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REVIEW 3 major objections 5 minor 68 references

Compound beams for direct experimental comparison of quantum operations

T0 review · 3 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Using compound beams, the paper finds that photon addition beats photon subtraction for thermal and sub-Poissonian beams, while photon subtraction wins for twin beams, and demonstrates nearly ideal photon addition by post-selection.

desk verdict Serious experimental platform, but the operation it calls 'photon addition' is an incoherent convolution with a heralded auxiliary state, not the standard a† operation, so the headline PA-vs-PS ordering is about a different operation. read the letter →

arxiv 2608.09518 v1 pith:6SGCY3U2 submitted 2026-08-10 quant-ph

Kishore Thapliyal , Jan Perina Jr. , Pavel Pavlicek , Antonin Cernoch This is my paper · ORCID
classification quant-ph
keywords compoundbeamsphotonadditionsubtractionnonclassicalitytwinthermalstatessub-Poissoniantemporalmultiplexing
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Compound beams—multi-mode fields assembled by concatenating many weak twin-beam detection windows from a single down-conversion source—let the authors compare photon addition and photon subtraction under identical experimental conditions. Previous comparisons were rare because different quantum operations usually need different sources, so results were not on the same footing. Using these beams, the paper finds that photon addition outperforms photon subtraction for multi-mode thermal and sub-Poissonian beams: addition induces nonclassicality in thermal states and enhances it in sub-Poissonian states, whereas subtraction cannot make a thermal state nonclassical. In twin beams the reverse holds: photon subtraction produces stronger marginal nonclassicality than photon addition, although it pays for this by disturbing the signal-idler quantum correlations more. The authors also exploit temporal photon-pair correlations in compound twin beams to demonstrate nearly ideal photon addition, which produces more nonclassical states than the realistic operation.

What carries the argument

The central object is the compound beam: a multi-mode field built from simple experimental blocks, here weak twin-beam detection windows concatenated in time. Photon addition is realized by taking additional detection windows from the same two channels, forming an auxiliary twin beam, and post-selecting on a fixed idler photocount number; the conditioned signal part is then added to the original beam. Photon subtraction is realized virtually by splitting the $M_w$ signal windows into $M_s$ and $M_w-M_s$ groups, mimicking a beam splitter with transmissivity $T_s=1-M_s/M_w$. The statistics are modeled by Mandel-Rice photon-pair and noise components, inverted from photocount histograms by maximum-likelihood reconstruction, and quantified by the Fano factor $F$, the noise-reduction parameter $R$, and the nonclassicality depth, defined as the amount of thermal noise needed to conceal the field's nonclassical features.

What would settle it

Construct the same photon-addition and photon-subtraction states using a genuine spatially multi-mode field detected by a photon-number-resolving camera at matched mean photon numbers and matched added and subtracted counts, then compare the Fano factors and noise-reduction parameters with the temporally concatenated compound-beam results; a systematic divergence would show that the temporal-to-spatial mapping fails for those states.

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Extended reading notes

Core claim

On the paper's own terms, the central claim is that compound beams provide a common experimental platform on which quantum operations can be compared directly, and that this platform changes the practical answer to the question 'which operation is better?'. For thermal states, photon addition creates nonclassicality (Fano factor $F<1$) while photon subtraction only lowers the intensity and cannot cross the quantum–classical border; for sub-Poissonian states, addition and subtraction both preserve the existing nonclassicality, with ideal photon addition clearly enhancing it. For twin beams, photon subtraction gives lower Fano factors in the marginal beams than photon addition, but at the cost of a larger increase in the noise-reduction parameter $R$; at high twin-beam intensity the two operations become indistinguishable because adding or subtracting a few photons barely changes a bright beam. The paper further claims nearly ideal photon addition by post-selecting on temporal photon-pair correlations in compound twin beams, with ideal addition of one, two, and three photons producing stronger nonclassicality than the realistic operation.

Load-bearing premise

The load-bearing premise is that concatenating many short, weak twin-beam measurements produces a compound beam whose statistics faithfully represent a real multi-mode quantum state that exists simultaneously; the paper acknowledges that these compound beams do not exist in real time and depends on a claimed one-to-one mapping between temporal and spatial multiplexing.

