{"id":"b2966b82-eac6-42ac-8f81-980c3f24c330","arxiv_id":"2504.19170","paper_version":2,"verdict":"REJECT","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"high","formal_verification":"none","parameter_count":3,"one_line_summary":"A modulation scheme called PRSS is claimed to linearize Rydberg-based atomic MIMO detection, but the key equations do not produce the claimed linear model.","lead":"This paper proposes a two-slot phase-spreading trick that lets Rydberg atomic receivers recover complex wireless signals from magnitude-only measurements, turning a nonlinear problem into a linear one. The central derivation as written contains an algebraic error, so the main claim is not supported in its current form.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (19) misstates the second-slot magnitude, so the linear model (23) does not follow as written; swapping Re/Im in Eq. (19) repairs the derivation and preserves the central claim.","rationale":"The reader's weakest assumption identifies exactly the equation on which the entire linearization depends. I verified the algebra: for z_{k,2}=h_k^T x exp(j 3pi/2)+v_{k,2}, the real part of the received phasor z_{k,2}+r_k is Re z_{k,2}+r_k, not Im z_{k,2}+r_k. Thus Eq. (19) is false, and Eqs. (21)-(23) do not follow as written. This is the single most load-bearing concern because if it were not repairable there would be no linear MIMO/OFDM model. However, the intended construction is sound after a one-line correction: with Re and Im exchanged in Eq. (19), the two slot measurements give Re and Im of h_k^T x up to the reference offset and real noise parts, so Eq. (23) holds. Therefore the correct verdict is the same as the reader's: reject the current manuscript, with a clear path to revision rather than a fatal flaw in the PRSS concept. No other concern examined (e.g., the magnitude-versus-squared-magnitude receiver model) is as central to the claimed result.","tokens_in":9058,"tokens_out":8331,"duration_ms":80695,"concrete_test":"Independently re-derive Eq. (19) from Eq. (17) for phi=3pi/2 and compare |(Re z+r)+j Im z| with |(Im z+r)-j Re z| for z=-j h^T x+v; then rerun the linearization of Eqs. (21)-(23) with the correct second-slot expression and verify that it yields h^T x+(1+j)r_k+Re v_{k,1}+j Re v_{k,2}. If the corrected derivation reproduces Eq. (23) term-by-term, the central claim is mathematically sound and the paper needs only a revision; if it does not, the PRSS linearization is unsupported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing step is the claim that PRSS turns two envelope samples into the linear model (23)-(24). The derivation fails at Eq. (19). With z_{k,2}=h_k^T x exp(j 3pi/2)+v_{k,2} = -j h_k^T x+v_{k,2}, the actual magnitude is |z_{k,2}+r_k| = |(Re z_{k,2}+r_k) + j Im z_{k,2}|, not |(Im z_{k,2}+r_k) - j Re z_{k,2}|. The correct large-reference expansion is y_{k,2} approx r_k + Re z_{k,2} = r_k + Im(h_k^T x) + Re v_{k,2}; the printed Eq. (19) instead forces y_{k,2} approx r_k + Im z_{k,2} = r_k - Re(h_k^T x) + Im v_{k,2}. Consequently Eqs. (21)-(23) do not follow from Eqs. (16)-(19), and the simulated BER curves validate a model different from the one written. The defect is a local algebraic error rather than a broken concept: replacing Eq. (19) with |(Re z_{k,2}+r_k) + j Im z_{k,2}| gives y_{k,1}+j y_{k,2} = (1+j)r_k + h_k^T x + Re v_{k,1} + j Re v_{k,2}, which is exactly the linear structure of Eq. (23) with v_k = Re v_{k,1} + j Re v_{k,2}. Thus the concept is recoverable, but the manuscript as submitted does not contain a valid derivation of its headline result.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a transmitter-side phase-rotated symbol spreading (PRSS) technique for Rydberg-atomic MIMO receivers. Each symbol is transmitted in two time slots with a deterministic phase offset, and a strong local reference is injected at each atomic receiver. The authors claim that PRSS converts the nonlinear envelope-detection (phase retrieval) model into a standard linear MIMO model, enabling conventional detection algorithms (ZF, LMMSE, MLD) and FFT-based OFDM processing. Simulations show BER gains up to 2.5 dB over envelope-only MLD and over 10 dB gain under suboptimal detection in large MIMO configurations, and the paper also reports gains for atomic OFDM.","tokens_in":9432,"tokens_out":7796,"duration_ms":70329,"significance":"If the linearization claim were rigorously