Crosstalk-Resilient Quantum MIMO for Scalable Quantum Communications

Seid Koudia; Symeon Chatzinotas

REVIEW 5 major objections 8 minor 22 references

Crosstalk-Resilient Quantum MIMO for Scalable Quantum Communications

T0 review · 5 major / 8 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Encoding quantum information in GKP bosonic codes makes crosstalk between multiplexed modes harmless at rational transmissivity values $\eta = q/(q + p d_1 d_2)$, preserving the logical data.

desk verdict Genuinely novel idea about rational crosstalk and GKP gauge absorption, but the central theorem's proof is wrong for generic parameters and the decoder is not coherent; deserves a referee but needs major repair. read the letter →

arxiv 2506.21704 v1 pith:MRVP32MZ submitted 2025-06-26 quant-ph

Seid Koudia , Symeon Chatzinotas This is my paper

classification quant-ph

keywords GKPcodescrosstalkquantummultiplexingMIMOgaugesubsystembeamsplittercontinuous-variablecommunicationerrorcorrection

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

Multiplexing many quantum channels in one physical medium is limited by crosstalk: mode-mixing interference between channels corrupts the transmitted states. This paper proposes to fight that interference with the encoding itself: send discrete-variable (DV) logical information through continuous-variable (CV) bosonic modes using Gottesman-Kitaev-Preskill (GKP) codes, whose stabilizer lattices can be matched to the crosstalk. The central claim is that when the crosstalk strength $\eta$ takes the rational values $\eta = q/(q + p d_1 d_2)$, the displacements induced by mode mixing land inside the stabilizer lattices of both codes, so the logical information is perfectly preserved. The output state then splits into a logical factor and a maximally entangled gauge factor, and the paper constructs a gauge-fixing decoder from modular arithmetic and GKP Clifford gates that recovers the logical state. Numerical simulations under Gaussian displacement noise show fidelity peaks at these rational points and quantify a rate–fidelity tradeoff, establishing a coding-theoretic path to crosstalk-resilient quantum multiplexing and quantum MIMO.

What carries the argument

The central object is the GKP stabilizer lattice and its image under the beam-splitter crosstalk. A GKP code $\mathcal{C}_{d,S}$ is defined by a lattice of displacement stabilizers with symplectic area $2\pi d$, and its logical operators are shifts by $\mathbf{u}/d$ and $\mathbf{v}/d$ along the lattice generators. Crucially, the beam-splitter $\hat{U}_\eta$ maps a displacement on one mode into a correlated displacement on the other, so the paper requires every induced displacement to fall inside the other mode's stabilizer lattice; this forces the ratio $\eta/(1-\eta)$ to equal $d_1/d_2$ times a rational factor and yields the condition $\eta = q/(q + p d_1 d_2)$. The same lattice matching shows that the output codes have areas scaled by $n = q + p d_1 d_2$, producing an $n$-fold gauge degeneracy, and it is this enlarged lattice that the gauge-fixing decoder exploits through modular arithmetic (Bézout inverses and modular inversion of step sizes) combined with GKP logical Clifford gates.

What would settle it

Simulate or directly compute the beam-splitter output of two GKP-encoded states at a rational transmissivity of the stated form where the coprimality condition fails, for example $d_1 = d_2 = 2$, $q = 2$, $p = 1$ (yielding $\eta = 1/3$ and $n = 6$); since $\gcd(q, p d_1 d_2) = 2$, the Bézout integers of Theorem 2 do not exist, and if the logical information is not perfectly recoverable by the proposed decoder in this case, the theorem's coverage is narrower than claimed.

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Extended reading notes

Core claim

The paper proves Theorem 1: two GKP codes $\mathcal{C}_{S_1,d_1}$ and $\mathcal{C}_{S_2,d_2}$ with stabilizer areas $2\pi d_1$ and $2\pi d_2$, carried by two bosonic modes undergoing beam-splitter crosstalk $\hat{U}_\eta$, admit a choice of stabilizers such that logical information is perfectly preserved if and only if $\eta = q/(q + p d_1 d_2)$ for integers $q,p$. Under this rational condition the crosstalk-induced displacements act on a gauge subsystem rather than on the logical content: the output lies in the enlarged codes $\mathcal{C}_{n d_1} \otimes \mathcal{C}_{n d_2}$ with $n = q + p d_1 d_2$, and the output state factorizes as $|\mu_1,\mu_2\rangle_L \otimes |\Phi_n\rangle_G$, where $|\Phi_n\rangle$ is a maximally entangled gauge state. The paper further gives an operational decoder: entangle each output mode with an ancilla, measure in the computational basis, recover the gauge index $j$ by modular inversion, and apply Clifford corrections conditioned on $j$. It also derives an upper bound on entanglement fidelity for finite-energy GKP states under Gaussian displacement noise, showing sharp resonance peaks near the rational $\eta$ values and a clear improvement over unencoded EPR pairs.

