648 Hilbert-space dimensionality in a biphoton frequency comb: entanglement of formation and Schmidt mode decomposition

Abstract Qudit entanglement is an indispensable resource for quantum information processing since increasing dimensionality provides a pathway to higher capacity and increased noise resilience in quantum communications, and cluster-state quantum computations. In continuous-variable time–frequency en...

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Autores principales:	Kai-Chi Chang, Xiang Cheng, Murat Can Sarihan, Abhinav Kumar Vinod, Yoo Seung Lee, Tian Zhong, Yan-Xiao Gong, Zhenda Xie, Jeffrey H. Shapiro, Franco N. C. Wong, Chee Wei Wong
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Physics QC1-999 Electronic computers. Computer science QA75.5-76.95
Acceso en línea:	https://doaj.org/article/49322c33b24b4e269f032adb4ba6025b
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spelling	oai:doaj.org-article:49322c33b24b4e269f032adb4ba6025b2021-12-02T13:19:24Z648 Hilbert-space dimensionality in a biphoton frequency comb: entanglement of formation and Schmidt mode decomposition10.1038/s41534-021-00388-02056-6387https://doaj.org/article/49322c33b24b4e269f032adb4ba6025b2021-03-01T00:00:00Zhttps://doi.org/10.1038/s41534-021-00388-0https://doaj.org/toc/2056-6387Abstract Qudit entanglement is an indispensable resource for quantum information processing since increasing dimensionality provides a pathway to higher capacity and increased noise resilience in quantum communications, and cluster-state quantum computations. In continuous-variable time–frequency entanglement, encoding multiple qubits per photon is only limited by the frequency correlation bandwidth and detection timing jitter. Here, we focus on the discrete-variable time–frequency entanglement in a biphoton frequency comb (BFC), generating by filtering the signal and idler outputs with a fiber Fabry–Pérot cavity with 45.32 GHz free-spectral range (FSR) and 1.56 GHz full-width-at-half-maximum (FWHM) from a continuous-wave (cw)-pumped type-II spontaneous parametric downconverter (SPDC). We generate a BFC whose time-binned/frequency-binned Hilbert space dimensionality is at least 324, based on the assumption of a pure state. Such BFC’s dimensionality doubles up to 648, after combining with its post-selected polarization entanglement, indicating a potential 6.28 bits/photon classical-information capacity. The BFC exhibits recurring Hong–Ou–Mandel (HOM) dips over 61 time bins with a maximum visibility of 98.4% without correction for accidental coincidences. In a post-selected measurement, it violates the Clauser–Horne–Shimony–Holt (CHSH) inequality for polarization entanglement by up to 18.5 standard deviations with an S-parameter of up to 2.771. It has Franson interference recurrences in 16 time bins with a maximum visibility of 96.1% without correction for accidental coincidences. From the zeroth- to the third-order Franson interference, we infer an entanglement of formation (E of) up to 1.89 ± 0.03 ebits—where 2 ebits is the maximal entanglement for a 4 × 4 dimensional biphoton—as a lower bound on the 61 time-bin BFC’s high-dimensional entanglement. To further characterize time-binned/frequency-binned BFCs we obtain Schmidt mode decompositions of BFCs generated using cavities with 45.32, 15.15, and 5.03 GHz FSRs. These decompositions confirm the time–frequency scaling from Fourier-transform duality. Moreover, we present the theory of conjugate Franson interferometry—because it is characterized by the state’s joint-temporal intensity (JTI)—which can further help to distinguish between pure-state BFC and mixed state entangled frequency pairs, although the experimental implementation is challenging and not yet available. In summary, our BFC serves as a platform for high-dimensional quantum information processing and high-dimensional quantum key distribution (QKD).Kai-Chi ChangXiang ChengMurat Can SarihanAbhinav Kumar VinodYoo Seung LeeTian ZhongYan-Xiao GongZhenda XieJeffrey H. ShapiroFranco N. C. WongChee Wei WongNature PortfolioarticlePhysicsQC1-999Electronic computers. Computer scienceQA75.5-76.95ENnpj Quantum Information, Vol 7, Iss 1, Pp 1-11 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999 Electronic computers. Computer science QA75.5-76.95