established, the paper would make an important contribution: it would remove the nonlinear phase-retrieval bottleneck for atomic MIMO detection and enable standard signal-processing tools to be applied unchanged. The paper is honest in its scope: it does not claim that atomic receivers outperform RF across all regimes, but uses an experimentally reported receiver SNR gain G_atom from the literature. The simulations are extensive and the qualitative observation that a large reference plus phase-rotated spreading can linearize the envelope measurement is physically plausible. However, the central algebraic derivation in Section III-B contains an error that invalidates the written proof of the linear model, and the capacity/spectral-efficiency comparison in Section III-C is not supported as stated. These issues are correctable in principle, so the concept is recoverable, but the manuscript in its current form does not contain a valid derivation of its headline result.","major_comments":[{"comment":"Equation (19) is algebraically incorrect. For z_{k,2} = Re(z_{k,2}) + j Im(z_{k,2}), the actual received magnitude satisfies |z_{k,2} + r_k| = |(Re(z_{k,2}) + r_k) + j Im(z_{k,2})|, not |(Im(z_{k,2}) + r_k) - j Re(z_{k,2})| as printed. Under the large-reference condition (20), the printed expression leads to y_{k,2} ≈ r_k + Im(z_{k,2}) = r_k - Re(h_k^T x) + Im(v_{k,2}) for the chosen phase offset ϕ = 3π/2. Consequently, combining (21) and (22) does not yield the claimed linear model (23); it yields y_{k,1} + j y_{k,2} - (1+j)r_k ≈ (1 - j) Re(h_k^T x) + Re(v_{k,1}) + j Im(v_{k,2}). Replacing Eq. (19) with |(Re(z_{k,2}) + r_k) + j Im(z_{k,2})| gives the correct expansion y_{k,2} ≈ r_k + Im(h_k^T x) + Re(v_{k,2}), which does produce the linear structure of (23). As written, the paper's derivation of the key enable step is invalid.","section":"III-B, Eq. (19)"},{"comment":"The paper presents two inconsistent detection models. Equation (2) states y(t) ∝ |E_RF(t)|^2 (square-law detection), whereas Eq. (4) and all subsequent analysis use the envelope (amplitude) model y = |Σ h_n x_n + v|. These are physically distinct: for a large reference r, the square-law model yields |z+r|^2 ≈ r^2 + 2r Re(z) + |z|^2, while the envelope model yields |z+r| ≈ r + Re(z). The PRSS linearization depends on the envelope model. The manuscript must either justify the envelope model as the correct output of the atomic receiver for the communication setup, or redo the large-reference expansion for the square-law model and show that the linearization still holds with appropriate noise statistics.","section":"II-A and II-B, Eqs. (2) and (4)"},{"comment":"The spectral-efficiency comparison is internally inconsistent. The PRSS capacity in Eq. (25) contains a factor 1/2 because each symbol occupies two time slots, while the envelope-only capacity in Eq. (32) has no such factor. The text concludes that \"even with time-domain symbol spreading, the PRSS-assisted approach does not compromise spectral efficiency in theory,\" but for the same channel and input distribution Eqs. (25) and (32) would give C_prss = (1/2) C_env (in the unitary-channel case), not equality. The simulations compensate for the rate loss by using 16-QAM instead of 4-QAM, but the capacity analysis does not. This claim needs to be reworded or supported by a rate-constrained comparison that accounts for the higher-order modulation.","section":"III-C, Eqs. (25) and (32)"},{"comment":"The capacity formula in Eq. (25) is not derived from the linear model (24). The effective noise covariance of v_eff = Re(v_{k,1}) + j Re(v_{k,2}) is not computed, and the relation between σ_eff^2 and the conventional RF noise parameter σ_RF^2, including the gain factor G_atom, is stated without derivation. Since the paper claims that PRSS enables standard linear MIMO capacity results, the noise covariance and SNR normalization should be specified precisely, otherwise Eq. (25) is an ad hoc insertion of an external gain parameter rather than a consequence of the model.","section":"III-C, Eq. (25)"}],"minor_comments":[{"comment":"The notation in Eqs. (18)-(19) is confusing because z_{k,1} and z_{k,2} are defined as the entire argument of the absolute value in (16)-(17), but then the equations (18)-(19) write them as if they were already split into real and imaginary parts. Defining a = Re(z_{k,i}), b = Im(z_{k,i}) explicitly would make the large-reference