Load-bearing premise

The argument assumes that the integers appearing in the crosstalk-strength ratio can always be chosen so that the decoder's modular arithmetic steps—the Bézout identities $\alpha_i q + \beta_i p d_1 d_2 = 1$ and the inverses of the step sizes $r_i$ modulo $n$—actually exist, but the paper does not state the coprimality conditions that guarantee them.

Editorial extensions

If this is right

At rational transmissivities $\eta = q/(q + p d_1 d_2)$, crosstalk between two GKP-encoded modes can be absorbed entirely into a gauge subsystem, so logical information in both modes survives without per-mode crosstalk correction.
The output state lives in the enlarged code space $\mathcal{C}_{n d_1} \otimes \mathcal{C}_{n d_2}$ with $n = q + p d_1 d_2$ and decomposes as $|\mu_1,\mu_2\rangle_L \otimes |\Phi_n\rangle_G$, making the gauge degree of freedom explicit.
A decoder built from modular arithmetic and GKP logical Clifford operations fixes the gauge and recovers the logical state deterministically when the receiver has channel state information about the average crosstalk strength.
Under Gaussian displacement noise, entanglement fidelity peaks sharply near rational $\eta$ values and decays with the distance to the nearest rational point, and larger code dimension $d$ trades lower fidelity for higher rate.
The framework provides a coding-theoretic foundation for crosstalk-resilient quantum MIMO communication, where multiple spatial modes can be multiplexed without crosstalk-induced logical errors at the rational operating points.

Reading between the lines

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

The commensurability condition is essentially a lattice-matching (commensurability) condition between the two stabilizer lattices; a natural but untested extension is to $N$-mode crosstalk, where perfect absorption would require a joint commensurability condition across all modes.
Because realistic crosstalk is stochastic (the paper models $\eta$ as log-normal), the perfect-transmission points form a set of measure zero; a practical protocol would need to lock the hardware to a rational operating point or estimate and adapt, and the paper leaves the no-CSI adaptive decoder as future work.
The decoder's modular inversion steps require coprimality conditions that are not guaranteed by the theorem's hypotheses; a robust decoder would need to handle non-invertible cases directly on the lattice quotient.
Averaging the single-peak fidelity over the log-normal distribution of $\eta$ would predict which rational operating points dominate the practical performance and what code dimension optimally balances rate against resonance width; this average-fidelity calculation is not performed in the paper.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Here's my take on 2506.21704. The new idea is real: if the crosstalk transmissivity takes rational values η = q/(q+p d1 d2), the beamsplitter can map two GKP lattices into a larger lattice, and the logical information may ride in a subsystem while the excess is gauge. That is a genuinely different route than the GKP and MIMO literature I know, and the basic area-matching in Theorem 1 is sound. But the paper as written does not support its main claim. Theorem 2's output formula is wrong for generic admissible parameters. The proof derives Eq. (23) and then silently reindexes away the cross terms and replaces q_i μ_i with μ_i. That requires q_i ≡ 1 mod d_i, which is not stated and not implied by the Bézout conditions. For a concrete case, take d1=3, d2=5, q1=q2=2, p1=p2=1, so η=4/19. Eq. (23) gives first-mode labels 2+15j mod 57, while the theorem gives 19+15j mod 57. These differ by 17, which is not divisible by 3, so no shift in the gauge index can reconcile them. The formula, the factorization in Theorem 3, and the decoder's modular inversion all rest on this incorrect reindexing. Theorem 3 also swaps the step sizes r1,r2 relative to Theorem 2. The decoder in Section V-E has an independent problem: it measures ancillas in the computational basis, which projects the logical superposition. For an unknown input or an EPR state, that destroys the very coherence the scheme is supposed to protect. The paper says the decoder is intended for the with-CSI regime and suboptimal under Gaussian noise, but that does not address the projective collapse. The numerical fidelity bound uses δ(η,η_i)=|η-η_i| L with L unspecified and not derived from the declared noise model, so the bright bands around rational η are illustrative, not quantitative. What survives is the underlying gauge-absorption mechanism and the rational-point condition. With corrected conditions (likely q_i units modulo d_i, plus explicit gcd requirements) and a properly coherent gauge-fixing step, the idea could become a usable contribution. As it stands, the central theorem is false as stated and the decoder does not do what it claims. I would not cite this version, but I would send it to a referee: the core idea is worth serious scrutiny and the errors, while load-bearing, look repairable.

