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Demonstration of a Simple Entangling Optical Gate and Its Use in Bell-State Analysis
Open accessAbstract
We demonstrate a new architecture for an optical entangling gate that is significantly simpler than previous realizations, using partially polarizing beam splitters so that only a single optical mode-matching condition is required. We demonstrate operation of a controlled-z gate in both continuous-wave and pulsed regimes of operation, fully characterizing it in each case using quantum process tomography. We also demonstrate a fully resolving, nondeterministic optical Bell-state analyzer based on this controlled-z gate. This new architecture is ideally suited to guided optics implementations of optical gates.
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TL;DR
The paper demonstrates a simplified optical entangling controlled-z gate using partially-polarising beamsplitters, requiring only one nonclassical mode-matching condition and no classical interferometers. It fully characterizes the gate in continuous-wave and pulsed regimes and uses it as a nondeterministic Bell-state analyser.
Key findings
- The PPBS controlled-z gate uses three partially-polarising beamsplitters, two half-wave plates, no classical interferometers, and no ancilla photons; the controlled-z operation succeeds with probability 1/9 and is heralded by one photon in each output.
- Quantum process tomography gives CW and pulsed process fidelities of 74.6±0.3% and 84.0±0.1%, and average gate fidelities of 79.7±0.2% and 87.2±0.1%; with modelled single-qubit unitary corrections these rise to 77.0±0.3% and 86.6±0.2% process fidelity, and 81.6±0.2% and 89.3±0.1% average gate fidelity.
- As a Bell-state analyser, the average fidelity of measured output states with separable states is 79±3%, and the directly measured average probability of success is 78±3%.
- The pulsed-gate PPBS reflectivities were η = 0.28, 0.28, and 0.29 (±0.01); modelling a gate with 0.28 reflectivities gives an optimum process fidelity of 96%, indicating the gate is relatively forgiving of exact splitting ratios.
Methods
- Photon pairs were generated by spontaneous parametric downconversion in a BBO crystal using both continuous-wave and femtosecond-pulsed sources, collected into single-mode fibers, and injected into the PPBS controlled-z gate; a coincidence window of ∼5 ns was used with no correction for accidental counts.
- The gate was characterized by quantum process tomography in both CW and pulsed regimes, using process fidelity and average gate fidelity metrics.
- The Bell-state analyser was tested with entangled CW input states, including the four maximally entangled states |ψ′± and |φ′±, using quantum state tomography and a directly measured truth table.
Limitations
- The paper states that PPBS beamsplitting ratios are fixed at manufacture, unlike schemes where a half-wave plate sets effective reflectivity; performance is limited almost exclusively by mode matching, primarily spatial.
- The paper reports systematic fixed rotations of input and output polarisations, probably from birefringent effects in non-ideal PPBSs, which could be compensated with wave plates.
- The Bell measurement is nondeterministic, and the paper notes that a protocol using this gate would be less efficient than ordinary classical communication; the measured output Bell states are unentangled but somewhat mixed (average linear entropy SL = 0.42 ± 0.07).
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14 Own result · 8 Own interpretation · 7 Not checked yet · 2 No basis given · 1 Own method
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In the paper
“by comparing the two we find that temporal mode mismatch was not a significant factor in the gate's performance.”
§ Demonstration of a Simple Entangling Optical Gate and Its Use in Bell-State Analysis > Abstract
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In the paper
“Their average tangle, T = 0.04 ± 0.05, and linear entropy, SL = 0.42 ± 0.07, indicates that they are unentangled, albeit somewhat mixed.”
§ Demonstration of a Simple Entangling Optical Gate and Its Use in Bell-State Analysis > Abstract
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“In our experiment, we observed systematic, fixed rotations of the input and output polarisations, probably due to birefringent effects in non-ideal PPBSs.”
§ Demonstration of a Simple Entangling Optical Gate and Its Use in Bell-State Analysis > Abstract
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In the paper
“We also demonstrate a fully-resolving, nondeterministic optical Bell-state analyser based on this controlled-z gate.”
