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arXiv:2205.11160 · Physical Review Applied

Quantum State Tomography of Qudits via Hong-Ou-Mandel Interference

Yoshiaki Tsujimoto, Rikizo Ikuta, Kentaro Wakui, Toshiki Kobayashi, Mikio Fujiwara

Published Jan 4, 2023• 7 citations
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Abstract

We propose a method to perform the quantum state tomography (QST) of an $n$-partite qudit state embedded in single photons based on the Hong-Ou-Mandel interference between the target photon and ancillary probe light. Our method requires only passive beam splitters in the target modes by shifting all of the active devices used in conventional QST methods to the probe preparation system. This feature is useful when the active optical devices for QST have large optical losses. Moreover, even when the probe is prepared by a laser light having a mode mismatch with the target photon, the method offers an accurate estimation of the target state. As a proof-of-principle, we perform the experimental demonstration using a polarization qubit. Regardless of the photon statistics of the probe light, the estimated results of state reconstruction are as accurate as those verified by the conventional QST.

DOI
10.1103/physrevapplied.19.014008

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We propose a method to perform the quantum state tomography (QST) of an nnn-partite qudit state embedded in single photons based on the Hong-Ou-Mandel interference between the target photon and ancillary probe light. Our method requires only passive beam splitters in the target modes by shifting all of the active devices used in conventional QST methods to the probe preparation system. This feature is useful when the active optical devices for QST have large optical losses. Moreover, even when the probe is prepared by a laser light having a mode mismatch with the target photon, the method offers an accurate estimation of the target state. As a proof-of-principle, we perform the experimental demonstration using a polarization qubit. Regardless of the photon statistics of the probe light, the estimated results of state reconstruction are as accurate as those verified by the conventional QST.
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Hong-Ou-Mandel (HOM) interference [1] is a bunching phenomenon based on the bosonic nature of photons. When two photons that are perfectly indistinguishable from each other are mixed using a half beam splitter (HBS), they always bunch and exhibit the absence of coincidence resulting in a specific interferogram called HOM dip. The important property of the HOM interference is that the decrease in coincidence reflects the degree of indistinguishability of the input photons, i.e., it provides information regarding the probability of overlap of the input photons. Thus, this property should enable the estimation of a target photon in an unknown quantum state using a probe photon in a known state. In this work, we realize the above concept as the quantum state tomography (QST) applicable to d-dimensional photonic qudits, which we call HOM-QST [2]. Interestingly, we observe that HOM-QST is robust against various imperfections and that the probe photon can be replaced by classical light. Furthermore, we confirm this by demonstrating a proof-of-principle experiment using two-dimensional polarization qubits.
Quantum state tomography (QST) has been the traditional method for characterization of an unknown state. Recently, many direct measurement methods have been implemented to reconstruct the state in a resource efficient way. In this Letter, we present an interferometric method, in which any qubit state, whether mixed or pure, can be inferred from the visibility, phase shift, and average intensity of an interference pattern using a single-shot measurement-hence, we call it quantum state interferography. This provides us with a "black box" approach to quantum state estimation, wherein, between the incidence of the photon and extraction of state information, we are not changing any conditions within the setup, thus giving us a true single shot estimation of the quantum state. In contrast, standard QST requires at least two measurements for pure state qubit and at least three measurements for mixed state qubit reconstruction. We then go on to show that QSI is more resource efficient than QST for quantification of entanglement in pure bipartite qubits. We experimentally implement our method with high fidelity using the polarization degree of freedom of light. An extension of the scheme to pure states involving d-1 interferograms for d-dimensional systems is also presented. Thus, the scaling gain is even more dramatic in the qudit scenario for our method, where, in contrast, standard QST, without any assumptions, scales roughly as d^{2}.
We provide a comprehensive analysis of the reconstruction of the density matrix for entangled photon pairs, utilizing polarization measurements within a Hong-Ou-Mandel (HOM) interference framework. The purpose of this study is to develop a new efficient approach for quantum state characterization, leveraging quantum interference to reduce wave dispersion and utilizing the maximum likelihood method for density matrix reconstruction. The model involves projecting the entangled photons onto a set of sixteen unique polarization states, enabling the observation of detailed quantum interference patterns. We use these patterns to reconstruct the density matrix, revealing the system’s quantum state and degree of entanglement. Our findings demonstrate the effectiveness of this method in accurately characterizing the quantum state of light, while leveraging quantum interference to reduce wave dispersion and improve signal quality and resolution. Our study underscores the effectiveness of this method in accurately characterizing the quantum state of light and highlights the essential role of precise density matrix reconstruction in a Hong-Ou-Mandel interferometer without the use of polarizers. The methodology and results presented lay a strong foundation for further research, with implications for improving measurement accuracy and exploring more complex quantum systems in various quantum information applications. • Density matrix of entangled photon pairs using Hong-Ou-Mandel interference profiles. • Quantum interference and density matrix improve signal quality. • Density matrix is reconstructed using HOM interference and maximum likelihood. • Theoretical study on quantum state reconstruction and its role in quantum information.
We report a technique for experimental characterization of an M -mode quantum optical process, generalizing the single-mode coherent-state quantum-process tomography method [ 1 , 2 ]. By measuring the effect of the process on multi-mode coherent states via balanced homodyne tomography, we obtain the process tensor in the Fock basis. This rank- tensor, which predicts the effect of the process on an arbitrary density matrix, is iteratively reconstructed directly from the experimental data via the maximum-likelihood method. We demonstrate the capabilities of our method using the example of a beam splitter, reconstructing its process tensor within the subspace spanned by the first three Fock states. In spite of using purely classical probe states, we recover quantum properties of this optical element, in particular the Hong–Ou–Mandel effect.
Entanglement is not only fundamental for understanding multipartite quantum systems but also generally useful for quantum information applications. Despite much effort devoted so far, little is known about minimal resources for detecting entanglement and also comparisons to tomography which reveals the full characterization. Here, we show that all entangled states can in general be detected in an experimental scheme that estimates the fidelity of two pure quantum states. An experimental proposal is presented with a single Hong-Ou-Mandel interferometry in which only two detectors are applied regardless of the dimensions or the number of modes of quantum systems. This shows measurement settings for entanglement detection are in general inequivalent to tomography: the number of detectors in quantum tomography increases with the dimensions and the modes whereas it is not the case in estimation of fidelity which detects entangled states.