The DOI matches its Crossref record; 30 of the 31 references it cites were found in a registry or an index; 9 of the 34 sources its claims cite were checked for support.
Nonmaximally Entangled States: Production, Characterization, and Utilization
Open accessAbstract
Using a spontaneous-down-conversion photon source, we produce true nonmaximally entangled states, i.e., without the need for postselection. The degree and phase of entanglement are readily tunable, and are characterized both by a standard analysis using coincidence minima, and by quantum state tomography of the two-photon state. Using the latter, we experimentally reconstruct the reduced density matrix for the polarization. Finally, we use these states to measure the Hardy fraction, obtaining a result that is $122\ensuremath{\sigma}$ from any local-realistic result.
Overview
AI snapshot
Written from the paper’s full text.
TL;DR
The paper demonstrates production of true non-maximally entangled photon pairs via spontaneous downconversion, without post-selection, with tunable degree and phase of entanglement. It characterizes these states by coincidence minima and quantum state tomography, then uses them to measure a Hardy fraction that violates local realism by 122 σ.
Key findings
- Non-maximally entangled states were produced with degree of entanglement ε = tan χ, set by rotating the pump polarization, and phase φ, set by a UV quarter-wave plate.
- Coincidence minima for a variety of states and analyzer settings fell in the range 0.2–1.0%, indicating very high purities; the maximally entangled case had visibility 97.8 ± 0.1%, while the source had previously attained visibilities better than 99%.
- Quantum state tomography reconstructed the reduced polarization density matrix using 16 analyzer settings, showing controllable variation in both ε and φ.
- The maximum measured Hardy fraction was 9.2% (24222 counts) at ε = 0.470, with analysis angles α = 55.2° and β = 72.1° and corresponding minima of 0.43%, 0.52%, and 0.49% (1132, 1372, and 1279 counts); this Hardy fraction is 122 σ larger than any local realistic result.
Methods
- The source used two thin, adjacent Type-I beta-barium-borate (BBO) crystals with perpendicular optic axes, pumped by a 351 nm laser; pump polarization angle χ sets ε = tan χ, and a UV quarter-wave plate sets φ.
- Detection used adjustable quarter- and half-wave plates and polarizing beamsplitters for polarization analysis, 702 nm ± 2.5 nm interference filters, single-photon counters, and coincidence detection with a 5.27 ns window; accidental coincidences were negligible at ∼0.4 s⁻¹.
- States were characterized by coincidence-minima analysis and by two-photon Stokes-parameter tomography with 16 analyzer settings, reconstructing the density matrix from M⁻¹·P.
Limitations
- The paper states there are small uncertainties in the final reconstructed density matrix and notes that measurement drift and uncertainty are discussed elsewhere; it also notes a slight deviation from ideal ε = tan χ because pump power at the second crystal is slightly attenuated by absorption in the first.
- The paper states that the density matrix cannot be uniquely decomposed into pure and mixed submatrices to gain a direct measure of state purity, and that developing tomography for the full hyperentangled density matrix remains a considerable challenge.
- Evident from the text: small |HV⟩ and |VH⟩ components appear even in the maximally entangled case, likely from analyzer/source axis misalignment or non-orthogonal source optic axes, and these components become proportionally more important as the state becomes less entangled.
Model-written summary. Check it against the paper before relying on it.
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Cites
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Verification
Claims the paper makes
9 of 34 cited sources checked · 2 supported · 1 flagged · accuracy not yet measured
Every source the paper cites for this claim was checked and supports it.
In the paper
“This entanglement is of a specific and limited kind: the states are maximally entangled, e.g., ( | HV 〉 ± ε | VH 〉 ) / √ 1 + | ε | 2 , where H and V respectively represent the horizontal and vertical polarizations of two separated photons, and ε = 1.”
What the sources say
- Supportedcites [10] source
The Concept of Quantum Teleportation (p. 2) describes the photon pair as an equal superposition of horizontal–vertical and vertical–horizontal polarization states. Experimental Realization (p. 3) says the entangled pair was produced by spontaneous type II parametric down-conversion. Equal amplitudes correspond to ε = 1 in the citing sentence’s expression. (LLM, conf=0.89)
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- Supported
The cited sources that could be checked couldn’t confirm or dispute this claim.