- Also stated in: § Abstract · boosted
“we also demonstrate the use of this kind of gate for fully-resolving Bell measurements.”
§ Demonstration of a Simple Entangling Optical Gate and Its Use in Bell-State Analysis > Abstract
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- Rests on an assumption: The four Bell states can be discriminated by the cz gate after a Hadamard rotation.
- Rests on an assumption: An ideal cz gate takes the four maximally entangled states |ψ′±, |φ′± to the four separable orthogonal states |DD, |AD, |DA, and |AA respectively.
- Also stated in: § Abstract · boosted
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In the paper
“The circuit of Fig. 1(b) therefore performs a cz gate with additional x gates on the control and target qubits.”
§ Demonstration of a Simple Entangling Optical Gate and Its Use in Bell-State Analysis > Abstract
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In the paper
“In the cw case, the major deviation from ideal operation is the larger than expected ii term (0.36 instead of 0.25).”
§ Demonstration of a Simple Entangling Optical Gate and Its Use in Bell-State Analysis > Abstract
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In the paper
“Modelling a gate using 0.28 reflectivities, we find the optimum process fidelity that can be obtained is F 0.28 P = 96%-near ideal.”
§ Demonstration of a Simple Entangling Optical Gate and Its Use in Bell-State Analysis > Abstract
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In the paper
“In fact, they are close to the four orthogonal separable states (|H ± e iϕ1 |V ) ⊗ (|H ± e iϕ2 |V ), where ϕ 1 = -3.07 and ϕ 2 = 0.32 as determined by a best fit.”
§ Demonstration of a Simple Entangling Optical Gate and Its Use in Bell-State Analysis > Abstract
plain- Asserted: passes — The authors put it forward as true.
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- Rests on an assumption: An ideal cz gate takes the four maximally entangled states |ψ′±, |φ′± to the four separable orthogonal states |DD, |AD, |DA, and |AA respectively.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“We demonstrate operation of a controlled-z gate in both continuous-wave and pulsed regimes of operation, fully characterising it in each case using quantum process tomography.”
- Also stated in: § Abstract · boosted
“We demonstrate the operation of this type of gate using photons generated both by continuous-wave (CW) and by femtosecond pulsed parametric downconversion”
§ Demonstration of a Simple Entangling Optical Gate and Its Use in Bell-State Analysis > Abstract
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In the paper
“Here we take an alternative approach which does not require interferometric stability.”
- Also stated in: § Abstract · plain
“The key advantage of the PPBS gate is that the polarisation modes are never spatially separated and recombined, and consequently no classical interference conditions are required.”
§ Demonstration of a Simple Entangling Optical Gate and Its Use in Bell-State Analysis > Abstract
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- It may state two separate claims as one. 15
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In the paper
“Due to the geometry of the source, and birefringence and geometric effects in the single mode fibers, the near-maximally entangled state produced is of the form |HH + e iϕ |V V .”
- Also stated in: § Abstract · plain
“The tangle T = 0.93 ± 0.01 and linear entropy S L = 0.05 ± 0.01 show that this state is highly entangled and highly pure, the fidelity with a maximally entangled state is F = 98.0 ± 0.4%.”
§ Demonstration of a Simple Entangling Optical Gate and Its Use in Bell-State Analysis > Abstract
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In the paper
“The CW and pulsed gates have process fidelities of 74.6±0.3% and 84.0±0.1% respectively; and average gate fidelities of 79.7±0.2% and 87.2±0.1% [20].”
§ Demonstration of a Simple Entangling Optical Gate and Its Use in Bell-State Analysis > Abstract
What the sources say
- Not checked yetcites [20] source
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In the paper
“The four experimentally produced density matrices are shown in Fig. 3(e): the average of their fidelities is F = 95.8 ± 0.7%; the average of the tangles and linear entropies are T = 0.94 ± 0.02 and SL = 0.04 ± 0.01, respectively.”