Editorial extensions

If this is right

  • Photon addition is the operation of choice for generating nonclassicality from thermal light and for pushing sub-Poissonian light further from the classical border.
  • Photon subtraction is the operation of choice for making the marginal beams of twin beams nonclassical, though it weakens the signal-idler correlations more than addition does.
  • The larger the number of added or subtracted photons (up to 20), the stronger the induced nonclassicality, but the weaker the remaining quantum correlations; when the beam is much brighter than the number of photons operated on, the effect becomes negligible.
  • Post-selection based on temporal photon-pair correlations can simulate an ideal photon-number-resolving detector, and the resulting ideal photon-added states are more nonclassical than realistically added states.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the temporal–spatial mapping holds, the same compound-beam construction could benchmark other non-Gaussian operations—photon catalysis, noiseless amplification, or general post-selection filters—on identical footing, giving protocol designers a direct way to choose operations for a given task.
  • The ideal photon-addition result suggests that improved photon-number-resolving detectors could make heralded addition and subtraction approach ideal nonclassicality limits, potentially strengthening entanglement distillation and cat-state generation.
  • Since compound beams can be concatenated almost arbitrarily, the method could also serve as a predictive tool: it can estimate the properties of high-intensity multi-mode states before the corresponding real source is built.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. This manuscript introduces 'compound beams'—concatenated weak twin-beam detection windows—as a platform to compare photon addition (PA) and photon subtraction (PS) applied to multi-mode thermal states, sub-Poissonian states, and twin beams. The authors present experimental photocount histograms for all nine state groups, with beam intensities spanning two orders of magnitude, and analyze Fano factors, noise-reduction parameters, and nonclassicality depths. They conclude that PA is advantageous for thermal and sub-Poissonian states, while PS outperforms PA for twin beams, and that temporal correlations in compound twin beams enable a nearly ideal PA. The theoretical model is fitted to the original TWB characterization and then used to predict the PA/PS outcome histograms, which is a genuine predictive check. A central caveat is that the implemented 'photon addition' is an incoherent convolution with an auxiliary heralded source, not the standard operator a† applied to the state; this affects the interpretation of the headline comparison.

Significance. The compound-beam technique is versatile, and the dataset is substantial; the model's predictive structure—parameters fixed by the original TWB characterization and then compared with independent PA/PS histograms—is a genuine strength. The nonclassicality-depth analysis goes beyond simple Fano-factor tests and gives quantitative lower bounds. If the operation implemented were standard photon addition, the systematic side-by-side comparison over a wide intensity range would be valuable for quantum-state engineering. However, because the 'photon addition' analyzed is a convolution with an independently heralded photon-number distribution rather than the standard a† operation, the headline comparison and the 'nearly ideal PA' demonstration do not support conclusions about the standard non-Gaussian operation. The paper will be of interest to specialists in photocounting statistics and compound-beam techniques, but the broader quantum-optics claims require substantial revision.

major comments (3)
  1. [SM Sec. III, Eqs. (20) and (24); Abstract] The operation labeled 'photon addition' is defined by the convolution of the original photon-number distribution with the conditional distribution p_a of an auxiliary TWB: p_a_th(n) = Σ p_th(n−n') p_a(n') and p_a_TWB(n_s,n_i) = Σ p_TWB(n_s−n'_s,n_i) p_a(n'_s). For an ideal auxiliary source p_a(n')=δ_{n',1}, this gives p_out(n)=p_in(n−1), a rigid shift of the photon-number distribution. Standard photon addition a†ρa on a Fock-diagonal state gives p'_m ∝ m p_{m−1}, which is not a shift. For a single-mode thermal state with mean \bar n, the shift yields F = \bar n, whereas standard PA yields F = 2\bar n(1+\bar n)/(1+2\bar n); these are unequal for all \bar n>0. Thus the abstract's claims about comparing 'photon addition' with photon subtraction, and about demonstrating 'nearly ideal experimental photon addition', refer to an incoherent convolution operation rather than the standard non-Gaussian operation. Please rename the operation (e.g., 'heralded photon-number convolution') or provide a rigorous argument that this convolution reproduces the physically relevant effects of standard PA in the multimode setting.
  2. [§2, 'Experimental data analysis' and Fig. 2(a,b)] The headline result that photon subtraction outperforms photon addition in twin beams compares the Fano factor F_s^a of the signal beam after PA with F_i^s of the idler beam after PS. These are different marginal beams with different mean photon numbers: PA increases the signal mean, while PS leaves the idler mean unchanged. The text itself states that the smaller F_i^s is 'attributed to smaller mean photon numbers ⟨n_i⟩_s in PS compared to ⟨n_s⟩_a'. Since the Fano factor is mean-dependent for these multi-mode fields, this comparison does not establish superiority of PS over PA; it may reflect the different means rather than the operation. A controlled comparison—same marginal beam, matched mean photon number, or equal nonclassicality depth—is needed to support the conclusion.
  3. [SM Eqs. (9) and (13)] The histograms f_a_sP and f_s_sP are defined with a normalization by the total sum over both cs and ci, which yields a joint distribution rather than the conditional distribution f(cs|ci) implied by the notation and by the main-text Eq. (4). If this is not a typographical error, the PASPS and PSSPS Fano factors in Fig. 3(d) are not computed from the post-selected states claimed. Please correct the normalization to match the conditional definition and confirm that the data processing used the conditional normalization.
minor comments (5)
  1. [Reference [56]] The reference title contains a typo: 'Suplementary material' should be 'Supplementary material'.
  2. [Table 1] The heading 'T able 1' appears with an erroneous space; please correct the formatting.
  3. [Fig. 2 caption] The notation 'F_a^s [F_i^s]' is confusing; please define the superscript/subscript convention clearly (e.g., F_x^y with x = beam and y = operation) and use it consistently in the text and figures.
  4. [Introduction, compound-beam mapping] The Introduction asserts a 'one-to-one mapping between the temporal and spatial multiplexing' but does not provide an argument or derivation. Since the physical interpretation of the temporal compound beams rests on this mapping, a brief explanation or a reference to a dedicated derivation would strengthen the paper.
  5. [SM Eq. (5)] The definition of the success probability p_suc would benefit from an explicit statement of the normalization by the total number of realizations M_m, to avoid ambiguity in the histograms built from repeated use of the same weak-TWB data.

