Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2101.06360 · Physical Review A

Positive operator-valued measure for two-photon detection via sum-frequency generation

Sofiane Merkouche, Valérian Thiel, Brian J. Smith

Published Apr 14, 2021• 4 citations
arXivHTMLPDF

Abstract

Spontaneous parametric down conversion (PDC), in the perturbative limit, can be considered as a probabilistic splitting of one input photon into two output photons. Conversely, sum-frequency generation (SFG) implements the reverse process of combining two input photons into one. Here we show that a single-photon projective measurement in the temporal-mode basis of the output photon of a two-photon SFG process affects a generalized measurement on the input two-photon state. We describe the positive operator-valued measure (POVM) associated with such a measurement and show that its elements are proportional to the two-photon states produced by the time-reversed PDC process. Such a detection acts as a joint measurement on two photons and is thus an important component of many quantum information processing protocols relying on photonic entanglement. Using the retrodictive approach, we analyze the properties of the two-photon POVM that are relevant for quantum protocols exploiting two-photon states and measurements.

DOI
10.1103/physreva.103.043711

Related papers

The POVM for two-photon detection based on sum-frequency generation

Sofiane Merkouche, Brian J. Smith

The positive operator-valued measure (POVM) for two-photon detection based on temporal-mode resolved sum-frequency generation is presented and characterized in terms ofthe projectivity, orthogonality, and entanglement of its elements.

The Rochester Conferences on Coherence and Quantum Optics and the Quantum Information and Measurement meeting•Jan 1, 2019•0 citations

Spectral characterization of photon-pair sources via classical sum-frequency generation

Fumihiro Kaneda, Jo Oikawa, Masahiro Yabuno +5 more

Tailoring spectral properties of photon pairs is of great importance for optical quantum information and measurement applications. High-resolution spectral measurement is a key technique for engineering spectral properties of photons, making them ideal for various quantum applications. Here we demonstrate spectral measurements and optimization of frequency-entangled photon pairs produced via spontaneous parametric downconversion (SPDC), utilizing frequency-resolved sum-frequency generation (SFG), the reverse process of SPDC. A joint phase-matching spectrum of a nonlinear crystal around 1580 nm is captured with a 40 pm resolution and a > 40 dB signal-to-noise ratio, which is significantly improved compared to traditional frequency-resolved coincidence measurements. Moreover, our scheme is applicable to collinear degenerate sources whose characterization is difficult with previously demonstrated stimulated difference frequency generation (DFG). We also illustrate that the observed phase-matching function is useful for finding an optimal pump spectrum to maximize the spectral indistinguishability of SPDC photons. We expect that our precise spectral characterization technique will be useful tool for characterizing and tailoring SPDC sources for a wide range of optical quantum applications.

arXiv:2010.07678•Optics Express•Nov 30, 2020•14 citations

How to project onto an arbitrary single-photon wave packet

Tzula B. Propp, S. J. van Enk

The time-frequency degree of freedom of the electromagnetic field is the final frontier for single-photon measurements. The temporal and spectral distribution a measurement retrodicts (that is, the state it projects onto) is determined by the detector's intrinsic resonance structure. In this paper, we construct ideal and more realistic positive operator-valued measures (POVMs) that project onto arbitrary single-photon wave packets with high efficiency and low noise. We discuss applications to super-resolved measurements and quantum communication. In doing so we will give a fully quantum description of the entire photodetection process, give prescriptions for (in principle) performing single-shot Heisenberg-limited time-frequency measurements of single photons, and discuss fundamental limits and trade-offs inherent to single-photon detection.

arXiv:2005.11305•Physical Review A•Nov 9, 2020•6 citations

Time-frequency quantum process tomography of parametric down-conversion

Malte Avenhaus, Benjamin Brecht, Kaisa Laiho +1 more

Parametric down-conversion (PDC) is the established standard for the practical generation of a multiplicity of quantum optical states. These include two-mode squeezed vacuum, heralded non-Gaussian states and entangled photon pairs. Detailed theoretical studies provide insight into the time-frequency (TF) structure of PDC, which are governed by the complex-valued joint spectral amplitude (JSA) function. However in experiments, the TF structure of PDC is mostly characterised by intensity measurementsthat forbid access to the important phase of the JSA. In this paper, we present an amplitude-sensitive quantum process tomography technique that combines methods from ultrafast optics and classical three-wave mixing. Our approach facilitates a direct and phase-sensitive time-frequency tomography of PDC with high spectral resolution and excellent signal-to-noise ratio. This is important for all quantum optical applications, which rely on engineered parametric processes and base on minute knowledge of the quantum wave-function for the generation of tailored photonic quantum states.

arXiv:1406.4252•Jun 17, 2014•2 citations

Efficient Bi-Photon State Characterisation and Its Applications in Quantum Technologies

Ebrahim Karimi

High-dimensional photonic entangled states are key resources for advancing quantum imaging, quantum sensing, secure communication, and quantum computation. The most common method for generating such states is spontaneous parametric down-conversion (SPDC), in which a pump photon splits into two daughter photons that share correlations across multiple photonic degrees of freedom. Characterising these high-dimensional states, however, is highly challenging, as it scales quadratically with the state dimensionality and usually requires large sets of projective measurements within the framework of positive operator-valued measures (POVMs).