In the paper
“Non-maximally entangled states have been shown to reduce the required detector efficiencies for loophole-free tests of Bell inequalities [13]”
What the sources say
- Could not verifycites [13] sourceExperimental — accuracy not yet measured
Section 1.2 (p. 4) says that every entangled pure state violates some Bell-type inequality, but it does not discuss detector efficiency. Searches for detector efficiency, detection loopholes, and non-maximally entangled states in Bell tests found no passage addressing whether such states reduce the efficiency required for a loophole-free test. (LLM, conf=0.76)
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- Could not verify
The cited sources that could be checked couldn’t confirm or dispute this claim.
In the paper
“There is no possibility of varying the intrinsic degree of entanglement , ε [11], to produce non-maximally entangled states without compromising the purity of the state, i.e., introducing mixture [12].”
What the sources say
- Could not verifycites [11] sourceExperimental — accuracy not yet measured
The experiment description (page unavailable) discusses preparing an entangled photon pair, but does not discuss varying its intrinsic degree of entanglement. The passage on an impure teleported state explains how to adapt a measurement analysis; it does not say that producing a non-maximally entangled state necessarily introduces mixture. Searches for non-maximal entanglement and purity found no passage establishing the claimed constraint. (LLM, conf=0.76)
- Not checked — no full text of the sourcecites [12] source
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- Could not verify
The cited sources support only part of this claim — read each source’s verdict below.
In the paper
“To date, the 'cleanest' and most accessible source of such entanglement arises from the process of spontaneous optical parametric downconversion in a nonlinear crystal (for a review, see [10]).”
What the sources say
- Partly supportedcites [10] sourceExperimental — accuracy not yet measured
The Experimental Realization section (p. 3) says entangled photon pairs can readily be generated by spontaneous parametric down-conversion in a nonlinear crystal, supporting the accessibility of the method for producing two-particle entanglement. The paper does not call it the cleanest source; its introduction (p. 1) also says entanglement of more than two quanta had not yet been produced, so it does not support the claim if “multi-particle” means more than two. (LLM, conf=0.88)
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passes- Partly supported
Every source the paper cites for this claim was checked and supports it.
In the paper
“For a polarization angle of χ with respect to the vertical, the output state is, | ψ 〉 = ( | HH 〉 + ε e i φ | VV 〉 ) / √ 1 + ε 2 , where the degree of entanglement, ε = tan χ [21].”
What the sources say
- Supportedcites [21] source
On p. 3, the paper says that rotating the pump polarization produces states of the form HH + εVV, with ε = tan θ for a pump angle θ measured from the vertical. On p. 1, it gives the relative phase as e^{iφ} and notes that normalization factors are omitted; the citing sentence supplies that normalization and uses χ instead of θ. (LLM, conf=0.91)
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- The authors state this as an assumption: The two downconversion processes have coherence and high spatial overlap.
- Supported
The cited sources that could be checked couldn’t confirm or dispute this claim.
In the paper
“Thus 3 and 15 analyzer settings are respectively required to obtain the single- [28] and two-photon Stokes parameters.”
What the sources say
- Could not verifycites [28] sourceExperimental — accuracy not yet measured
The citation is attached to the single-photon part of the sentence. Our copy discusses quantum secret sharing and qubits (pp. 1–2), but the passages found when searching for Stokes parameters and analyzer settings do not address the three-setting requirement. (LLM, conf=0.77)
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- Could not verify
The cited sources that could be checked couldn’t confirm or dispute this claim.
In the paper
“directly yield the polarization density matrix for an ensemble of identicallyprepared single photons [27]”
What the sources say
- Could not verifycites [27] sourceExperimental — accuracy not yet measured
The discussion on p. 3 describes reconstructing a two-qubit nuclear-spin density matrix from proton and carbon spectral lines. Searches for Stokes parameters and single-photon polarization found no passage addressing whether Stokes parameters yield a polarization density matrix. (LLM, conf=0.77)
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- Could not verify
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
“Finally, we use these states to measure the Hardy fraction, obtaining a result that is 122 σ from any localrealistic result.”