expansion easier to follow.","section":"III-B, Eq. (18)-(19)"},{"comment":"The approximation obtained by dropping the imaginary terms in (18)-(19) is claimed to hold under r_k >> |z_{k,i}|, but no error bound is given. The simulation uses a 35 dB reference, but the theoretical part would benefit from an explicit first-order error analysis, e.g., showing the residual is O(|z|^2/r).","section":"III-B, after Eq. (20)"},{"comment":"The expression for the differential entropy of a Rayleigh distribution in Eq. (29) and the conditional entropy in Eq. (30) appear to have incorrect additive constants (the constant should be (1 + γ/2 - ln 2)/ln 2 in bits, not (1+γ)/2). The mutual information in Eq. (31) is correct because the constants cancel, but the intermediate entropy formulas as written are not accurate.","section":"III-C, Eq. (31)"},{"comment":"The abstract promises a gain of 20 dB for OFDM, but Experiment 3 does not compare against an envelope-only atomic OFDM baseline (which the paper states is incompatible with DFT receivers). The observed gain is essentially the fixed G_atom=20 dB offset from the RF-OFDM curve, so the claim of a 20 dB gain is not a new result of PRSS itself but an assumption about the atomic receiver sensitivity.","section":"I, Introduction, and IV, Experiment 3"},{"comment":"The symbol h_P is described as the reduced Planck constant; the standard symbol for the reduced Planck constant is ħ. If h_P is intended to denote Planck's constant h, then the denominator should be h (not ħ) or the reduced constant ħ appears in the numerator/denominator consistently. Please check the definition.","section":"II-A, Eq. (1)"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: the PRSS idea is genuinely new and the paper reads well, but the central derivation in Section III-B contains an algebraic sign error that invalidates the linear model as written. The fix is straightforward, so this is major-revision material, not a reject.\n\nWhat is actually new: the two-slot phase-rotated spreading combined with reference injection is a real extension of the reference-injection idea in [8]. The paper correctly identifies the phase-retrieval bottleneck in atomic MIMO and shows a plausible way to get a linear model without coherent downconversion. The review of existing A-MIMO detection algorithms in Section II is useful and the performance comparison is fair on spectral efficiency (16-QAM over two slots vs 4-QAM for the envelope-only baseline).\n\nThe load-bearing flaw: Eq. (19) misstates the second-slot magnitude. For z_{k,2} = Re z + j Im z, the actual magnitude is |(Re z + r_k) + j Im z|, not |(Im z + r_k) - j Re z|. The large-reference expansion therefore gives r_k + Re z_{k,2}, not r_k + Im z_{k,2}. As a result, Eqs. (21) and (22) do not follow from Eqs. (16)-(19), and Eq. (23) is not derived. The stress-test note is right: swapping Re and Im in Eq. (19) and re-deriving gives exactly the linear structure of Eq. (23) with v_k = Re v_{k,1} + j Re v_{k,2}. So the concept is repairable, but the manuscript as submitted does not contain a valid derivation of its headline result.\n\nOther soft spots, in proportion: the paper switches from y ∝ |E_RF|^2 in Eq. (2) to y = |h^T x + v| in Eq. (4) without discussing the envelope relationship for a real RF carrier; this is inherited from [8] but deserves a sentence. The reference injection is set 35 dB above the signal, which makes the large-reference approximation valid, but no error analysis is given, and the simulations appear to use the idealized linear model rather than the original nonlinear model with the approximation. That means the BER curves validate the theory of the linearized system but not the actual atomic receiver front-end. No code or data is shipped, which limits reproducibility.\n\nCitation pattern is fine: the paper engages honestly with the prior atomic-MIMO literature, and the self-citation to [16] is appropriate for the detector used as a baseline.