Proposals for quantum coherence in neural computation lack quantitative frameworks for evaluating when -- and whether -- coherence provides computational benefits at biologically calibrated parameters. Here we construct such a framework by integrating a three-layer model parameterized by \textit{ab initio} spin Hamiltonian calculations of monoamine oxidase~A (MAO-A) with approximate covariant quantum error correction (CQEC) based on energy-conserving recursive swap tests. The three layers -- ${}^{31}$P nuclear spin memory ($d = 4$, $T_2 = 3.2$~ms), electron spin quantum-classical interface ($d = 8$, $T_2^e = 1.1$~ns), and classical radical-pair electrochemistry -- are evaluated on error correction benchmarks and a symmetric binary decision task. We find a layer-specific dichotomy: Layer~1 operates in the naturally coherence-preserving regime ($γ_\mathrm{eff} \approx 10^{-6}$) while Layer~2 is decoherence-dominated ($γ_\mathrm{eff} \approx 4.5$, $F \approx 0.51$ versus random baseline $F = 0.125$). In the decision task, CQEC maintains L$\leftrightarrow$R tunneling coherence (up to 168-fold at $γ= 0.5$), extending the time window during which a symmetric double-well system can oscillate between degenerate states before decoherence-induced symmetry breaking. Crucially, a matched classical stochastic model with equivalent noise structure reproduces the symmetry-breaking phenomenon but not the oscillatory dynamics, establishing coherent tunneling as a genuinely quantum signature. We explicitly identify what this toy model cannot address: state preparation at 310~K, spatial entanglement distribution, metabolic costs of error correction, and the 62-fold gap between nuclear spin $T_2$ (3.2~ms) and behaviorally relevant timescales ($\sim$200~ms). These limitations define the quantitative targets that any serious quantum brain proposal must meet.
Proposals for quantum coherence in neural computation lack quantitative frameworks for evaluating when -- and whether -- coherence provides computational benefits at biologically calibrated parameters. Here we construct such a framework by integrating a three-layer model parameterized by \textit{ab initio} spin Hamiltonian calculations of monoamine oxidaseA (MAO-A) with approximate covariant quantum error correction (CQEC) based on energy-conserving recursive swap tests. The three layers -- 31P nuclear spin memory (d=4, T2=3.2ms), electron spin quantum-classical interface (d=8, T2e=1.1ns), and classical radical-pair electrochemistry -- are evaluated on error correction benchmarks and a symmetric binary decision task. We find a layer-specific dichotomy: Layer1 operates in the naturally coherence-preserving regime (γeff≈10−6) while Layer2 is decoherence-dominated (γeff≈4.5, F≈0.51 versus random baseline F=0.125). In the decision task, CQEC maintains L↔R tunneling coherence (up to 168-fold at γ=0.5), extending the time window during which a symmetric double-well system can oscillate between degenerate states before decoherence-induced symmetry breaking. Crucially, a matched classical stochastic model with equivalent noise structure reproduces the symmetry-breaking phenomenon but not the oscillatory dynamics, establishing coherent tunneling as a genuinely quantum signature. We explicitly identify what this toy model cannot address: state preparation at 310K, spatial entanglement distribution, metabolic costs of error correction, and the 62-fold gap between nuclear spin T2 (3.2ms) and behaviorally relevant timescales (∼200ms). These limitations define the quantitative targets that any serious quantum brain proposal must meet.