§ Demonstration of a Simple Entangling Optical Gate and Its Use in Bell-State Analysis > Abstract
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In the paper
“To demonstrate this, we modelled their effect numerically, identifying single qubit unitary corrections which increased the CW and pulsed process fidelities to 77.0±0.3% and 86.6±0.2%respectively; and average gate fidelities to 81.6±0.2% and 89.3±0.1%.”
§ Demonstration of a Simple Entangling Optical Gate and Its Use in Bell-State Analysis > Abstract
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“The CW and pulsed gates have process fidelities of 74.6±0.3% and 84.0±0.1% respectively; and average gate fidelities of 79.7±0.2% and 87.2±0.1% [20].”
§ Demonstration of a Simple Entangling Optical Gate and Its Use in Bell-State Analysis > Abstract
What the sources say
- Not checked yetcites [20] source
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In the paper
“While the PPBSs for the CW gate (optimized for 702.2 nm) were measured to be within ±0.01 of the required reflectivities, for the pulsed gate (820 nm), the values for the three PPBSs were η = 0.28, 0.28 and 0.29 (±0.01; normalised to output power).”
§ Demonstration of a Simple Entangling Optical Gate and Its Use in Bell-State Analysis > Abstract
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In the paper
“Despite more stringent temporal modematching requirements in the pulsed regime, the extra spatial filtering led to better gate operation, equivalent to the previous best demonstration [7].”
§ Demonstration of a Simple Entangling Optical Gate and Its Use in Bell-State Analysis > Abstract
What the sources say
- Not checked yetcites [7] source
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“The average of the fidelities between all combinations of the measured output states is 24 ± 5% (ideally zero), demonstrating that the states are close to orthogonal.”
§ Demonstration of a Simple Entangling Optical Gate and Its Use in Bell-State Analysis > Abstract
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In the paper
“The results are shown in Fig. 3(c), and the average probability of success is 78 ± 3%, in agreement with the tomography results.”
§ Demonstration of a Simple Entangling Optical Gate and Its Use in Bell-State Analysis > Abstract
plaincorrelational- Asserted: passes — The authors put it forward as true.
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- Rests on an assumption: The four Bell states can be discriminated by the cz gate after a Hadamard rotation.
- Rests on an assumption: An ideal cz gate takes the four maximally entangled states |ψ′±, |φ′± to the four separable orthogonal states |DD, |AD, |DA, and |AA respectively.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The average fidelity of the measured output states with the above separable states is F = 79 ± 3%: if we analyzed the output of the circuit in this rotated basis, we would correctly identify the Bell-state with a probability of 79%.”
§ Demonstration of a Simple Entangling Optical Gate and Its Use in Bell-State Analysis > Abstract
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In the paper
“As originally anticipated in Ref. [13], the cz gate is relatively forgiving of the exact splitting ratios-making it an eminently suitable gate to be realised with a PPBS architecture.”
§ Demonstration of a Simple Entangling Optical Gate and Its Use in Bell-State Analysis > Abstract
What the sources say
- Not checked yetcites [13] source
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In the paper
“This cz gate is the simplest entangling (or dis-entangling) linear optics gate realized to date, requiring only three partially-polarising beam splitters (PPBSs), two half-wave plates, no classical interferometers, and no ancilla photons.”
§ Demonstration of a Simple Entangling Optical Gate and Its Use in Bell-State Analysis > Abstract
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In the paper
“It is nondeterministic and success is heralded by detection of a single photon in each of the outputs.”
§ Demonstration of a Simple Entangling Optical Gate and Its Use in Bell-State Analysis > Abstract
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In the paper
“Finally, we have demonstrated the operation of this gate as a Bell-state analyser which has the advantage of higher success probability and no ancillae compared to alternative recent demonstrations [9,27].”
§ Demonstration of a Simple Entangling Optical Gate and Its Use in Bell-State Analysis > Abstract
What the sources say
- Not checked yetcites [9] source
- Not checked yetcites [27]
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In the paper
“In practice, these have no effect on gate quality and, if necessary, could be compensated for with appropriate wave plates.”