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesNone of the sources cited for this claim have been checked yet.
In the paper
“Non-maximally entangled states are produced simply by rotating the pump polarization.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- The authors state this as an assumption: The two downconversion processes have coherence and high spatial overlap.
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 degree and phase of entanglement are readily tunable”
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- The authors state this as an assumption: The two downconversion processes have coherence and high spatial overlap.
- It may state two separate claims as one. 6
- Probably not a substantial claim. 12
At least one cited source doesn’t support this claim or points to a different paper, and none confirmed it — see the verdicts below.
In the paper
“However, the underlying state is factorizable, and so is not truly entangled.”
What the sources say
- Disputedcites [18] sourceExperimental — accuracy not yet measured
On p. 1, the paper calls the earlier photon and massive-particle experiments studies of entangled states and says their processes were selectable rather than deterministic. It does not say their underlying states were factorizable or that the states were not truly entangled; its distinction is whether entanglement is generated on demand. (LLM, conf=0.87)
Checked by a reasoning model — may be wrong.
- Not checked — no full text of the sourcecites [19] source
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
- Disputed
The cited sources support only part of this claim — read each source’s verdict below.
In the paper
“there have been several optical experiments where non-maximally entangled states were controllably generated via post-selection , i.e., selective measurement of a product state, after the state had been produced [18,19].”
What the sources say
- Partly supportedcites [18] sourceExperimental — accuracy not yet measured
The introduction (p. 1) says earlier photon-entanglement experiments involved random processes and were selectable rather than deterministic. It does not say those experiments controllably generated non-maximally entangled states, or describe post-selection as selective measurement of a product state after production. (LLM, conf=0.85)
- Not checked — no full text of the sourcecites [19] source
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim.
- Partly supported
In the paper
“with this source we recently attained visibilities of better than 99% [20]”
What the sources say
- Not checked — no full text of the sourcecites [20] source
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
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
“Coincidence minima were found for a variety of states and analyzer settings, and fell in the range 0.2-1.0%, indicating very high purities.”
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
“the analysis angles at this point were α = 55 . 2 ◦ and β = 72 . 1 ◦”
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim.
What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“A coincidence window of 5.27 ns was sufficient to capture true coincidences; since the resulting rate of accidental coincidences was negligible ( ∼ 0.4s -1 ), no corrections for this were necessary.”
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
In the paper
“States with a fi xed degree of entanglement, ε ≃ 4 / 3, have been deterministically generated in ion traps [17]”
What the sources say
- Not checked — no full text of the sourcecites [17] source
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“Tomography is also possible with discrete variables [25].”
What the sources say
- Not checked — no full text of the sourcecites [25] source
Load-bearingStrength:hedged· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim.
In the paper
“a statistical measure composed of coincidence measurements from a variety of analyzer settings, was first proposed by Bell [5]”
What the sources say
- Not checked — no full text of the sourcecites [5] source
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“the Stokes parameters, which characterize the mean polarization of a classical beam [26]”
What the sources say
- Not matchedcites [26]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Strength:plain· not yet calibratedCausal:correlational· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
- Not matched
A claim is checked only against the cited paper’s full text, never its abstract, and none is available for its sources.
In the paper
“For continuous variables, tomography has been implemented in both quantum [23] and atom [24] optics.”
What the sources say
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
A claim is checked only against the cited paper’s full text, never its abstract, and none is available for its sources.
In the paper
“All tests have found that, modulo some physically reasonable assumptions, nature does indeed violate local realism in accordance with quantum mechanics.”
What the sources say
Strength:boosted· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“More generally, P 12 ( β, -β ) > P 12 ( α, -α ) + P 12 ( β, -α ⊥ ) + P 12 ( α ⊥ , -β ), which is the inequality to be tested experimentally [16].”
What the sources say
- Not checked — no full text of the sourcecites [16] source
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim. It may state two separate claims as one.
What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“The data points are normalized coincidence rates measured at ± β , (to within 0 . 5 ◦ , the inherent uncertainty in our polarization analyzers).”