Circularity Check

1 steps flagged · score 6.0 of 10

The paper's 'photon addition' is defined as a convolution with an independent heralded field (SM Eqs. 20 and 24), not the standard a† operation; the central PA-vs-PS comparison is therefore a comparison of a renamed operation, although the underlying compound-beam data analysis is self-contained.

  1. renaming known result [Supplemental Material, Sec. III, Eqs. (20) and (24); main text 'ideal PA' paragraph; Abstract]
    "A state obtained by combining a sub-Poissonian field reached by post-selecting ̄ca photocounts with a TS is described by the convolution of photon-number distributions given in Eqs. (17) and (18): p^a_th(n; ̄ca) = ∑_{n'_s=0}^n p_th(n − n'_s) p_a(n'_s; ̄ca). ... exploiting temporal photon-pair correlations in compound twin beams when post-selecting, nearly ideal experimental photon(s) addition is demonstrated."

    This equation defines the 'photon-added' state as an incoherent convolution of the input distribution with p_a, the conditional distribution of an independent auxiliary TWB. For an ideal auxiliary source p_a(n')=δ_{n',1}, the result is p_th(n−1), a rigid shift of the photon-number distribution, whereas the standard operation a†ρa on a Fock-diagonal state gives p'_m ∝ m p_{m−1}, which is not a shift. The same convolution structure appears in Eq. (24) for PATWBs, where the added photon is not correlated with the idler. Thus the states called PATS/PATWB and the abstract's claim that 'photon addition is advantageous' are statements about a convolution operation renamed as photon addition, not about the a† operation that the term denotes in the cited literature and in the title of the paper.

full rationale

The quantitative core of the paper is not statistically circular: the multimode TWB parameters (B_p=0.159, B_s=0.003, M_p=5M_w/2, M_s=5M_w/2) are fixed from the characterization of the original weak TWBs, and the PA/PS histograms are constructed independently by concatenating extra or split detection windows. The Fano factors and noise-reduction parameters for the PA/PS states are then genuine predictions, not fits to the PA/PS data; Table 2's agreement (within 1%) is a predictive check. The circularity concern is terminological/definitional. The paper calls the convolution with a conditioned independent field 'photon addition' and even 'ideal photon addition'; the standard a† operation has a different photon-number action (p'_m ∝ m p_{m−1} rather than p(n−1)). Consequently, the headline ordering 'photon addition is advantageous... photon subtraction outperforms photon addition in twin beams' is an ordering of the paper's renamed operation, not of photon addition in the sense of Refs. [11,12]. Because the central terminology is loaded into the definition, the comparison is partially circular even though the data handling is self-contained. The self-citations to [31,37,60] are normal and not load-bearing for a forbidden-uniqueness argument; the equations are reproduced in the SM.