§ Demonstration of a Simple Entangling Optical Gate and Its Use in Bell-State Analysis > Abstract
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The paper relies on this without support.
The short pump pulses in pulsed parametric downconversion lead to more stringent temporal mode-matching requirements.
“However, the short pump pulses lead to a larger bandwidth of downconverted photons, and to more stringent temporal mode-matching requirements.”
The paper relies on this without support.
The four Bell states can be discriminated by the cz gate after a Hadamard rotation.
“These are just the usual four Bell states, with the second qubit rotated by a Hadamard so that they can be discriminated by the cz gate.”
The paper relies on this without support.
An ideal cz gate takes the four maximally entangled states |ψ′±, |φ′± to the four separable orthogonal states |DD, |AD, |DA, and |AA respectively.
“An ideal cz gate would take the four maximally entangled states |ψ ′± , |φ ′± to the four separable orthogonal states: |DD , |AD , |DA , and |AA respectively.”
Claims other papers make about this one
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In the citing paper
“An even simpler set-up becomes possible with polarization encoding (Kiesel et al., 2005b;Langford et al., 2005;Okamoto et al., 2005) which in turn could be already applied, e.g., to observe cluster states for one-way quantum computing (see below, Kiesel et al., 2005a).”
From Multiphoton entanglement and interferometry (2012) · cites this paper as Langford et al., 2005
In the citing paper
“These results show that we have near-ideal algorithm performance, far better than we have any right to expect given the known errors inherent in the logic gates [8,29].”
From Experimental Demonstration of a Compiled Version of Shor’s Algorithm with Quantum Entanglement (2007) · cites this paper as [8]
In the citing paper
“We use a pair of compact optical gates [8,9,10], Fig 2c),e), each operating on a dependent pair of photons, resulting in measured visibilities for both of V r =98±2%.”
From Experimental Demonstration of a Compiled Version of Shor’s Algorithm with Quantum Entanglement (2007) · cites this paper as [8]
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Zhu, M.-Z., & Guang-yu, Y. (2011) · International Journal of Quantum Information · doi:10.1142/s0219749911007915 · Cited by 1
Efficient scheme for remote preparation of an arbitrary tripartite four-particle entangled state
Ma, P., Chen, G.-B., Li, X., & Zhan, Y.-B. (2017) · International Journal of Modern Physics B · doi:10.1142/s0217979218500236 · Cited by 1
Single-Copy Certification of Two-Qubit Gates Without Entanglement
Choi, Y., Singal, T., Cho, Y., Han, S.-W., Oh, K., Moon, S., Kim, Y., & Bae, J. (2022) · Physical Review Applied · doi:10.1103/physrevapplied.18.044046 · Cited by 1
Krupych, O. M., Martynyuk-Lototska, I. Y., Orykhivskyi, I., Adamenko, D., Kostyrko, M., & Vlokh, R. O. (2021) · Ukrainian Journal of Physical Optics · doi:10.3116/16091833/22/4/198/2021 · Cited by 1
Ringbauer, M. (2017) · Springer theses · doi:10.1007/978-3-319-64988-7_2 · Cited by 1
Detector entanglement: Quasidistributions for Bell-state measurements
Sperling, J., Gianani, I., Barbieri, M., & Agudelo, E. (2023) · Physical Review A · doi:10.1103/physreva.107.012426 · Cited by 1
Quantum Communication Experiments with Discrete Variables
Weinfurter, H. (2006) · Wiley eBooks · doi:10.1002/9783527618637.ch16 · Cited by 1
