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Physica Scripta

Homodyne detection of temporally resolved quantum states

Owen Sandner, Brendan Mackey, Yuyang Liu, Connor Kupchak, Andrew MacRae

Published May 7, 2026• 1 citation
Publisher

Abstract

Abstract We present an analysis of the time domain measurement of temporally resolvable quantum states using balanced homodyne detection. Our approach outlines a formalism of detecting quantum states in arbitrary temporal modes via projection of the temporal mode onto a natural detector basis. We then present an algorithm for simulating the resultant photocurrent of continuous homodyne detection in the presence of a temporally resolved mode, and use this algorithm to explore the effects of realistic measurement errors on reconstruction of the marginal probability distribution and quantum state tomography. A complete implementation of the method is provided through open source code on a GitHub repository.

DOI
10.1088/1402-4896/ae6a30

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Abstract We present an analysis of the time domain measurement of temporally resolvable quantum states using balanced homodyne detection. Our approach outlines a formalism of detecting quantum states in arbitrary temporal modes via projection of the temporal mode onto a natural detector basis. We then present an algorithm for simulating the resultant photocurrent of continuous homodyne detection in the presence of a temporally resolved mode, and use this algorithm to explore the effects of realistic measurement errors on reconstruction of the marginal probability distribution and quantum state tomography. A complete implementation of the method is provided through open source code on a GitHub repository.
We present an analysis of the time domain measurement of temporally resolvable quantum states using balanced homodyne detection. Our approach outlines a formalism of detecting quantum states in arbitrary temporal modes via projection of the temporal mode onto a natural detector basis. We then present an algorithm for simulating the resultant photocurrent of continuous homodyne detection in the presence of a temporally resolved mode, and use this algorithm to explore the effects of realistic measurement errors on marginal reconstruction and quantum state tomography. A complete implementation of the method is provided through open source code on a GitHub repository.
We have developed a technique for dual-temporal-mode, ultrafast, time-domain, balanced homodyne detection. We have tested it by performing homodyne measurements on pairs of picosecond-duration temporal modes (or “time bins”) carrying a delocalized single photon. The experimental homodyne data have been used to reconstruct both the density matrix and the two-mode Wigner function of the delocalized state, thus showing the correlations existing between the pair of temporal modes carrying the single photon.
Homodyne detection is a typical continuous-variable measurement scheme, ubiquitously used in quantum optics and quantum information. A conventional homodyne detector performs a projective measurement onto a quadrature of the electromagnetic field mode, thus yielding a continuously distributed measurement outcome. The outcome distribution is the marginal of the Wigner function of the state. Homodyne detection also forms the basis of heterodyne, or “dual homodyne” detection, which corresponds to measuring the Q function of the state.
In this work, a continuous variable quantum tomography is presented. This is done using two approaches, one using simulated data and another one using data from measurements performed in the laboratory. The Radon inverse transform, under the approximation of filtered back projection, alongside the details on the implementa- tion of balanced homodyne detection needed to perform the tomography are clearly explained. Density matrices in the quadrature and number representation are also obtained from the Wigner function. Additionally, complete documentation of the computational implementation and a user-friendly interface for the tomography is reported
We present a method for measuring quantum states encoded in the temporal modes of photons. The basis for the multilevel quantum states is defined by the use of modes propagating in a dispersive medium, which is a fiber in this case. The propagation and time-resolved single-photon detection allow us to define a positive-operator valued measure (POVM). The POVM depends on the amount of dispersion and the characteristics of a detector. This framework is numerically tested by performing quantum state tomography on a large number of states for a set of realistic experimental settings. Finally, the average fidelity between the expected and reconstructed states is computed for qubits, qutrits, and entangled qubits.
This thesis is concerned with the generation of non-classical quantum states of light, the photon-level manipulation of quantum states and the accurate tomography of both quantum states and quantum processes. In optics, quantum information can be encoded and processed in both discrete and continuous variables. Hybrid approaches combining for example homodyne detection with conditional state preparation and manipulation are gaining increasing prominence. The development and characterization of a time-domain balanced homodyne detector (BHD) is presented. The detector has a bandwidth of 80 MHz, a signal-to-noise ratio of 14.5 dB and an efficiency of 86% making it well-suited to pulse-to-pulse measurement of quantum optical states. The BHD is employed to perform quantum state tomography (QST) of non-classical multi-photon Fock states generated by spontaneous parametric down-conversion. A detailed investigation of the mode-matching between the local oscillator used for homodyne detection and the generated Fock states is presented. The one-, two- and three-photon Fock states are reconstructed with a combined preparation and detection efficiency exceeding 50%. Fock states have a number of applications in quantum state engineering, where non-classical ancilla states and conditional measurements enable photon-level manipulation of quantum states. Fock state filtration (FSF) is investigated - an example of a post-selected beam splitter which is a basic building block for many quantum state engineering protocols. A model is developed incorporating the effect of experimental imperfections. An experimental implementation of a Fock state filter is fully characterized by means of coherent-state quantum process tomography (QPT). The reconstructed process is found to be consistent with the model. The filter preferentially removes the single-photon component from an arbitrary input quantum state. Calibration of optical detectors in the quantum regime is discussed. Quantum detector tomography (QDT) is reviewed and contrasted with a new technique for performing QST with a calibrated detector known as the fitting of data patterns (FDP). The first experimental characterization of a BHD is performed by probing the detector with phase-averaged coherent states. The FDP method is shown to be applicable to the estimation of quantum processes, where a detector response is not assumed - thus demonstrating the versatility of the FDP approach as a new method in the quantum tomography toolbox.