Assumptions & free parameters 7 free parameters · 5 assumptions · 0 invented entities

The central claims rest on the temporal-to-spatial multiplexing simulation assumption, the standard photodetection model, and the PA/PS model from the authors' prior work. The free parameters are detector calibrations, TWB model parameters, and detection-window choices; none is fitted to the PA/PS comparison outcomes themselves.

free parameters (7)
  • Detection efficiency eta = 0.266 +/- 0.005
    Detector efficiency in the detection matrix T (Eq. 3); calibrated for this setup and used in all maximum-likelihood reconstructions and model predictions.
  • Dark count rate d = 6.6e-3
    Mean dark count rate per detection window in the detection matrix T; from detector calibration.
  • Pair-component mean photon number Bp = 0.159
    Mandel-Rice parameter for the photon-pair component of the TWB model (Eq. 4); fitted to the original TWB photon-number statistics.
  • Noise-component mean photon number Bs = 0.003
    Mandel-Rice parameter for the noise components of the TWB model (Eq. 4); fitted to the original TWB statistics.
  • Number of modes per symmetrized double window = 5
    Determined in earlier characterization of the setup [31,62]; sets Mp=Ms=5Mw/2 in the model.
  • Auxiliary window number M_a for PA = 4, 22, 90 for 1, 5, 20 added photons
    Chosen to maximize the success probability of photon addition for each target number of added photons.
  • Subtraction window number M_s for PS = 4, 22, 90 for 1, 5, 20 subtracted photons
    Chosen to maximize the success probability of photon subtraction; sets effective beam-splitter transmissivity Ts=1-Ms/Mw.
assumptions (5)
  • domain assumption Compound beams formed by temporal concatenation of detection windows faithfully represent the statistical properties of the corresponding multi-mode quantum states.
    Stated in the Introduction: temporal multiplexing gives a simulation because the realized states do not exist in real time, but there is a claimed one-to-one mapping to spatial multiplexing. The entire comparison rests on this identification.
  • standard math The detection matrix T(c,n;eta,Mw,d) correctly models the photodetection process with the stated efficiency and dark count rate.
    Standard photodetection model (Eq. 3) used for histogram inversion and theoretical predictions; from Refs. [57,58].
  • domain assumption The TWB photon-number distribution is the twofold convolution of Mandel-Rice distributions with independent pair, signal-noise, and idler-noise components (Eq. 4).
    Gaussian model of the multi-mode TWB from Ref. [60]; used to generate all theoretical curves.
  • domain assumption Photon addition and subtraction on these multi-mode fields are described by convolution with a post-selected sub-Poissonian field and by a beam-splitter with binomial statistics (SM Eqs. 19-24).
    Model from Ref. [37]; underlies the theoretical PA/PS distributions.
  • ad hoc to paper Post-selection on idler photocounts of an auxiliary weak TWB produces a field that behaves as an ideal photon-number-resolving addition.
    The claim of nearly ideal photon addition relies on temporal correlations in weak TWBs producing a field close to a Fock state; no direct fidelity check is provided.

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Cite this review

Pith. "Pith review of Compound beams for direct experimental comparison of quantum operations." pith.science (2026). https://pith.science/paper/6SGCY3U2

@misc{pith2026260809518,
  author       = {Pith},
  title        = {Pith review of: Compound beams for direct experimental comparison of quantum operations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6SGCY3U2}},
  note         = {Machine review of arXiv:2608.09518}
}
read the original abstract

Compound beams composed of simple experimental blocks (detected in simultaneous detection windows) that form specific quantum-correlated structures are suggested for simulating the properties of different quantum operations used for creating highly nonclassical and entangled multi-mode states needed in quantum communication, metrology, and information protocols. Qualitative and quantitative comparison of multi-photon addition and subtraction in compound multi-mode thermal as well as sub-Poissonian beams and multi-mode twin beams with their intensities extending over two orders in magnitude is provided. Adding and subtracting up to twenty photocounts, optimal conditions for the generation of experimental nonclassical states are identified. In general, photon addition is identified as advantageous over photon subtraction for the multi-mode thermal and sub-Poissonian beams: It induces (enhances) the nonclassicality in the former (latter) state. Contrary to this, photon subtraction outperforms photon addition in the multi-mode twin beams. Moreover, exploiting temporal photon-pair correlations in compound twin beams when post-selecting, nearly ideal experimental photon(s) addition is demonstrated.

Figures

Figures reproduced from arXiv: 2608.09518 by the authors.