Referee Report

5 major / 8 minor

Summary. The paper proposes a crosstalk-mitigation scheme for quantum multiplexing by encoding discrete-variable information into GKP code states. The central claim (Theorem 1) is that perfect logical transmission under a beam-splitter crosstalk U_eta is possible if and only if the transmissivity takes the rational form eta = q/(q + p d1 d2), where d1 and d2 are the GKP code dimensions. The authors further derive an explicit output-state formula (Theorem 2), factor the output into logical and gauge subsystems (Theorem 3), and propose a gauge-fixing decoder (Theorem 4 and Section V-E). Numerical simulations are presented to illustrate fidelity behavior and rate-fidelity trade-offs.

Significance. If the central result is correct, it would identify a concrete, falsifiable condition under which mode-mixing crosstalk is harmless for GKP-encoded communications, and the gauge-subsystem viewpoint is conceptually interesting. The paper attempts a rigorous mathematical treatment with theorems and proofs, which is commendable, and the rational-eta condition is a sharp prediction. However, the proofs in the current manuscript have substantial gaps, and one key formula is demonstrably false for parameters allowed by the stated assumptions. The numerical section does not provide independent evidence because the fidelity peaks are introduced by hand. No machine-checked proofs, reproducible code, or parameter-free derivations are included, so the significance rests entirely on the analytic claims, which are not yet established.

major comments (5)

[Section IV-B, Theorem 1] The claimed "if and only if" is not proved. The derivation establishes only a sufficient condition: if the stabilizer lattices are related by the scaling S2 = ... and the induced displacements land in the stabilizer lattices, then the logical information is preserved. No argument is given for the converse, that perfect preservation forces eta to be of the form q/(q + p d1 d2). In addition, the quantities q1, p1, q2, p2 in the matching condition are not defined before use, and the factorization q = q1 q2, p = p1 p2 is introduced without justification. Since q and p are arbitrary integers, the stated condition is equivalent to "eta is rational" for fixed d1, d2; this equivalence and its proof should be stated explicitly.
[Section V-B, Theorem 2, Eq. (23)] The transition from Eq. (23) to the claimed output-state formula is invalid for the stated hypotheses. The first label q1 mu1 + p2 d1 mu2 + j p d1 d2 is replaced by mu1 alpha1 n + j p d1 d2, which requires q1 mu1 = mu1 (mod d1) for all mu1, i.e. q1 = 1 (mod d1), and similarly q2 = 1 (mod d2). These congruences are not consequences of the Bezout identities and are not stated. For example, with d1=3, d2=5, q1=q2=2, p1=p2=1, we have q=4, p=1, n=19, gcd(q, p d1 d2)=1; Eq. (23) with mu1=1, mu2=0 gives first-mode labels 2 + 15j mod 57, whereas the claimed formula gives 19 + 15j mod 57. These sets are incongruent modulo 3 for every j, so no reindexing of the gauge sum can reconcile them. The output-state formula, and therefore Theorem 3 and the decoder, are unsupported for the parameter range claimed.
[Section V-C, Theorem 3, and Section V-E] The bijective relabeling (mu_i, j) -> mu_i alpha_i n + j r_i mod n d_i and the modular-inversion step j = x r_i^{-1} mod n require conditions that are not stated and can fail. The paper asserts that gcd(r1,n)=gcd(r2,n)=1 "by construction," but this is false. For instance, with d1=3, d2=5, p2=2, q=1, p=1, we get r1 = p2 d1 d2 = 30 and n = q + p d1 d2 = 16, with gcd(30,16)=2. The correct condition for the relabeling is at least gcd(r_i/d_i, n)=1, which is also not guaranteed. The decoder's modular inverse is therefore not generally well-defined, and the claimed gauge factorization does not hold for admissible parameter choices.
[Section V-D, Theorem 4] The proof that a gauge-fixing unitary exists is not rigorous. The listed operations (modular inverse, modular subtraction, Bell-to-product change) are asserted to be constructible from GKP logical Clifford gates, but no explicit construction or proof of correctness is given. Moreover, Section V-E's decoder uses measurement and classical feedforward, which is not a unitary operation; the relationship between the unitary statement of Theorem 4 and the measurement-based protocol is not reconciled. The claim "since gcd(r1,n)=gcd(r2,n)=1 by construction, hence this is a physical unitary gate" is false as shown above and does not establish the required map.
[Section V-F, numerical fidelity bound] The fidelity bound F_e(eta,sigma^2) <= max_{eta_i} exp(-delta(eta,eta_i)^2/(2 sigma^2)) F_ideal(sigma) is ad hoc. The rational points eta_i are chosen by the authors and the Gaussian decay around them is assumed, so the bright bands in Fig. 4 are built into the bound rather than emerging from the theory. The scale L in delta(eta,eta_i)=|eta-eta_i|L is not defined or derived, and no argument connects this bound to the actual GKP error-correction dynamics. Consequently, the numerical simulations do not provide independent evidence for the central claim; they plot an assumed formula.

