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Quantum Computing, Communication, and Simulation

Efficient generation and evaluation of single photons propagating in the multiple optical modes

Shigeki Takeuchi, Takayuki Kiyohara, Ryo Okamoto

Published Mar 9, 2022• 0 citations
Publisher

Abstract

In this talk, 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. We will also report a novel method to produce a multi-photon parallel state efficiently with reducing excess photon components using multiple heralding single photon sources and N x N active optical switch.

DOI
10.1117/12.2613930

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In this talk, 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. We will also report a novel method to produce a multi-photon parallel state efficiently with reducing excess photon components using multiple heralding single photon sources and N x N active optical switch.
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.
Efficient analysis of the quantum states of photons are essential for photonic quantum technologies. In the first part, 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. In the second part, we report our experimental demonstration of adaptive quantum state estimation for quantum states of photons changing in time.
Single photon sources can be used to generate and control highly non-classical states of light. Here, we consider the possibility of generating bi-partite entanglement between two separate multi-photon states by splitting the input modes of the single photon sources into a mode distributed to AAA and a mode distributed to BBB. If multiple photons are combined at AAA and at BBB, the large variety of photon patterns observed after linear optics transformations of the local multi-mode systems can be used to characterize the non-classical correlation of this entangled state. However, the transformation between different photon number states in linear optics is a complicated problem, and further analysis is needed to understand the possible applications of this scalable quantum system. To obtain maximal complementarity between two measurements, we consider the unbiased interference of all input modes represented by a discrete Fourier transform of the multi-mode field. We identify characteristic patterns that can be used to identify non-classical correlations between the two multi-photon systems at AAA and BBB and derive a quantitative criterion for entanglement verification. Our results indicate that the large scale quantum operations can be achieved by a comparatively simple quantum network interfering the outputs of multiple single photons, where the size of the system mainly depends on the number of available single photon sources.
Entangled states of photons form the foundation of quantum communication, computation, and metrology. Yet their generation remains fundamentally constrained: in the absence of intrinsic photon-photon interactions, the generation of such states is inherently probabilistic rather than deterministic. The prevalent technique of post-selection verifies the creation of an entangled state by detecting and thus destroying it. Heralding offers a solution in which measuring ancillary photons in auxiliary modes signals the state generation without the need to measure it. Here, we introduce and experimentally demonstrate a scheme to generate a three-mode two-photon NOON state, where the detection of a single photon in one heralding mode signifies the presence of the state in three target modes. We validate the generated state by estimating a fidelity of 0.823 +/- 0.018 with respect to an ideal three-mode NOON state and certifying genuine multipartite entanglement. By virtue of the high success probability and small resource overhead of our scheme, our work provides a theoretical and experimental stepping stone for entangled multi-mode state generation, which is realizable with current technology. These multi-mode entangled states represent a key direction for linear optical quantum information that is complementary to multi-qubit state encoding.
Optical multi-mode systems provide large scale Hilbert spaces that can be accessed and controlled using single photon sources, linear optics and photon detection. Here, we consider the bipartite entanglement generated by coherently distributing M photons in M modes to two separate locations, where linear optics and photon detection is used to verify the non-classical correlations between the two M -mode systems. We show that the entangled state is symmetric under mode shift operations performed in the two systems and use this symmetry to derive correlations between photon number distributions detected after a discrete Fourier transform (DFT) of the modes. The experimentally observable correlations can be explained by a simple and intuitive rule that relates the sum of the output mode indices to the eigenvalue of the input state under the mode shift operation. Since the photon number operators after the DFT do not commute with the initial photon number operators, entanglement is necessary to achieve strong correlations in both the initial mode photon numbers and the photon numbers observed after the DFT. We can therefore derive entanglement witnesses based on the experimentally observable correlations in both photon number distributions, providing a practical criterion for the evaluation of large scale entanglement in optical multi-mode systems. Our method thus demonstrates how non-classical signatures in large scale optical quantum circuits can be accessed experimentally by choosing an appropriate combination of modes in which to detect the photon number distributions that characterize the quantum coherences of the state.
Multiphoton interference results in a wide variety of non-classical photon number statistics, including characteristic signatures of entanglement between two or more sets of optical modes. Here, we consider the photon number statistics observed after applying discrete Fourier transformations (DFTs) to bipartite entangled states generated using single photon sources and beam splitters. It is shown that the output photon number states of DFTs are eigenstates of a translational mode shifting operator in the input. The complex eigenvalues of the mode shift can be identified by a phase number K obtained from the output photon distribution. For each output distribution, the possible input states are limited to mode shift eigenstates with the same K-value. Using this mode shift rule, we can identify the quantum coherence between different photon number distributions in the input with experimentally observable K-values in the output of the DFT. In the case of multi-photon entanglement obtained by post-selection and beam splitting single photons, this coherence is non-local, resulting in correlated pairs of K-values that always sum up to zero. We can therefore observe both the correlations between the input photon number distributions and a complementary correlation between the output photon numbers of two DFTs to obtain a reliable characterization of the entanglement between the two multi-mode multi-photon systems. Importantly, the K-value allows a classification of large sets of possible photon number distributions, resulting in a significant simplification of the experimental evaluation of the multi-photon output statistics and opening up the road towards more efficient applications of non-classical multi-photon states