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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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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
“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
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesA 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
“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
Load-bearingStrength:hedged· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA 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
“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
Strength:hedged· not yet calibratedCausal:conditional· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesA 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 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
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- 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
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
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
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
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
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesA 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
“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
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA 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
“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
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- 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
Load-bearingStrength:boosted· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- Also stated in: § Abstract · boosted
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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
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- Also stated in: § Abstract · plain
- It may state two separate claims as one. 15
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
“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
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
- Also stated in: § Abstract · plain
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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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 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
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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
“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
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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
“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
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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In the paper
“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
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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 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
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
- 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
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
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
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
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
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
None of the sources cited for this claim have been checked yet.
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]
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
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
Load-bearingStrength:hedged· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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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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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