\n\nBottom line: this is a paper for a serious referee, not a desk reject. I would send it out and request a corrected derivation of Eq. (19), a proper error analysis of the large-reference approximation, and simulations that actually simulate the nonlinear magnitude model with reference injection. If the authors fix the sign error, the contribution is worth publishing.","headline":"PRSS is a genuinely new idea and the paper is well organized, but the central derivation in Section III-B has an algebraic sign error that invalidates the linear model as written; the fix is easy, so this deserves major revision, not rejection.","tokens_in":9931,"tokens_out":1937,"would_cite":false,"duration_ms":20697,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A two-slot phase trick turns atomic receivers into linear MIMO.","keywords":["Rydberg atomic receiver","phase-rotated symbol spreading (PRSS)","Scalable Atomic-MIMO (SA-MIMO)","atomic MIMO","phase retrieval","OFDM","quantum wireless","envelope detection"],"falsifier":"A direct check of Eq. (19) settles the linearization: take $z_{k,2}=a+jb$ and $r_k>0$, and compare $|z_{k,2}+r_k|$ with $|(b+r_k)-ja|$; they are equal only for special choices of $a,b$, so the printed identity must be read with the correct quadrature assignment for the linear model to follow.","tokens_in":8838,"feed_emoji":"⚛️","tokens_out":9564,"duration_ms":84385,"temperature":0.7,"pith_summary":"The paper tries to establish that a transmitter-side spreading scheme, phase-rotated symbol spreading (PRSS), can turn a Rydberg-atom receiver array—which measures only the magnitude of the received field, a nonlinear phase-retrieval problem—into an equivalent linear MIMO channel. If true, conventional linear detectors such as zero-forcing, LMMSE, and maximum-likelihood detection apply directly to atomic receivers, and the same spreading makes FFT-based OFDM reception possible. The paper reports that PRSS preserves spectral efficiency in theory and yields BER gains over envelope-only atomic MIMO: roughly 2.5 dB under MLD and more than 10 dB under suboptimal detection, with the gap growing in large-scale settings.","feed_headline":"Two-slot phase trick turns atomic receivers into linear MIMO","feed_subtitle":"Standard MIMO and OFDM detection could ride on Rydberg atoms' quantum sensitivity gains.","key_machinery":"The mechanism is PRSS: every transmitter sends $x_n$ in slot one and $x_n e^{j\\theta}$ in slot two, with $\\theta=3\\pi/2$, while each atomic receiver superimposes a strong known reference $r_k$. Because the reference dominates, the absolute-value nonlinearity is linearized as $y_{k,1}\\approx r_k+\\Re\\{\\mathbf{h}_k^T\\mathbf{x}\\}$ and $y_{k,2}\\approx r_k+\\Im\\{\\mathbf{h}_k^T\\mathbf{x}\\}$. De-spreading is the vector subtraction $\\tilde{y}_k-\\tilde{r}_k=y_{k,1}+j y_{k,2}-(r_k+j r_k)$, which requires no channel state information. This linearization is the load-bearing object; on top of it, conventional MIMO detectors, channel estimation, and FFT-based OFDM processing all carry over unchanged.","core_discovery":"The central claim is that spreading each symbol over two time slots with code $\\mathbf{c}=[1,e^{j\\theta}]^T$, choosing $\\theta=3\\pi/2$, and injecting a known strong reference $r_k$ at each atomic receiver transforms $y_k=|\\mathbf{h}_k^T \\mathbf{x}+v_k+r_k|$ into the linear model $\\tilde{\\mathbf{y}}-\\tilde{\\mathbf{r}}=\\mathbf{H}\\mathbf{x}+\\mathbf{v}$. Under the condition $r_k\\gg|z_{k,1}|,|z_{k,2}|$, the first slot reads the real part of the complex projection and the second slot reads the imaginary part, so combining the two slots and subtracting the reference recovers the full complex channel output. The paper therefore claims the nonlinear phase retrieval problem is replaced by a standard linear multiplexing problem, and that this is what allows atomic MIMO and atomic OFDM to scale.","pith_inferences":["The same two-slot quadrature trick could be applied to other magnitude-only sensors, such as photonic envelope detectors or low-cost RF energy harvesters, wherever a strong local reference can be injected.","Because de-spreading is independent of the channel matrix, PRSS could be combined with precoding or pilot designs from conventional MIMO without redesign, which points to a fast integration path for atomic receivers in existing standards.","The required condition $r_k\\gg|z|$ suggests an SNR-dependent trade-off: the reference must be strong enough to linearize the magnitude but not so strong that it consumes the receiver's dynamic range; an adaptive reference level is a natural testable extension."],"forward_implications":["Zero-forcing, LMMSE, matched-filter, and MLD detectors can be reused as-is on atomic receiver arrays, removing the need for specialized phase-retrieval detection algorithms.","PRSS extends to OFDM: when the channel matrix has the form $\\mathbf{H}=\\mathbf{C}\\mathbf{F}^H$, the de-spread model reduces to a standard OFDM receiver, so FFT-based demultiplexing works on atomic links.","Spectral efficiency is not sacrificed in theory: under the paper's Gaussian-input, unitary-channel capacity comparison, the PRSS capacity $C_{\\mathrm{prss}}=\\frac{1}{2}\\log_2\\det(\\mathbf{I} + \\frac{G_{\\mathrm{atom}}}{\\sigma_{\\mathrm{RF}}^2}\\mathbf{H}\\mathbf{Q}\\mathbf{H}^H)$ matches the envelope-only mutual-information scaling.","The reported atomic-receiver SNR advantage over RF front-ends ($G_{\\mathrm{atom}}\\gtrsim20$ dB from reference [2]) carries into the linear model, so atomic MIMO can improve link budget or coverage relative to conventional RF MIMO.","In large-scale settings the paper's simulations show PRSS avoids the error floors of envelope-only detection; at $N=64$ transmit antennas the reported gap reaches 20 dB."],"supporting_citations":[{"why":"Provides the A-MIMO envelope signal model and the reference-injection technique on which PRSS is built.","marker":"[8]"},{"why":"Supplies the experimental atomic-receiver SNR gain used in the capacity comparison and in the RF-MIMO benchmark.","marker":"[2]"},{"why":"Defines the maximum-likelihood detection baseline and the detection-theoretic framework for the comparisons.","marker":"[11]"},{"why":"Provides the p-Jacobi detector used to demonstrate PRSS's suboptimal-detection and large-scale gains.","marker":"[16]"},{"why":"Frames the magnitude-squared phase-retrieval and quantized-MIMO problem whose nonlinearity PRSS is designed to bypass.","marker":"[12]"}],"fun_headline_variants":["Two-slot trick linearizes atomic MIMO detection","Atomic receivers go linear with phase-rotated spreading","PRSS makes quantum MIMO scalable and linear","Rydberg atoms get scalable MIMO via two-slot trick"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The derivation's key step is the claim that in the second time slot the injected reference adds to the imaginary component of the signal while the real component is measured on the orthogonal axis; if that algebraic identification does not match the physical magnitude, the two-slot combination no longer produces the linear equation.","fun_headline_variants_meta":{"raw":{"variants":["Two-slot trick linearizes atomic MIMO detection","Atomic receivers go linear with phase-rotated spreading","PRSS makes quantum MIMO scalable and linear","Rydberg atoms get scalable MIMO via two-slot trick"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000205,"raw_usage":{"total_tokens":1382,"prompt_tokens":923,"completion_tokens":459,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":539,"completion_tokens_details":{"reasoning_tokens":394}},"tokens_in":539,"tokens_out":459,"duration_ms":4939,"temperature":1.0,"reasoning_tokens":394,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T06:00:22.488782+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A direct check of Eq. (19) settles the linearization: take $z_{k,2}=a+jb$ and $r_k>0$, and compare $|z_{k,2}+r_k|$ with $|(b+r_k)-ja|$; they are equal only for special choices of $a,b$, so the printed identity must be read with the correct quadrature assignment for the linear model to follow.","supporting_citations":[{"cited_title":"Towards atomic MIMO receivers,","cited_arxiv_id":null,"evidence_quote":"Provides the A-MIMO envelope signal model and the reference-injection technique on which PRSS is built."},{"cited_title":"Digital communication with Rydberg atoms and amplitude-modulated microwave fields,","cited_arxiv_id":null,"evidence_quote":"Supplies the experimental atomic-receiver SNR gain used in the capacity comparison and in the RF-MIMO benchmark."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines the maximum-likelihood detection baseline and the detection-theoretic framework for the comparisons."},{"cited_title":"Achieving maximum-likelihood detec- tion performance with square-order complexity in large quasi-symmetric MIMO systems,","cited_arxiv_id":null,"evidence_quote":"Provides the p-Jacobi detector used to demonstrate PRSS's suboptimal-detection and large-scale gains."},{"cited_title":"Hermite expansion model and LMMSE analysis for low-resolution quantized MIMO detection,","cited_arxiv_id":null,"evidence_quote":"Frames the magnitude-squared phase-retrieval and quantized-MIMO problem whose nonlinearity PRSS is designed to bypass."}],"review_version":1}