Discarding an output subsystem is a local post-processing operation, so an entanglement-breaking channel remains entanglement breaking after output reduction. The converse need not hold: a reduced channel can be entanglement breaking even when a richer output still carries reference entanglement. This preprint gives an exactly solvable two-parameter benchmark that quantifies this asymmetry. On two qubits, let (\Pi_\pm=(I\pm Z\otimes I)/2), let (\mathcal L(X)=\sum_s\Pi_sX\Pi_s) be sector dephasing, let (\mathcal M(X)=\sum_s\operatorname{Tr}(\Pi_sX)\Pi_s/2) be measure-and-prepare within the two sectors, and let (\mathcal D_4(X)=\operatorname{Tr}(X)I_4/4). The channel family is [\Phi_{t,\eta}=(1-\eta)\big[(1-t)\mathcal L+t\mathcal M\big]+\eta\mathcal D_4,\qquad 0\le t,\eta\le1.] For the reduced task, a variable second-qubit input is embedded with an arbitrary fixed first-qubit state and the first output qubit is discarded. The induced qubit channel is depolarizing with parameter (q=(1-\eta)(1-t)), and is entanglement breaking exactly when (q\le1/3). For the full four-dimensional output, the partially transposed normalized Choi state has one potentially negative eigenvalue, [\lambda_- = \frac{-4(1-\eta)+6(1-\eta)t+\eta}{16},] with multiplicity two. The block structure makes PPT sufficient for separability in this family. Hence, for (\eta<1), [t_{\rm red}(\eta)=\max!\left{0,1-\frac{1}{3(1-\eta)}\right},\qquadt_{\rm full}(\eta)=\max!\left{0,\frac{4-5\eta}{6(1-\eta)}\right}.] The exact region in which the reduced channel is already entanglement breaking while the full channel is not is (t_{\rm red}(\eta)\le t<t_{\rm full}(\eta)). Its width is [w(\eta)=\begin{cases}\eta/[6(1-\eta)],&0\le\eta\le2/3,\(4-5\eta)/[6(1-\eta)],&2/3\le\eta<4/5,\0,&4/5\le\eta\le1,\end{cases}] and reaches the exact maximum (w_{\max}=1/3) at (\eta=2/3). The Choi negativities are [\mathcal N_{\rm red}=\frac{[3(1-\eta)(1-t)-1]+}{4},\qquad\mathcal N{\rm full}=\frac{[4-5\eta-6(1-\eta)t]_+}{8}.] Therefore the maximal full-output Choi negativity compatible with an already entanglement-breaking reduced output is (1/12), attained at ((\eta,t)=(2/3,0)). The result is a controlled benchmark for output-access dependence: the same physical channel family can cross the entanglement-breaking boundary at different noise values solely because an output subsystem is retained or discarded.
A Bell pair distributed through a link that combines amplitude damping with dephasing at time-dependent rates has dynamics that separate into a fixed part and a moving one. The negativity, fully entangled fraction, discord, and average teleportation fidelity depend on time only through the accumulated damping parameters p(t) and q(t). Every threshold is therefore a curve fixed in the unit square, and the rates select nothing but a trajectory across it. The Horodecki fidelity formula Fˉ=21+61Tr∣T∣ covers one- and two-sided exposure alike: the condition detT≤0 under which it takes this form holds throughout the unit square for both. Under symmetric two-sided noise the entanglement vanishes when p+q≥1, where the exact relation Fˉ2s=32+31N2s ties disentanglement and the loss of quantum advantage to the same instant. One-sided exposure admits no finite-time sudden death for any rate profile, and the discord stays strictly positive throughout the open square, so the distributed state can be separable, useless for teleportation, and still nonclassical. For harmonically modulated rates, complete positivity caps the backflow at one modulation period of static decay, ΔΓk≤2πγk,0/Ω, equivalently at a modulation depth ξk≤4.6033 independent of Ω. Inside that window the trajectory reverses, producing finite intervals of restored quantum advantage and entanglement sudden birth.
Structured dephasing from a massive scalar memory field What this is -> A model of quantum decoherence, and the record of what happenedwhen it was tested against itself. An earlier version of this work proposed that a qubit's loss of coherence isshaped by an auxiliary scalar field acting as an "informational memory", andreported that an oscillatory decay law fitted simulated data far better than thestandard exponential and stretched-exponential laws. This version retracts thatevidence and reports what survives. What went wrong -> The statistical advantage was an artefact. The simulated databegan at a coherence value above 1 — physically impossible — which no admissiblecompeting model could follow. Once the coherence function is correctlynormalised, the proposed law drops from first to fourth place. Worse, datagenerated by an ordinary structured boson bath, containing no memory field of anykind, are fitted equally well by the same law. Goodness of fit cannot tell the twoapart. Fitted oscillation frequencies are biased estimators of the field mass byroughly 50%. What else failed -> Memory measures do not single the field out either. Atmatched decoherence, an ordinary narrow Lorentzian pseudomode is thirteen timesmore non-Markovian than the field. And the system–field mutual information turnsout to be a function of the coherence alone, for *every* dephasing environment —measuring it is measuring the coherence again in different units. The"informational" reading is not supported and has been dropped. Whether it was already dead -> If the field were fundamental and coupled tomatter density, a spectral threshold in the GHz band would require a Compton rangeof centimetres, exactly where torsion-balance experiments are most sensitive. Aqubit's differential charge under such a coupling — the two states contain the sameatoms and differ only by the transition energy — falls short of observability byabout 35 orders of magnitude. As new fundamental physics, the model is excludedoutright. What survives, and it is testable -> Read instead as an effective mode of thedevice's own environment — a phonon branch, a packaging mode, a structureddefect bath — the model needs no new physics and makes two sharp predictions.The noise spectrum acquires a hard threshold with a square-root edge, absent insmooth Lorentzian environments and resolvable by CPMG noise spectroscopy at the 1%level. And for two qubits at separation *r*, the cross-spectrum is the self-spectrummodulated by sinc(*kr*), whose zeros overdetermine the band edge and theseparation, and whose correlation reverses sign with distance — exchanging whichBell state is protected. Ordinary crosstalk is monotonic in separation and cannotreverse. Why it may be worth reading anyway. -> The methodological lesson generalises wellbeyond this model: in non-Markovian decoherence, fit quality is close to worthlessas evidence, because too many physically different environments produce the samecurve. What discriminates is structure — thresholds, zeros, sign changes — notgoodness of fit. The three admissibility constraints derived here (boundedcoherence, quadratic short-time onset, and the plateau implied by a spectral gap)are cheap to apply and reject most published fitting forms. All numerical results are reproducible: code, seeds, figures and a verificationsuite are included. Status: preprint, not peer reviewed. All data are simulated; nothing hereestablishes that the predicted signatures exist in any real device. The paperstates what would have to be observed, and what would have to be excluded, forthem to count.