minor comments (8)

[General] The manuscript contains numerous typos and formatting errors, including "Gottesman-Kitael-Preskill" (Introduction), "thethroughput" (Introduction), "interfecrence" (Section III-A), "transmofrmation" (Section IV-B), "dipslacement" and "entangleemnt" (Fig. 4 caption), and "bĳective" (Theorem 3 proof).
[Section III-A] The log-normal model in Eq. (2) uses eta both as the random variable and as the integration variable, and the relationship between the stochastic eta and the deterministic value in Theorem 1 is not clarified; the paper should state whether Theorem 1 applies to a fixed realization or to the mean.
[Section III-A] The decoder D(eta) introduced in the problem statement (Eq. (3)) is never explicitly constructed or connected to the later gauge-fixing decoder; the paper should define the notion of decoding used in the problem statement.
[Section IV-B] The claim that Eq. (8) provides "a discrete set of values" for eta is misleading, since for fixed d1, d2 the set {q/(q+p d1 d2) : q,p in Z} is countably infinite and dense in the interval (0,1).
[Section V-A, Lemma 1] The proof of Lemma 1 contains undefined symbols and unclear statements, e.g., "if we choose alpha = k d1 ~u1 = m u1" and the jump to Eq. (14); the derivation of omega_out,1 = 2 pi n d1 is not shown.
[Section V-F] The comparison in Fig. 5 between GKP-encoded EPR pairs and polarization-encoded EPR pairs is between different noise models (mode-mixing crosstalk versus XX coupling with depolarizing noise), so the claimed improvement is not a controlled comparison.
[Section V] The notation "mod n" in Theorem 2 and Section V-E is ambiguous: the first-mode labels are modulo n d1 and the second-mode labels modulo n d2, but the text sometimes omits the d_i factor.
[Section VI] The conclusion claims direct applicability to Quantum MIMO communications, but the paper analyzes only two modes; the extension to multiple spatial modes is not demonstrated and should be described as future work rather than a direct application.

Circularity Check

1 steps flagged · score 4.0 of 10

Numerical 'confirmation' of rational-η peaks is circular because the fidelity bound is constructed to peak at those very rational points; the core theoretical derivation remains independent.

fitted input called prediction [Section V-F, 'Derivation of Ideal Decoder Fidelity' and Fig. 4 discussion]
"The effective fidelity is bounded by: F_e(η,σ2)≤ max_{η_i} exp(−δ(η,η_i)^2/(2σ^2)) F_ideal(σ), where δ(η,η_i)=|η−η_i|/L is the geometric mismatch between the actual η and rational alignment points η_i ... bright bands indicating regions of high-fidelity transmission centered around rational η-values, with exponential decay in the neighberhood of each peak. These simulations confirm the analytical expectations that high-fidelity code transmission occurs near rational values of η."