Figure 1
Figure 1. (a) Experimental setup involving nonlinear crystal LiIO3 as the source of photon pairs with the signal and idler photons propagating along different directions and synchronously detected by two APDs Ds and Di ; F - frequency filter; L1, L2, L3 - lenses, MMF - multi-mode fiber. Schematic diagrams for PA and PS in a TWB are shown in (b) and (c), respectively, using the synchronized signal and idler channels. Whereas r… view at source ↗
Figure 2
Figure 2. (a) Mean photon numbers ⟨ns⟩ a [⟨ni⟩ s ] and (b) Fano factors F a s [F s i ] of the signal [idler] beam and (c) noise-reduction parameter Ra [Rs ] for signal PATWB [PSTWB] as they depend on the number Mw of concatenated windows in the original TWB; logarithmic scale is used for Mw/2. PA [PS] states are shown by red smooth [blue dashed] curves for 1 (□), 5 (◦), and 20 (∗) added [subtracted] photons. Solid [dashed] cu… view at source ↗
Figure 3
Figure 3. (a) [(c)] Mean photon number ⟨n⟩ s,a th [⟨n⟩ s,a sP ] and (b) [(d)] Fano factor F s,a th [F s,a sP ] in PSTS and PATS [PSSPS and PASPS] as they depend on the number of concatenated windows Mw in the original TS [SPS]; logarithmic scale is used for Mw/2. Dotted curves correspond to the original TS and SPS. More details are given in the caption to [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: (a) [(b)] Fano factor F a th ≡ F a s [F a sP] for ideal-PA in TS [SPS] as it depends on the number Mw of concatenated windows for 1 (red ∗), 2 (blue □), and 3 (magenta ∆) ideally-added photons; logarithmic scale is used for Mw/2. Curves originate in the Gaussian model …
Figure 5
Figure 5. Figure 5: (a) Noise-reduction parameter Ra , and nonclassicality depths (b) τ a F a s , (c) τ a Ra , and (d) τ a P as they depend on the number Mw of concatenated windows for 1 (red ∗), 2 (blue □), and 3 (magenta ∆) photons ideally added into TWBs; logarithmic scale is used for …
Figure 1
Figure 1. Figure 1: Schematic diagrams elucidating processing the photocount data in the signal and the idler experimental photocount channels when constructing the photocount histograms of (a) PATWBs and (b) PSTWBs. To compensate for different detection parameters of the signal and idler…

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Works this paper leans on

68 extracted references · 68 canonical work pages

  1. [1]

    Dowling J P and Milburn G J 2003 Quantum technology: the second quantum revolution Philos. Trans. Royal Soc. Lond. A Math. Phys. Eng. Sci.\/ 361 1655--1674

    work page 2003

  2. [2]

    Deutsch I H 2020 Harnessing the power of the second quantum revolution PRX Quantum\/ 1 020101

    work page 2020

  3. [3]

    Rev.\/ 131 2766---2788

    Glauber R J 1963 Coherent and incoherent states of the radiation field Phys. Rev.\/ 131 2766---2788

    work page 1963

  4. [4]

    Sudarshan E C G 1963 Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams Phys. Rev. Lett.\/ 10 277---179

    work page 1963

  5. [5]

    Kok P, Munro W J, Nemoto K, Ralph T C, Dowling J P and Milburn G J 2007 Linear optical quantum computing with photonic qubits Rev. Mod. Phys.\/ 79 135--174

    work page 2007

  6. [6]

    Photon.\/ 12 724--733

    Pirandola S, Bardhan B R, Gehring T, Weedbrook C and Lloyd S 2018 Advances in photonic quantum sensing Nat. Photon.\/ 12 724--733

    work page 2018

  7. [7]

    Bouwmeester D, Pan J W, Mattle K, Eibl M, Weinfurter H and Zeilinger A 1997 Experimental quantum teleportation Nature\/ 390 575---579

    work page 1997

  8. [8]

    Gisin N, Ribordy G, Tittel W and Zbinden H 2002 Quantum cryptography Rev. Mod. Phys.\/ 74 145---195

    work page 2002

Show all 68 references
  1. [9]

    Photon.\/ 18 1024--1036

    Defienne H, Bowen W P, Chekhova M, Lemos G B, Oron D, Ramelow S, Treps N and Faccio D 2024 Advances in quantum imaging Nat. Photon.\/ 18 1024--1036

    2024

  2. [10]

    Braunstein S L and van Loock P 2005 Quantum information with continuous variables Rev. Mod. Phys.\/ 77 513

    2005

  3. [11]