We prove a generalized quantum Stein lemma for parallel discrimination of an arbitrary finite-dimensional channel against families of alternative channels. The alternatives are compact and convex, closed under tensor products, and contain a faithful replacer. At every fixed type-I error tolerance, the optimal type-II error exponent equals the regularized Umegaki channel relative entropy minimized over the alternatives, and both defining limits exist. Inputs may be entangled across channel uses and with a reference system. The main technical result constructs exactly trace-preserving approximations with exponentially small diamond error, dominated in completely positive order by free channels at every rate above the common exponent. The proof combines uniform auxiliary map approximation, iterative reduction of the domination rate, and tensor amplification. It yields asymptotic equipartition with trace-preserving smoothing at every subexponentially vanishing error, an exponential strong converse, and stability under vanishing diamond-norm perturbations. Under additional permutation invariance and closure under insertion of a fixed faithful input state and discarding of its output, we also prove an explicit finite-block completion bound. This quantitative construction uses weighted discarding, local operator corrections, and comparison with auxiliary extensions. Applications include state-preserving, coherence-restricted, covariant, entanglement-breaking, and positive-partial-transpose channels. For isometric targets against entanglement-breaking or positive-partial-transpose alternatives, we obtain exact finite-block testing and smoothing formulas.
The quantum capacity of a noisy channel quantifies the maximum rate at which quantum information can be transmitted reliably. For general channels, its evaluation requires an optimization over arbitrarily many channel uses. Degradable channels form a central exception: their capacity is given by the single-letter coherent information, while antidegradable channels have zero capacity. Nevertheless, even for these fundamental classes, it has remained open whether communication above capacity becomes possible when a fixed non-maximal error is tolerated. Here we resolve this problem by proving an exponential strong converse for every finite-dimensional degradable and antidegradable channel: at any rate above capacity, the fidelity of every coding scheme decays exponentially with the number of channel uses. As an immediate consequence, we establish the first all-code exponential strong converse for the quantum erasure channel throughout its full parameter range, strengthening previous results that applied only to almost all codes. We also show that exponential strong-converse bounds are preserved under receiver post-processing. This yields efficiently computable semidefinite-programming bounds for arbitrary finite-dimensional channels, improved bounds for Pauli channels, and an exact exponential strong converse for a nondegradable multilevel amplitude-damping family.
We consider a generalized central spin model, consisting of two central qubits and an environmental spin chain (with periodic boundary condition) to which these central qubits are locally and weakly connected either at the same site or at two different sites separated by a distance d. Our purpose is to study the subsequent temporal generation of entanglement, quantified by concurrence, when initially the qubits are in an unentangled state. In the equilibrium situation, we show that the concurrence survives for a larger value of d when the environmental spin chain is critical. Importantly, a common feature observed both in the equilibrium and the nonequilibrium situations while the latter is created by a sudden but global change of the environmental transverse field is that the two qubits become maximally entangled for the critical quenching. Following a nonequilibrium evolution of the spin chain, our study for $d\ensuremath{\ne}0$ indicates that there exists a threshold time above which concurrence attains a finite value. Additionally, we show that the number of independent decohering channels (DCs) is determined by d as well as the local difference of the transverse field of the two underlying Hamiltonians governing the time evolution; the concurrence can be enhanced by a higher number of independent channels. The qualitatively similar behavior displayed by the concurrence for critical and off-critical quenches, as reported here, is characterized by analyzing the nonequilibrium evolution of these channels. The concurrence is maximum when the decoherence factor or the echo associated with the most rapidly DC decays to zero; on the contrary, the condition when the concurrence vanishes is determined nontrivially by the associated decay of one of the intermediate DCs. Analyzing the reduced density of a single qubit, we also explain the observation that the dephasing rate is always slower than the unentanglement rate. We further establish that the maximally and minimally decohering channels show singular behavior which can be explained by invoking upon a quasiparticle picture.