best result and reduces the gate complexity from scaling as the cube to the square of the number of causal diamonds. Within our interactive protocol framework, we construct an operational definition of quantum summoning, and use this definition to present a verification test. We prove that our verification test is sound and complete, thereby showing that quantum summoning can be verified by a resource-limited verifier in an adversarial setting. Our protocol and verification procedures are amenable to implementation by passive interferometry, thereby extending the reach of passive interferometry in the field of relativistic quantum information processing.
This thesis reports advances in the theory of design, characterization and simulation of multi-photon multi-channel interferometers. I advance the design of interferometers through an algorithm to realize an arbitrary discrete unitary transformation on the combined spatial and internal degrees of freedom of light. This procedure effects an arbitrary nsnp×nsnp unitary matrix on the state of light in ns spatial and np internal modes. I devise an accurate and precise procedure for characterizing any multi-port linear optical interferometer using one- and two-photon interference. Accuracy is achieved by estimating and correcting systematic errors that arise due to spatiotemporal and polarization mode mismatch. Enhanced accuracy and precision are attained by fitting experimental coincidence data to a curve simulated using measured source spectra. The efficacy of our characterization procedure is verified by numerical simulations. I develop group-theoretic methods for the analysis and simulation of linear interferometers. I devise a graph-theoretic algorithm to construct the boson realizations of the canonical SU(n) basis states, which reduce the canonical subgroup chain, for arbitrary n. The boson realizations are employed to construct D-functions, which are the matrix elements of arbitrary irreducible representations, of SU(n) in the canonical basis. I show that immanants of principal submatrices of a unitary matrix T are a sum of the diagonal D(Ω)-functions of group element Ω over t determined by the choice of submatrix and over the irrep (λ) determined by the immanant under consideration. The algorithm for SU(n)D-function computation and the results connecting these functions with immanants open the possibility of group-theoretic analysis and simulation of linear optics.
We obtain coincidence rates for passive optical interferometry by exploiting the permutational symmetries of partially distinguishable input photons, and our approach elucidates qualitative features of multiphoton coincidence landscapes. We treat the interferometer input as a product state of any number of photons in each input mode with photons distinguished by their arrival time. Detectors at the output of the interferometer count photons from each output mode over a long integration time. We generalize and prove the claim of Tillmann et al. [Phys. Rev. X 5, 041015 (2015)] that coincidence rates can be elegantly expressed in terms of immanants. Immanants are functions of matrices that exhibit permutational symmetries and the immanants appearing in our coincidence-rate expressions share permutational symmetries with the input state. Our results are obtained by employing representation theory of the symmetric group to analyze systems of an arbitrary number of photons in arbitrarily sized interferometers.
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.
This thesis reports advances in the theory of design, characterization and simulation of multi-photon multi-channel interferometers. I advance the design of interferometers through an algorithm to realize an arbitrary discrete unitary transformation on the combined spatial and internal degrees of freedom of light. This procedure effects an arbitrary nsnptimesnsnp unitary matrix on the state of light in ns spatial and np internal modes. I devise an accurate and precise procedure for characterizing any multi-port linear optical interferometer using one- and two-photon interference. Accuracy is achieved by estimating and correcting systematic errors that arise due to spatiotemporal and polarization mode mismatch. Enhanced accuracy and precision are attained by fitting experimental coincidence data to a curve simulated using measured source spectra. The efficacy of our characterization procedure is verified by numerical simulations. I develop group-theoretic methods for the analysis and simulation of linear interferometers. I devise a graph-theoretic algorithm to construct the boson realizations of the canonical SU(n) basis states, which reduce the canonical subgroup chain, for arbitrary n. The boson realizations are employed to construct mathcalD-functions, which are the matrix elements of arbitrary irreducible representations, of SU(n) in the canonical basis. I show that immanants of principal submatrices of a unitary matrix T are a sum of the diagonal mathcalD(Omega)-functions of group element Omega over t determined by the choice of submatrix and over the irrep (lambda) determined by the immanant under consideration. The algorithm for mathrmSU(n)mathcalD-function computation and the results connecting these functions with immanants open the possibility of group-theoretic analysis and simulation of linear optics.
This dissertation explores the use of single photons in integrated photonic circuits as a platform for quantum computation and quantum simulation. In the noisy intermediate-scale quantum (NISQ) era, photonic implementations of boson sampling provide one of the most promising routes to demonstrating quantum advantage, while also enabling insight-driven experiments that probe many-body interference and computational complexity. The first part of the thesis is devoted to the hardware development and characterization of programmable silicon nitride photonic processors. We demonstrate large-scale multi-photon interference in a 20-mode universal processor, establishing the potential of integrated photonics for scaling up boson sampling experiments. In parallel, we introduce a validation protocol based on detector binning, implemented on a 12-mode predecessor of the device. Together, these studies advance the photonic platform itself, focusing on scalability, versatility, and benchmarking, rather than direct applications. The second part turns to quantum simulation. We first present a photonic simulation of a spin-foam amplitude from loop quantum gravity, illustrating how multi-photon interference can provide a testbed for problems in fundamental physics. We then implement a particle-number-difference Maxwell demon using conditional operations on photon subsets in a multi-mode interferometer. This experiment probes the link between thermodynamics and information theory, showing how a photonic platform with single-photon resolution and quantum interference can be used to explore information-driven control of physical systems. The final part addresses quantum computation, where we demonstrate a boson-sampling-accelerated Monte Carlo integrator. This hybrid quantum–classical algorithm represents one of the few proposals to extend boson sampling toward practical applications while plausibly retaining its computational hardness. We validate the method in a proof-of-principle experiment reproducing perturbative corrections in a model inspired by Efimov physics. Altogether, the results presented in this thesis position integrated photonics as both a scalable hardware platform for multi-photon experiments and a versatile tool for advancing quantum simulation and computation.
Quantum information processing opens up completely new possibilities in communication and computation, that would be impossible in the realms of classical physics. While the benefits of quantum information processing are well understood in theory, it remains a formidable challenge to experimentally implement even simple quantum information processing tasks. Numerous physical architectures have been proposed for preparing and coherently manipulating quantum information. Amongst these, quantum optics has been identified as a particularly promising candidate. In particular this arises from the long decoherence times of single photon states, which can be used to encode logical qubits in a variety of ways. Nonetheless, there remain formidable challenges to implementing large scale quantum information processing using optical qubits. Most notably these include: the preparation of pure indistinguishable photons; efficient number-resolving photo-detection; mode-matching; photon loss; and the non-determinism of entangling gates. Any future large scale implementation of optical quantum information processing protocols will require significant advances on most, if not all these fronts. In this thesis we aim to present a comprehensive overview of the major requirements for optical quantum information processing, understand the effects they have, and how they can be modeled. From this we aim to understand what the realistic technological requirements are to achieve scalable optical quantum information processing, and, where possible, suggest means by which to help achieve these goals.