Wang, S., Cheng, Q., Gong, Y.-X., Xu, P., Li, L., Li, T., & Zhu, S. N. (2014) · arXiv (Cornell University) · doi:10.48550/arxiv.1408.2070 · Cited by 1
On the Squeezing and Over-Squeezing of Photons
Shalm, L. K. (2011) · TSpace (University of Toronto) · Cited by 1
Quantum Communication Experiments with Discrete Variables
Weinfurter, H. (2016) · Wiley eBooks · doi:10.1002/9783527805785.ch17 · Cited by 1
Experimental realization of an interferometric quantum circuit to increase the computational depth
Lipp, Y. O. (2011) · University of Vienna · doi:10.25365/thesis.17287 · Cited by 1
Photonic Toolbox for Quantum Simulation
Ma, X., Dakić, B., & Walther, P. J. (2014) · Advances in chemical physics · doi:10.1002/9781118742631.ch09
Efficient quantum-logic circuits: or, How I Learned to Stop Worrying and Love Hilbert Space
White, A. G., de Almeida, M. P., Barbieri, M., Biggerstaff, D. N., Dalton, R. B., Gilchrist, A., Gillett, G., James, D. F. V., Langford, N. K., Lanyon, B. P., et al. (2007) · Frontiers in Optics · doi:10.1364/fio.2007.jtua1
Self-citationAnalysis of errors in an optical controlled-NOT gate
Nagata, T., Okamoto, R., Sasaki, K., & Takeuchi, S. (2009) · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · doi:10.1117/12.829607
Optical quantum circuit combining tailored optical nonlinearities
Takeuchi, S., Okamoto, R., Fujiwara, M., Zhao, H.-Q., Hofmann, H. F., & O’Brien, J. L. (2011) · Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) · doi:10.1109/cleoe.2011.5943453
Self-citationJavadi, A., Rostami, A., Abbasian, K., & Gholizadeh, V. (2011) · Optik · doi:10.1016/j.ijleo.2010.12.032
Experimentally-friendly methods of generation and detection of quantum correlations
Bartkowiak, M. (2012) · Repozytorium Uniwersytetu im. Adama Mickiewicza (Adam Mickiewicz University in Poznań)
Multi Directional-Coupler Circuit for Quantum Logic
Matthews, J. C. F. (2012) · Springer theses · doi:10.1007/978-3-642-32870-1_4
applications in quantum information
Schmid, C. (2008)
Basic Concepts of Linear Optical System
Xu, X. (2016) · Springer theses · doi:10.1007/978-3-662-49804-0_1
Implementing quantum gates and channels using linear optics
Bonsma-Fisher, K. (2012) · UWSpace (University of Waterloo)
Experimental test of robust quantum detection and restoration of a qubit
Mičuda, M., Straka, I., Miková, M., Dušek, M., Ježek, M., Fiurášek, J., & Filip, R. (2015) · Physical Review A · doi:10.1103/physreva.92.012324
Room temperature caesium quantum memory for quantum information applicationsPreprint
Michelberger, P. (2015) · arXiv (Cornell University) · doi:10.48550/arxiv.1706.01104
Quantum Measurement and Control: Theory and Experiments in Solid-state and Quantum Optics
Daryanoosh, S. (2016) · Griffith Research Online · doi:10.25904/1912/238
Optical Experiments on Shared Quantum Correlations
Bennet, A. (2015) · Griffith Research Online · doi:10.25904/1912/1206
Efficient quantum logic circuits: or, How I Learned to Stop Worrying and Love Hilbert Space
White, A. G., de Almeida, M. P., Barbieri, M., Biggerstaff, D. N., Dalton, R. B., Gilchrist, A., Gillett, G., James, D. F. V., Langford, N. K., Lanyon, B. P., et al. (2007) · International Conference on Quantum Information · doi:10.1364/icqi.2007.ifb3
Self-citationOptimization of universal quantum gates with higher-dimensional spacesPreprint
Liu, W., Wei, H., & Kwek, L. C. (2021) · arXiv (Cornell University)
Quantum Computation: Integrated Quantum Gates for Polarization Encoded Qubits
Sansoni, L. (2014) · Springer theses · doi:10.1007/978-3-319-07103-9_6