Frontiers in Optics•Jan 1, 2025•0 citations

Joint Temporal Density Measurements for Two-Photon State Characterization

Onur Kuzucu, Franco N. C. Wong, Sunao Kurimura +1 more

We demonstrate a technique for characterizing two-photon quantum states based on joint temporal correlation measurements using time-resolved single-photon detection by femtosecond up-conversion. We measure for the first time the joint temporal density of a two-photon entangled state, showing clearly the time anticorrelation of the coincident-frequency entangled photon pair generated by ultrafast spontaneous parametric down-conversion under extended phase-matching conditions. The new technique enables us to manipulate the frequency entanglement by varying the down-conversion pump bandwidth to produce a nearly unentangled two-photon state that is expected to yield a heralded single-photon state with a purity of 0.88. The time-domain correlation technique complements existing frequency-domain measurement methods for a more complete characterization of photonic entanglement.

arXiv:0807.1573•Physical Review Letters•Oct 7, 2008•101 citations
Spontaneous parametric down conversion (PDC), in the perturbative limit, can be considered as a probabilistic splitting of one input photon into two output photons. Conversely, sum-frequency generation (SFG) implements the reverse process of combining two input photons into one. Here we show that a single-photon projective measurement in the temporal-mode basis of the output photon of a two-photon SFG process affects a generalized measurement on the input two-photon state. We describe the positive operator-valued measure (POVM) associated with such a measurement and show that its elements are proportional to the two-photon states produced by the time-reversed PDC process. Such a detection acts as a joint measurement on two photons and is thus an important component of many quantum information processing protocols relying on photonic entanglement. Using the retrodictive approach, we analyze the properties of the two-photon POVM that are relevant for quantum protocols exploiting two-photon states and measurements.
Tailoring spectral properties of photon pairs is of great importance for optical quantum information and measurement applications. High-resolution spectral measurement is a key technique for engineering spectral properties of photons, making them ideal for various quantum applications. Here we demonstrate spectral measurements and optimization of frequency-entangled photon pairs produced via spontaneous parametric downconversion (SPDC), utilizing frequency-resolved sum-frequency generation (SFG), the reverse process of SPDC. A joint phase-matching spectrum of a nonlinear crystal around 1580 nm is captured with a 40 pm resolution and a > 40 dB signal-to-noise ratio, which is significantly improved compared to traditional frequency-resolved coincidence measurements. Moreover, our scheme is applicable to collinear degenerate sources whose characterization is difficult with previously demonstrated stimulated difference frequency generation (DFG). We also illustrate that the observed phase-matching function is useful for finding an optimal pump spectrum to maximize the spectral indistinguishability of SPDC photons. We expect that our precise spectral characterization technique will be useful tool for characterizing and tailoring SPDC sources for a wide range of optical quantum applications.
The time-frequency degree of freedom of the electromagnetic field is the final frontier for single-photon measurements. The temporal and spectral distribution a measurement retrodicts (that is, the state it projects onto) is determined by the detector's intrinsic resonance structure. In this paper, we construct ideal and more realistic positive operator-valued measures (POVMs) that project onto arbitrary single-photon wave packets with high efficiency and low noise. We discuss applications to super-resolved measurements and quantum communication. In doing so we will give a fully quantum description of the entire photodetection process, give prescriptions for (in principle) performing single-shot Heisenberg-limited time-frequency measurements of single photons, and discuss fundamental limits and trade-offs inherent to single-photon detection.
Parametric down-conversion (PDC) is the established standard for the practical generation of a multiplicity of quantum optical states. These include two-mode squeezed vacuum, heralded non-Gaussian states and entangled photon pairs. Detailed theoretical studies provide insight into the time-frequency (TF) structure of PDC, which are governed by the complex-valued joint spectral amplitude (JSA) function. However in experiments, the TF structure of PDC is mostly characterised by intensity measurementsthat forbid access to the important phase of the JSA. In this paper, we present an amplitude-sensitive quantum process tomography technique that combines methods from ultrafast optics and classical three-wave mixing. Our approach facilitates a direct and phase-sensitive time-frequency tomography of PDC with high spectral resolution and excellent signal-to-noise ratio. This is important for all quantum optical applications, which rely on engineered parametric processes and base on minute knowledge of the quantum wave-function for the generation of tailored photonic quantum states.
High-dimensional photonic entangled states are key resources for advancing quantum imaging, quantum sensing, secure communication, and quantum computation. The most common method for generating such states is spontaneous parametric down-conversion (SPDC), in which a pump photon splits into two daughter photons that share correlations across multiple photonic degrees of freedom. Characterising these high-dimensional states, however, is highly challenging, as it scales quadratically with the state dimensionality and usually requires large sets of projective measurements within the framework of positive operator-valued measures (POVMs).
We demonstrate a technique for characterizing two-photon quantum states based on joint temporal correlation measurements using time-resolved single-photon detection by femtosecond up-conversion. We measure for the first time the joint temporal density of a two-photon entangled state, showing clearly the time anticorrelation of the coincident-frequency entangled photon pair generated by ultrafast spontaneous parametric down-conversion under extended phase-matching conditions. The new technique enables us to manipulate the frequency entanglement by varying the down-conversion pump bandwidth to produce a nearly unentangled two-photon state that is expected to yield a heralded single-photon state with a purity of 0.88. The time-domain correlation technique complements existing frequency-domain measurement methods for a more complete characterization of photonic entanglement.