    Agarwal G S and Tara K 1991 Nonclassical properties of states generated by the excitations on a coherent state Phys. Rev. A\/ 43 492

    1991

  4. [12]

    Agarwal G S and Tara K 1992 Nonclassical character of states exhibiting no squeezing or sub-Poissonian statistics Phys. Rev. A\/ 46 485---488

    1992

  5. [13]

    Agarwal G S 1992 Negative binomial states of the field-operator representation and production by state reduction in optical processes Phys. Rev. A\/ 45 1787

    1992

  6. [14]

    Photon.\/ 4 178--181

    Takahashi H, Neergaard-Nielsen J S, Takeuchi M, Takeoka M, Hayasaka K, Furusawa A and Sasaki M 2010 Entanglement distillation from Gaussian input states Nat. Photon.\/ 4 178--181

    2010

  7. [15]

    Lvovsky A and Mlynek J 2002 Quantum-optical catalysis: generating nonclassical states of light by means of linear optics Phys. Rev. Lett.\/ 88 250401

    2002

  8. [16]

    Bartley T J, Donati G, Spring J B, Jin X M, Barbieri M, Datta A, Smith B J and Walmsley I A 2012 Multiphoton state engineering by heralded interference between single photons and coherent states Phys. Rev. A\/ 86 043820

    2012

  9. [17]

    Podoshvedov M S, Podoshvedov S A and Kulik S P 2025 Gain of squeezing via photon subtraction JOSA B\/ 42 1753--1763

    2025

  10. [18]

    Zhang K, Li H, Jing J, Treps N and Walschaers M 2025 Purification of G aussian states by photon subtraction or addition Phys. Rev. A\/ 111 043719

    2025

  11. [19]

    Cochrane P T, Milburn G J and Munro W J 1999 Macroscopically distinct quantum-superposition states as a bosonic code for amplitude damping Phys. Rev. A\/ 59 2631

    1999

  12. [20]

    Gottesman D, Kitaev A and Preskill J 2001 Encoding a qubit in an oscillator Phys. Rev. A\/ 64 10--1103

    2001

  13. [21]

    Konno S, Asavanant W, Hanamura F, Nagayoshi H, Fukui K, Sakaguchi A, Ide R, China F, Yabuno M, Miki S et al\/ 2024 Logical states for fault-tolerant quantum computation with propagating light Science\/ 383 289--293

    2024

  14. [22]

    o ll L and Welsch D G 1997 Generating S chr \

    Dakna M, Anhut T, Opatrn \`y T, Kn \"o ll L and Welsch D G 1997 Generating S chr \"o dinger-cat-like states by means of conditional measurements on a beam splitter Phys. Rev. A\/ 55 3184

    1997

  15. [23]

    Ourjoumtsev A, Tualle-Brouri R, Laurat J and Grangier P 2006 Generating optical Schr\" odinger kittens for quantum information processing Science\/ 312 83---86

    2006

  16. [24]

    Gerrits T, Glancy S, Clement T S, Calkins B, Lita A E, Miller A J, Migdall A L, Nam S W, Mirin R P and Knill E 2010 Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum Phys. Rev. A\/ 82 031802

    2010

  17. [25]

    Vidrighin M D, Dahlsten O, Barbieri M, Kim M S, Vedral V and Walmsley I A 2016 Photonic Maxwell's demon Phys. Rev. Lett.\/ 116 050401

    2016

  18. [26]

    Zanin G L, Antesberger M, Jacquet M J, Ribeiro P H S, Rozema L A and Walther P 2022 Enhanced photonic Maxwell 's demon with correlated baths Quantum\/ 6 810

    2022

  19. [27]

    Neset M, Fadrn \`y J, Bielak M, Fiur \'a s ek J, Je z ek M and B \' lek J 2025 Experimental noiseless quantum amplification of coherent states of light by two-photon addition and subtraction Phys. Rev. A\/ 112 023710

    2025

  20. [28]

    Phys.\/ 17 023038

    Bartley T J and Walmsley I A 2015 Directly comparing entanglement-enhancing non- Gaussian operations New J. Phys.\/ 17 023038

    2015

  21. [29]

    Barnett S M, Ferenczi G, Gilson C R and Speirits F C 2018 Statistics of photon subtracted and photon-added states Phys. Rev. A\/ 98 013809

    2018

  22. [30]

    Zhang H, Xia Y, Ye W, Chang S and Liao Z 2024 Quantum illumination using non- Gaussian states with conditional measurements Phys. Rev. A\/ 109 062440