The η_i appearing in the simulation's upper bound are exactly the rational transmissivities derived in Theorem 1, η = q/(q + p d1 d2). The fidelity bound is defined by placing Gaussian peaks around those η_i, so the bright bands in Fig. 4 are inserted by construction rather than discovered by simulation. The subsequent statement that the simulations 'confirm' high fidelity near rational η therefore reports an input of the model as an output of the simulation. This is circular as a numerical validation, although it does not invalidate the independent algebraic derivation of the transmission condition.

full rationale

I examined the paper's main derivation chain. Theorem 1 follows from symplectic-area matching of transformed GKP stabilizers; Theorem 2 and Theorem 3 are algebraic characterizations of the output state and gauge structure; the decoder is a modular-arithmetic construction. These steps are not fitted parameters and do not reduce to their own inputs by definition. The paper's self-citations (refs. 3, 4, 7, 8, 9, 11, 12) are background and motivational, not load-bearing uniqueness theorems or smuggled ansatze, so they do not create circularity. Several unsupported technical claims appear in the proof chain — e.g., the silent congruence assumptions in passing from Eq. (23) to the final form in Theorem 2, and the assertion in Section V-E that gcd(r_i, n)=1 'by construction' — but these are correctness gaps, not circularity, because they do not make the target result an input. The one genuine circular element is the numerical 'confirmation' in Section V-F: the fidelity upper bound is explicitly peaked around the paper's own derived rational η_i, and then those peaks are cited as evidence for the theory. This affects only the numerical validation, not the central mathematical claim, so the appropriate overall circularity score is moderate rather than high.

Assumptions & free parameters 3 free parameters · 6 assumptions · 1 invented entities

The central claim rests on ideal GKP states, a passive beamsplitter crosstalk model, exact rational eta, and two unstated number-theoretic coprimality conditions. The fidelity plots also depend on an unspecified lattice scale and a hand-chosen set of rational peaks, which are free parameters for the numerics rather than derived quantities.

free parameters (3)

lattice scale L in fidelity bound δ(η,η_i)=|η-η_i| L = not specified
Introduced ad hoc to convert transmissivity mismatch into a displacement-like penalty; no derivation from the noise model and no value given, so figure results depend on an invisible parameter.
log-normal crosstalk parameters (μ, σ_c) = σ_c=0.4 mentioned in Fig. 4 caption; μ not given
Declared model of stochastic eta but never integrated into the fidelity computations; the simulations treat eta as deterministic, so these parameters are effectively decorative.
set of rational alignment points η_i = chosen grid of rational values
The bound maximizes over the paper's own rational eta values; the choice of which and how many points are included changes Fig. 4's band structure.

assumptions (6)

domain assumption Ideal infinite-energy GKP states with exact stabilizer invariance
All theorems assume perfect GKP codewords; finite-squeezing effects are only discussed qualitatively, never in the proofs. (Section II)
domain assumption Crosstalk is a passive beamsplitter with transmissivity eta
The entire analysis rests on Eq. (1), which models mode-mixing as a linear symplectic transformation; other crosstalk mechanisms (frequency shifts, nonlinearities) are out of scope. (Section III-A)
domain assumption eta takes exact rational values for perfect transmission
Theorem 1 and all code constructions require eta = q/(q+p d1 d2) exactly; a stochastic log-normal eta hits this set with probability zero, so the main result concerns measure-zero channel instances. (Section IV-B, V-E)
ad hoc to paper Bézout solvability gcd(q, p d1 d2)=1
Theorem 2 postulates integers alpha_i, beta_i with alpha_i q + beta_i p d1 d2 = 1; existence is not guaranteed and the condition is never stated. (Theorem 2 statement)
ad hoc to paper gcd(r_1,n)=gcd(r_2,n)=1 for modular inversion
The decoder needs to invert r_i mod n, and the paper claims this holds 'by construction', but e.g. d1=3, d2=5, p2=2, q=1 gives r1=30, n=16 with gcd=2. (Section V-E step 4)
domain assumption GKP logical Clifford gates can implement modular arithmetic and basis relabelings
Theorem 4 asserts these operations are constructible, but no explicit GKP circuit is given; whether the relabeling (mu,j) -> mu alpha n + j r is a symplectic operation on the GKP lattice is not demonstrated. (Section V-D)

invented entities (1)

Gauge subsystem with maximally entangled gauge state |Phi_n>
purpose: Absorbs the crosstalk-induced lattice displacements so logical labels remain intact; enables the claimed decoder.
A mathematical re-labeling of the enlarged code space C_nd1⊗C_nd2 into logical and gauge factors; no independently measurable signature is predicted beyond the internal consistency of the protocol.