spellingShingle	Physics QC1-999 Electronic computers. Computer science QA75.5-76.95 Kai-Chi Chang Xiang Cheng Murat Can Sarihan Abhinav Kumar Vinod Yoo Seung Lee Tian Zhong Yan-Xiao Gong Zhenda Xie Jeffrey H. Shapiro Franco N. C. Wong Chee Wei Wong 648 Hilbert-space dimensionality in a biphoton frequency comb: entanglement of formation and Schmidt mode decomposition
description	Abstract Qudit entanglement is an indispensable resource for quantum information processing since increasing dimensionality provides a pathway to higher capacity and increased noise resilience in quantum communications, and cluster-state quantum computations. In continuous-variable time–frequency entanglement, encoding multiple qubits per photon is only limited by the frequency correlation bandwidth and detection timing jitter. Here, we focus on the discrete-variable time–frequency entanglement in a biphoton frequency comb (BFC), generating by filtering the signal and idler outputs with a fiber Fabry–Pérot cavity with 45.32 GHz free-spectral range (FSR) and 1.56 GHz full-width-at-half-maximum (FWHM) from a continuous-wave (cw)-pumped type-II spontaneous parametric downconverter (SPDC). We generate a BFC whose time-binned/frequency-binned Hilbert space dimensionality is at least 324, based on the assumption of a pure state. Such BFC’s dimensionality doubles up to 648, after combining with its post-selected polarization entanglement, indicating a potential 6.28 bits/photon classical-information capacity. The BFC exhibits recurring Hong–Ou–Mandel (HOM) dips over 61 time bins with a maximum visibility of 98.4% without correction for accidental coincidences. In a post-selected measurement, it violates the Clauser–Horne–Shimony–Holt (CHSH) inequality for polarization entanglement by up to 18.5 standard deviations with an S-parameter of up to 2.771. It has Franson interference recurrences in 16 time bins with a maximum visibility of 96.1% without correction for accidental coincidences. From the zeroth- to the third-order Franson interference, we infer an entanglement of formation (E of) up to 1.89 ± 0.03 ebits—where 2 ebits is the maximal entanglement for a 4 × 4 dimensional biphoton—as a lower bound on the 61 time-bin BFC’s high-dimensional entanglement. To further characterize time-binned/frequency-binned BFCs we obtain Schmidt mode decompositions of BFCs generated using cavities with 45.32, 15.15, and 5.03 GHz FSRs. These decompositions confirm the time–frequency scaling from Fourier-transform duality. Moreover, we present the theory of conjugate Franson interferometry—because it is characterized by the state’s joint-temporal intensity (JTI)—which can further help to distinguish between pure-state BFC and mixed state entangled frequency pairs, although the experimental implementation is challenging and not yet available. In summary, our BFC serves as a platform for high-dimensional quantum information processing and high-dimensional quantum key distribution (QKD).
format	article
author	Kai-Chi Chang Xiang Cheng Murat Can Sarihan Abhinav Kumar Vinod Yoo Seung Lee Tian Zhong Yan-Xiao Gong Zhenda Xie Jeffrey H. Shapiro Franco N. C. Wong Chee Wei Wong
author_facet	Kai-Chi Chang Xiang Cheng Murat Can Sarihan Abhinav Kumar Vinod Yoo Seung Lee Tian Zhong Yan-Xiao Gong Zhenda Xie Jeffrey H. Shapiro Franco N. C. Wong Chee Wei Wong
author_sort	Kai-Chi Chang
title	648 Hilbert-space dimensionality in a biphoton frequency comb: entanglement of formation and Schmidt mode decomposition
title_short	648 Hilbert-space dimensionality in a biphoton frequency comb: entanglement of formation and Schmidt mode decomposition
title_full	648 Hilbert-space dimensionality in a biphoton frequency comb: entanglement of formation and Schmidt mode decomposition
title_fullStr	648 Hilbert-space dimensionality in a biphoton frequency comb: entanglement of formation and Schmidt mode decomposition
title_full_unstemmed	648 Hilbert-space dimensionality in a biphoton frequency comb: entanglement of formation and Schmidt mode decomposition
title_sort	648 hilbert-space dimensionality in a biphoton frequency comb: entanglement of formation and schmidt mode decomposition
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/49322c33b24b4e269f032adb4ba6025b
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648 Hilbert-space dimensionality in a biphoton frequency comb: entanglement of formation and Schmidt mode decomposition

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