Quantum Computing Using Optics
Milburn, G. J., & White, A. G. (2009) · Springer eBooks · doi:10.1007/978-0-387-30440-3_431
Self-citationSansoni, L. (2014) · Springer theses · doi:10.1007/978-3-319-07103-9_7
Quantum Computing Using Optics
Milburn, G. J., & White, A. G. (2013) · Springer eBooks · doi:10.1007/978-3-642-27737-5_431-3
Self-citationCertification of photon Fock states using second-order nonlinearity
Le, D. T., de Almeida, M. P., & An, N. B. (2022) · Physical Review A · doi:10.1103/physreva.106.062608
Multipartite Entanglement Distribution Using Separable States
McAleese, H., Laneve, A., & Paternostro, M. (2023) · Photonics & Electromagnetics Research Symposium (PIERS) · doi:10.1109/piers59004.2023.10221501
Linear Optics Quantum Information
Liu, Z. (2023) · Springer theses · doi:10.1007/978-981-99-6167-2_3
Storage and retrieval of two unknown unitary channels
Sedlák, M., Stárek, R., Horová, N., Mičuda, M., Fiurášek, J., & Bisio, A. (2026) · Physical Review A · doi:10.1103/56sd-xw8b · Cited by 4
Quantum Teleportation of Photon–Photon Diagonal Block Operations
Yang, Y., Zhang, Q., Zhai, X., Zeng, X., Zhang, S., Zhao, J., Wang, M., Liu, C., Liu, X., & Cao, L. (2025) · Advanced Quantum Technologies · doi:10.1002/qute.202400662
All-Photonic 2xN Cluster States in Frequency, Time and PolarizationPreprint
Gaeta, A. L., Blau, M., Ji, X., & Lipson, M. F. (2025) · Research Square · doi:10.21203/rs.3.rs-6696161/v1
Experimentos fotónicos de tomografía selectiva y eficiente de procesos cuánticos
Schmiegelow, C. T. (2011) · Repositorio Digital Institucional de la Universidad de Buenos Aires (Universidad de Buenos Aires)
Lee, G.-H., Kim, U.-S., & Kim, Y.-H. (2026) · Physical Review Research · doi:10.1103/g75t-x4bj
Modular variables in quantum information
Ketterer, A. (2016) · theses.fr (ABES) · doi:10.70675/6f8e3ef4zafc8z4a71z9600z8ba0861b2978
Linear optical fan-out gates using fewer ancillary single photons with enhanced success probability
Liu, W., & Wei, H. (2026) · Physical Review Applied · doi:10.1103/cs4d-lpfj
On-chip quantum nanophotonic spatial-polarization controlled-phase gate
Chang, K.-C., Chen, Y., Akyuz, K. E., Wang, N., Yu, M., Lo, G.-Q., Kwong, D., Kocaman, S., & Wong, C. W. (2026) · Conference on Lasers and Electro-Optics · doi:10.1364/cleo_at.2026.jtu.122
Metadata
- Authors
- Langford, N. K., Weinhold, T. J., Prevedel, R., Resch, K. J., Gilchrist, A., O’Brien, J. L., Pryde, G. J., & White, A. G.
- Affiliations
- The University of Queensland (AU)
- University of Vienna (AT)
- ORCID
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2005-11-18
- Volume
- 95
- Issue
- 21
- Pages
- 210504-210504
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W1998141297
- Semantic Scholar
- d9688239d7e905dd0699832575c8889049b0add1
- Cited by
- 262
- References
- 24
- Citations by year
- 2026: 7 · 2025: 6 · 2024: 6 · 2023: 9 · 2022: 9 · 2021: 11 · 2020: 8 · 2019: 6 · 2018: 14 · 2017: 9 · 2016: 19 · 2015: 13 · 2014: 18 · 2013: 12 · 2012: 11
- FWCI
- 13.75
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Griffith Research Online (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Explore Bristol Research (submittedVersion)
- arXiv (Cornell University)
- Funders
- Austrian Science Fund
- Queensland Government
- Agricultural Research Development Agency
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Keywords
- controlled-Z gate, quantum process tomography, continuous-wave operation, pulsed operation, guided optics
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