Abstract We have developed a theory for accessing quantum coherences in mutually unbiased bases associated with generalized Pauli operators in multiphoton multimode linear optics networks (LONs). We show a way to construct complementary Pauli measurements in multiphoton LONs and establish a theory for evaluation of their photonic measurement statistics without dealing with the computational complexity of Boson samplings. This theory extends characterization of complementary properties in single-photon LONs to multiphoton LONs employing convex-roof extension. It allows us to detect quantum properties such as entanglement using complementary Pauli measurements, which reveals the physical significance of entanglement between modes in bipartite multiphoton LONs.
Abstract We have developed a theory for accessing quantum coherences in mutually unbiased bases associated with generalized Pauli operators in multiphoton multimode linear optics networks (LONs). We show a way to construct complementary Pauli measurements in multiphoton LONs and establish a theory for evaluation of their photonic measurement statistics without dealing with the computational complexity of Boson samplings. This theory extends characterization of complementary properties in single-photon LONs to multiphoton LONs employing convex-roof extension. It allows us to detect quantum properties such as entanglement using complementary Pauli measurements, which reveals the physical significance of entanglement between modes in bipartite multiphoton LONs.
This thesis presents results under the topics of quantum correlations and quantum information processing using linear-optical networks. The first part of this thesis concerns with quantum correlations, specially in Gaussian states, which play a central role as resource in quantum protocols. The second part is about quantum information processing using linear-optical networks that are of great practical interest due to their simple physical realization. In the first part, we present a measurement-based method for verifying nonzero quantum discord, a measure of quantum correlations, in bipartite systems that can be used for both continuous and discrete-variable systems. Based on this method, we show that the only bipartite Gaussian states with zero quantum discord are product states. We also present a simple and efficient experimental method for verifying quantum correlations in Gaussian states using homodyne measurements. Moreover, we introduce an operational measure for quantifying quantum correlations in Gaussian states that is purely based on Gaussian measurements. We then illustrate the operational significance of the measure in terms of a Gaussian quantum protocol. In the second part, we present results on linear quantum-optics experiments, specifically boson sampling, an intermediate model of quantum computation that can be implemented using single-photon states, linear-optical networks, and photodetectors. We first present an efficient experimental method for characterization of linear-optical networks, which is essential for practical implementation of boson sampling. We show that using coherent states one can directly measure all the nontrivial phases and moduli of the matrix describing the network. Next, we consider the problem of boson sampling with Gaussian states. We derive a general formula for calculating the output photon-counting probabilities. We show that for input thermal states, sampling from the output probability distribution can be efficiently classically simulated. Using this, we find that permanents of positive-semidefinite Hermitian matrices can be approximated to within a multiplicative error in BPPNP. We also discuss boson sampling with squeezed vacuum states. Finally, we provide a sufficient condition for the efficient classical simulation of the general sampling problem using linear-quantum optics, which involves a multimode input quantum state to a linear-optical network and set of measurements at the output. This condition is based on the phase-space quasiprobability distributions, and suggests that negativity is a quantum resource. We apply this condition to implementations of boson sampling using single-photon or spontaneous parametric down-conversion sources. We show that above some threshold for loss and noise in the experiment, boson sampling is classically simulatable.
We propose a method for partial state reconstruction of multiphoton states in multimode ( N -photon M -mode) linear optical networks (LONs) employing only two bucket photon-number-resolving detectors. The reconstructed Heisenberg-Weyl-reduced density matrix captures quantum coherence and symmetry with respect to Heisenberg-Weyl operators. Employing deterministic quantum computing with one qubit (DQC1) circuits, we reduce the detector requirement from M to 2, while the requirement on measurement configurations is retained 2 M 3 − 2 M . To ensure physicality, maximum likelihood estimation is incorporated into the DQC1 reconstruction process, with numerical simulations demonstrating the efficiency of our approach and its robustness against interferometer noises. This method offers a resource-efficient solution for state characterization in large-scale LONs to advance photonic quantum technologies.
Linear-optic photonic networks with multiple single-photon inputs are attracting attention due to their great potential for quantum computation, quantum communication, and quantum sensing. They are also essential for verifying quantum advantages via boson sampling schemes. The quantum coherence of generated multimode–multiphoton states is crucial for various applications. However, the coherence is invisible in the normally obtained photon number distributions, which strictly limits the efficiency of entanglement verification between multimode–multiphoton systems since the required resources for quantum state tomography increase exponentially as the number of photons/modes increases. In this paper, we report the experimental demonstration of direct and efficient verification of entanglement between two multimode–multiphoton systems (one photon in three modes and two photons in three modes) using just two sets of classical correlation tables with and without a discrete Fourier transformation of the optical modes, clearly demonstrating a dramatic reduction in the resources required for entanglement verification. Our experimental demonstration paves the way to understanding the coherence and entanglement of multi-partite systems, not only for photons but for other quantum resources with high-dimensional degrees of freedom.
Multiphoton quantum interference underpins fundamental tests of quantum mechanics and quantum technologies. Consequently, the detrimental effect of photon distinguishability in multiphoton interference experiments can be catastrophic. Here we employ correlation measurements in the photonic inner modes, time or frequency, to restore quantum interference between photons differing in their colors or injection times in arbitrary linear optical networks, without the need for additional filtering or postselection. Interestingly, we demonstrate how harnessing the multiphoton inner-mode quantum information enables us to infer information about symmetries of multiphoton networks and states and to observe arbitrary degrees of W-state entanglement between a small number of photons with a fixed interferometer. These results are therefore of profound interest for future applications of universal inner-mode-resolved linear optics across fundamental science and quantum technologies with photons with experimentally different spectral properties.
The prominent role that linear optical networks have acquired in the engineering of photon states calls for physically intuitive and automatic methods to compute the probability amplitudes for the multiphoton quantum processes occurring in linear optics. A version of Wick's theorem for the expectation value, on any vector state, of products of linear operators, in general, is proved. We use it to extract the combinatorics of any multiphoton quantum processes in linear optics. The result is presented as a concise rule to write down directly explicit formulae for the probability amplitude of any multiphoton process in linear optics. The rule achieves a considerable simplification and provides an intuitive physical insight about quantum multiphoton processes. The methodology is applied to the generation of high-photon-number entangled states by interferometrically mixing coherent light with spontaneously down-converted light.
Linear optical networks driven by quantum states of light are important building blocks of photonic quantum technologies. They access large bosonic Hilbert spaces through multiphoton interference. At the same time, their dynamics are generated by single-particle mode transformations, thereby defining a highly structured subset of multiphoton unitaries and setting boundary on linear optics capability. To elucidate this boundary, we reveal an underlying fine-grained symmetry structure that partitions the multiphoton operator space into invariant subspaces and generates a hierarchy of invariants. We experimentally confirm the conservation of high-order invariants and demonstrate their operational utility in characterizing state reachability and the metrological capability of multiphoton probes. Our framework provides a symmetry-based perspective for understanding and harnessing structured multiphoton dynamics across photonic quantum technologies.