    2024

  23. [31]

    Pe r ina Jr J, C ernoch A and Soubusta J 2021 Compound twin beams without the need of genuine photon-number-resolving detection Phys. Rev. Appl.\/ 16 024061

    2021

  24. [32]

    Pe r ina Jr J, Mich\' a lek V, Machulka R and Haderka O 2021 Two-beam light with simultaneous anti-correlations in photon-number fluctuations and sub-Poissonian statistics Phys. Rev. A\/ 104 013712

    2021

  25. [33]

    Express\/ 29 29704

    Pe r ina Jr J, Mich\' a lek V, Machulka R and Haderka O 2021 Two-beam light with 'checkered-pattern' photon-number distributions Opt. Express\/ 29 29704

    2021

  26. [34]

    Express\/ 32 537--550

    Pe r ina Jr J, Thapliyal K, Haderka O, Mich\' a lek V and Machulka R 2024 Generalized sub-Poissonian states of two-beam fields Opt. Express\/ 32 537--550

    2024

  27. [35]

    Quantum\/ 2 148---155

    Pe r ina Jr J, Thapliyal K, Haderka O, Mich\' a lek V and Machulka R 2024 Generalized sub-Poissonian states Opt. Quantum\/ 2 148---155

    2024

  28. [36]

    Thapliyal K, Pe r ina Jr J, Mich\' a lek V, Haderka O and Machulka R 2024 Experimental characterization of multimode photon-subtracted twin beams Phys. Rev. Res.\/ 6 013065

    2024

  29. [37]

    Lett.\/ 49 4521--4524

    Thapliyal K, Pe r ina Jr J, Haderka O, Mich \'a lek V and Machulka R 2024 Experimental photon addition and subtraction in multi-mode and entangled optical fields Opt. Lett.\/ 49 4521--4524

    2024

  30. [38]

    Adesso G and Illuminati F 2007 Entanglement in continuous variable systems: Recent advances and current perspectives J. Phys. A: Math. Theor.\/ 40 7821---7880

    2007

  31. [39]

    Barasi \'n ski A, Pe r ina Jr J and C ernoch A 2023 Quantification of quantum correlations in two-beam Gaussian states using photon-number measurements Phys. Rev. Lett.\/ 130 043603

    2023

  32. [40]

    Sudak N, Pe r ina Jr J, Barasi\'nski A and C ernoch A 2025 Efficient characterization of N -beam Gaussian fields through photon-number measurements: Quantum universal invariants Phys. Rev. Res.\/ 7 023278

    2025

  33. [41]

    Pe r ina Jr J, Sudak N, Barasi\'nski A and C ernoch A 2025 Quantum correlations in three-beam symmetric Gaussian states accessed via photon-number-resolving detection and quantum universal invariants Phys. Rev. Res.\/ 7 043292

    2025

  34. [42]

    Davidovich L 1996 Sub-Poissonian processes in quantum optics Rev. Mod. Phys.\/ 68 127---173

    1996

  35. [43]

    Laurat J, Coudreau T, Treps N, Maitre A and Fabre C 2003 Conditional preparation of a quantum state in the continuous variable regime: Generation of a sub-Poissonian state from twin beams Phys. Rev. Lett.\/ 91 213601

    2003

  36. [44]

    Lett.\/ 41 2149---2152

    Iskhakov T S, Usenko V C, Andersen U L, Filip R, Chekhova M V and Leuchs G 2016 Heralded source of bright multi-mode mesoscopic sub-Poissonian light Opt. Lett.\/ 41 2149---2152

    2016

  37. [45]

    Mandel L and Wolf E 1995 Optical Coherence and Quantum Optics\/ (Cambridge University, Cambridge)

    1995

  38. [46]

    of SPIE\/ vol 13508 p 1350812

    Thapliyal K, Perina Jr J, Mich \'a lek V, Haderka O and Machulka R 2025 Addition and subtraction of photons: Sub- Poissonian twin beams Proc. of SPIE\/ vol 13508 p 1350812

    2025

  39. [47]

    Inf.\/ 5 80

    Maga\' na-Loaiza O S, de J Le\' on-Montiel R, Perez-Leija A, U'Ren A B, You C, Busch K, Lita A E, Nam S W, Mirin R P and Gerrits T 2019 Multiphoton quantum-state engineering using conditional measurements npj Quant. Inf.\/ 5 80

    2019

  40. [48]