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Cite this review

Pith. "Pith review of Crosstalk-Resilient Quantum MIMO for Scalable Quantum Communications." pith.science (2026). https://pith.science/paper/MRVP32MZ

@misc{pith2026250621704,
  author       = {Pith},
  title        = {Pith review of: Crosstalk-Resilient Quantum MIMO for Scalable Quantum Communications},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MRVP32MZ}},
  note         = {Machine review of arXiv:2506.21704}
}

read the original abstract

We address the challenge of crosstalk in quantum multiplexing -an obstacle to scaling throughput in quantum communication networks. Crosstalk arises when physically coupled quantum modes interfere, degrading signal fidelity. We propose a mitigation strategy based on encoding discrete-variable (DV) quantum information into continuous-variable (CV) bosonic modes using Gottesman-Kitaev-Preskill (GKP) codes. By analyzing the effect of mode-mixing interference, we show that under specific noise strength conditions, the interaction can be absorbed into a gauge subsystem that leaves the logical content intact. We provide rigorous conditions for perfect transmission in the ideal case, derive the structure of the output codes and prove the existence of a gauge-fixing decoder enabling recovery of the logical information. Numerical simulations under displacement Gaussian noise illustrate the fidelity behavior and rate-fidelity tradeoff. Our results establish a coding-theoretic foundation for crosstalk-resilient multiplexing in quantum networks.

Figures

Figures reproduced from arXiv: 2506.21704 by the authors.

**Figure 2.** The gauge fixing decoder. A logical Controlled [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** The scheme considered for the simulation. We [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 5.** Figure 5: Entanglement fidelity of two polarization encoded [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]

**Figure 6.** Figure 6: The rate-fidelity tradeoff decreases with code size due to practical effects of Gaussian noise, emphasizing the role of rational 𝜂 tuning and finite squeezing in real devices. We note that for both simulations, the ideal decoder from the previous section was considere…

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K. Fukui, R. N. Alexander, and P. van Loock, “All-optical long- distance quantum communication with gottesman-kitaev-preskill qubits,” Physical Review Research, vol. 3, no. 3, p. 033118, 2021. 10

2021
[22]

Phase- space methods for representing, manipulating, and correcting gottesman-kitaev-preskill qubits,

L. J. Mensen, B. Q. Baragiola, and N. C. Menicucci, “Phase- space methods for representing, manipulating, and correcting gottesman-kitaev-preskill qubits,” Physical Review A, vol. 104, no. 2, p. 022408, 2021. 11

2021

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [1]

The quantum internet,

H. J. Kimble, “The quantum internet,”Nature, vol. 453, no. 7198, pp. 1023–1030, 2008

2008

[2] [2]

Quantum internet: A vision for the road ahead,

S. Wehner, D. Elkouss, and R. Hanson, “Quantum internet: A vision for the road ahead,”Science, vol. 362, no. 6412, p. eaam9288, 2018

2018

[3] [3]

The quantum internet: an efficient stabilizer states distribution scheme,

S. Koudia, “The quantum internet: an efficient stabilizer states distribution scheme,”Physica Scripta, vol. 99, no. 1, p. 015115, 2023

2023

[4] [4]

Simulating photonic devices with noisy optical elements

M. Vischi, G. Di Bartolomeo, M. Proietti, S. Koudia, F. Cerocchi, M. Dispenza, and A. Bassi, “Simulating photonic devices with noisy optical elements,”arXiv preprint arXiv:2311.10613, 2023

work page Pith review arXiv 2023

[5] [5]

An entanglement-based wavelength-multiplexed quan- tum communication network,

S. Wengerowsky, S. K. Joshi, F. Steinlechner, H. Hübel, and R. Ursin, “An entanglement-based wavelength-multiplexed quan- tum communication network,”Nature, vol. 564, no. 7735, pp. 225– 228, 2018

work page 2018

[6] [6]

Continuous-variable quantum repeater based on quantum scissors and mode multi- plexing,

K. P. Seshadreesan, H. Krovi, and S. Guha, “Continuous-variable quantum repeater based on quantum scissors and mode multi- plexing,” Physical Review Research, vol. 2, no. 1, p. 013310, 2020

work page 2020

[7] [7]

Diver- sity and multiplexing in quantum mimo channels,

L. Oleynik, S. Koudia, M. Bayraktar, S. Chatzinotaset al., “Diver- sity and multiplexing in quantum mimo channels,”EPJ Quantum Technology, vol. 12, no. 1, pp. 1–11, 2025

work page 2025

[8] [8]

Mimo quantum communication in correlated pure-loss channels,

J. ur Rehman, S. M. A. Rizvi, S. Koudia, S. Chatzinotas, and H. Shin, “Mimo quantum communication in correlated pure-loss channels,” IEEE Communications Letters, 2025

work page 2025