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim. It may state two separate claims as one.
A claim is checked only against the cited paper’s full text, never its abstract, and none is available for its sources.
In the paper
“Recently Hardy proposed an 'all-or-nothing' test of local realism [14,15].”
What the sources say
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim.
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
“the ∼ 1% probability of measuring | HV 〉 and | VH 〉 terms signifies that either the axes of the analysis systems were not perfectly aligned with the axes of the source ('horizontal' at the analyzer is rotated with respect to 'horizontal' at the source), or that the optic axes of the source were not perfectly orthogonal”
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
The authors state this as an assumption.
The two downconversion processes have coherence and high spatial overlap.
“Given the coherence and high spatial overlap between these two processes”
The paper relies on this without support.
One application of such states is testing local realism.
“As mentioned earlier, one application of such states is testing local realism.”
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“The original proposal was experimentally demonstrated by Torgerson et al. (1995) and White et al.(1999)); as in the GHZ-type experiments, the results of the experiments were fed into specific inequalities, specially derived to take into account experimental imperfections (under the fair sampling assumption, of course).”
From Multiphoton entanglement and interferometry (2012) · cites this paper as White et al. (1999)
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“It has been shown theoretically and experimentally [56], [57], [58] that using the theory of the measurement of qubits, which includes a tomographic reconstruction of the DMOS due to the linear set of 16 polarization-measurements together with the numerical optimization method, the so-called maximum-likelihood-technique (MLT), one can obtain and reconstruct the non-negative definite density operat”
From Nonlocal realism tests and quantum state tomography in Sagnac-based type-II polarization-entanglement SPDC-source (2021) · cites this paper as [57]
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“Importantly, the complexity of the transformation only scales linearly with the number of photons in the state, in contrast to the exponential scaling in the number of measurements required in usual tomography.36”
From Scalable on-chip quantum state tomography (2018) · cites this paper as [36]
Experimental — accuracy not yet measuredThe cited source says what the claim attributes to it.
In the citing paper
“Experimentally, this technique was used for two-, three-, four-photon polarization states and also hyperentangled photon pairs (White et al. 1999;Resch et al. 2005;Walther et al. 2005b;Barreiro et al. 2005).”
From Multiphoton entanglement and interferometry (2012) · cites this paper as White et al. 1999
The cited source says what the claim attributes to it.
In the citing paper
“Parametric down-conversion (Kwiat et al. 1995;White et al. 1999) has been serving as the main workhorse for the multiphoton experiments reviewed here; up to eight entangled photons have been observed (Yao et al. 2007a).”
From Multiphoton entanglement and interferometry (2012) · cites this paper as White et al. 1999
In the citing paper
“The experimentally obtained density matrix, ρ exp , is reconstructed from a set of 1,296 local measurements using the maximum-likelihood technique[41, 42].”
From Quantum simulation of the wavefunction to probe frustrated Heisenberg spin systems (2011) · cites this paper as [41]
Citations
Cites
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Research works printed but not linked: 1
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Self-citation
Metadata
- Authors
- White, A. G., James, D. F. V., Eberhard, P. H., & Kwiat, P. G.
- Affiliations
- Los Alamos National Laboratory (US)
- Lawrence Berkeley National Laboratory (US)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1999-10-18
- Volume
- 83
- Issue
- 16
- Pages
- 3103-3107
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2073659633
- Semantic Scholar
- 615ec387673818556d60ca4756136618cb2e005a
- Cited by
- 511
- References
- 31
- Citations by year
- 2026: 7 · 2025: 15 · 2024: 18 · 2023: 11 · 2022: 17 · 2021: 19 · 2020: 14 · 2019: 16 · 2018: 15 · 2017: 21 · 2016: 14 · 2015: 18 · 2014: 17 · 2013: 18 · 2012: 21
- FWCI
- 23.61
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum optics and atomic interactions
- Keywords
- non-maximally entangled states, spontaneous parametric down-conversion, two-photon entanglement, polarization entanglement, quantum state tomography, reduced density matrix, Hardy inequality, local realism
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