    Phys.\/ 16 144--147

    Ra Y S, Dufour A, Walschaers M, Jacquard C, Michel T, Fabre C and Treps N 2020 Non- Gaussian quantum states of a multimode light field Nat. Phys.\/ 16 144--147

    2020

  41. [49]

    Walschaers M and Treps N 2020 Remote generation of Wigner negativity through Einstein-Podolsky-Rosen steering Phys. Rev. Lett.\/ 124 150501

    2020

  42. [50]

    Fei H B, Jost B M, Popescu S, Saleh B E A and Teich M C 1997 Entanglement-induced two-photon transparency Phys. Rev. Lett.\/ 78 1679---1682

    1997

  43. [51]

    Saleh B E A, Jost B M, Fei H B and Teich M C 1998 Entangled-photon virtual-state spectroscopy Phys. Rev. Lett.\/ 80 3483---3486

    1998

  44. [52]

    Svozil \'i k J, Pe r ina Jr J and de Le\' on-Montiel R 2018 Virtual-state spectroscopy with frequency tailored intense entangled beams J. Opt. Soc. Am. B\/ 35 460---467

    2018

  45. [53]

    Phys.\/ 510 54---59

    Svozil \'i k J, Pe r ina Jr J and de Le\' on-Montiel R 2018 Two-photon absorption spectroscopy using intense phase-chirped entangled beams Chem. Phys.\/ 510 54---59

    2018

  46. [54]

    Hong C K and Mandel L 1985 Theory of parametric frequency down conversion of light Phys. Rev. A\/ 31 2409---2418

    1985

  47. [55]

    Hong C K, Ou Z Y and Mandel L 1987 Measurement of subpicosecond time intervals between two photons by interference Phys. Rev. Lett.\/ 59 2044---2046

    1987

  48. [56]

    Thapliyal K, Pe r ina Jr J, Pavl\' c ek P and C ernoch A 2026 Suplementary material: Compound beams for direct experimental comparison of quantum operations

    2026

  49. [57]

    Saleh B E A 1978 Photoelectron Statistics\/ (Springer-Verlag, New York)

    1978

  50. [58]

    Pe r ina Jr J, Hamar M, Mich\' a lek V and Haderka O 2012 Photon-number distributions of twin beams generated in spontaneous parametric down-conversion and measured by an intensified CCD camera Phys. Rev. A\/ 85 023816

    2012

  51. [59]

    Royal Statist

    Dempster A P, Laird N M and Rubin D B 1977 Maximum likelihood from incomplete data via the EM algorithm J. Royal Statist. Soc. B\/ 39 1---38

    1977

  52. [60]

    Pe r ina Jr J, Haderka O, Mich\' a lek V and Hamar M 2013 State reconstruction of a multimode twin beam using photodetection Phys. Rev. A\/ 87 022108

    2013

  53. [61]

    Pe r ina J 1991 Quantum Statistics of Linear and Nonlinear Optical Phenomena\/ (Kluwer, Dordrecht)

    1991

  54. [62]

    Lett.\/ 37 2475---2477

    Pe r ina Jr J, Haderka O, Hamar M and Mich\' a lek V 2012 Absolute detector calibration using twin beams Opt. Lett.\/ 37 2475---2477

    2012

  55. [63]

    Lee C T 1991 Measure of the nonclassicality of nonclassical states Phys. Rev. A\/ 44 R2775---R2778

    1991

  56. [64]

    Pe r ina Jr J, Arkhipov I I, Mich\' alek V and Haderka O 2017 Non-classicality and entanglement criteria for bipartite optical fields characterized by quadratic detectors Phys. Rev. A\/ 96 043845

    2017

  57. [65]

    Gradshtein I S and Ryzhik I M 2000 Table of Integrals, Series, and Products, 6th ed.\/ (Academic Press, San Diego)

    2000

  58. [66]

    Miranowicz A, Bartkowiak M, Wang X, Liu Y X and Nori F 2010 Testing nonclassicality in multimode fields: A unified derivation of classical inequalities Phys. Rev. A\/ 82 013824

    2010

  59. [67]

    Pe r ina Jr J, Pavl\' c ek P, Mich\' a lek V, Machulka R and Haderka O 2022 Nonclassicality criteria for n-dimensional optical fields detected by quadratic detectors Phys. Rev. A\/ 105 013706

    2022

  60. [68]

    1\/ (McGraw---Hill, Amsterdam)

    Morse P M and Feshbach H 1953 Methods of Theoretical Physics, Vol. 1\/ (McGraw---Hill, Amsterdam)

    1953

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