Convex-Entropy Reservoirs and Conditional Ground-State Preparation: An Operational Separation of Thermodynamic Curvature, Accessible Cooling, and Dynamical Reset, with a Spectral-Obstruction Case Study in the D1-D5 CFT
The paper has two components. Parts I–IV develop a conditional operational theory of reservoir-assisted cooling and exact reset at the level of channels; Part V is a self-contained Hamiltonian-level case study of exact reset embeddings in a D1–D5 CFT reservoir. The two notions of “exact reset” are different and are kept distinct throughout. We separate three logically distinct questions in reservoir-assisted cooling: what the reservoir entropy implies thermodynamically, which low-temperature ancillas are accessible, and what extra dynamical resource exact ground-state preparation needs. Convex microcanonical entropy is neither sufficient nor necessary for a microscopic cooling operation; it is a thermodynamic route to an ancilla supply, under a stated local-Gibbsian hypothesis. For a resonant qubit target we prove that every energy-conserving collision with a qubit ancilla acts as p' = p + s(q − p), 0 ≤ s ≤ 1, so cooling to error ε is possible exactly when ancillas with excited population at most ε can be supplied. We then remove the two-level restriction: for an arbitrary energy-incoherent sink, within the stated collision model, the least reachable excited population is a sector-wise majorization (sorting) problem with an explicit closed-form solution. Its consequences are: (a) a cooling criterion: a sink can cool a target of population p if and only if some pair of its levels one target gap apart has population ratio below p/(1−p); (b) a Gibbs sink at any finite temperature leaves the exact floor min{p, (1−p)e^{−β E_sys}} > 0, and this floor is stable under arbitrary sequences of fresh sinks at the same temperature (the sequence extension is proved by a concavity lemma); (c) the floor is a single-temperature statement: a hot and a cold thermal sink used together cool every p ∈ (0,1), and iterating fresh pairs drives p → 0 with no work store, measurement or record, while sequential single-sink collisions already reach n̄_c / (1 + n̄_c + n̄_h); (d) sharpness of the energy support, or one classical record of entropy h_2(p), is what buys exactness in finitely many steps. Exact reset has two independent resource obstructions in the stated model. The optimal residual excitation of any energy-conserving reset is the sink weight on directions that lack spectral room (the room floor), with a criterion for measurement-free exact reset; against limited control, any circuit of m gates with rank(G − I) ≤ ρ leaves the target excited with probability at least the sink-spectrum tail beyond ρm, so, within this gate model, the number of gates needed for exactness is at least the corresponding tail rank divided by ρ, with the operational integer requirement expressed by the ceiling where a finite target error is specified. Within the shell-ancilla model, an explicit dimension requirement dim ≥ 1/ε follows, with the corresponding bound attained by the stated construction. The room floor and the rank–error bound are energy-conserving, sector-wise and gate-rank refinements of the Ticozzi–Viola purification bound, and are presented as such. We also give a conditional zero-designated-work SWAP construction with N = O(log log(1/ε)) collisions for a quadratic-entropy family, a dimension-counting reset criterion with an exact ladder-sink cost–error curve, an error budget for measurement–feedback completion, and a finite birth–death noise model with a positive spectral gap. Black holes, Na⁺_147 nanoclusters, structured-vacuum engines and Casimir experiments are treated as delimited case studies, not demonstrations. The contribution is a conditional operational characterisation with falsifiable requirements; it is not a claim that the third law has been circumvented. Finite instances of the principal formulas were checked by exact arithmetic and numerical sampling (random energy-conserving unitaries against the closed forms, and exact evaluation of tabulated values; Section 27); these checks are consistency tests, not substitutes for the proofs. Part V. The case study proves two conditional obstructions to exact spectral reset embeddings in a D1–D5 CFT reservoir. The first is a sector-specific capacity bound: under explicit component-string, single-strand, graded-orbifold and constant-character hypotheses, the maximal-left-charge Ramond-ground-state sector has dimension 4N, so a larger source cannot embed into it. The second is a finite-dimensional perturbative criterion: for an exactly degenerate source block transported by a regular family, the second-order effective Hamiltonian must act as a scalar on the transported block, equivalently the block must lie in a single second-order eigenspace, which gives an eigenspace-multiplicity bound for a prescribed target sector. At level four, under an explicit Hermiticity and perturbative-matching hypothesis, fifteen long-multiplet primaries with distinct second-order lifts give a fixed-label non-scalar target block. All obstructions are conditional and local, no universal no-go theorem for the full D1–D5 Hilbert space is claimed, and no microscopic reset dynamics are constructed.
The paper has two components. Parts I–IV develop a conditional operational theory of reservoir-assisted cooling and exact reset at the level of channels; Part V is a self-contained Hamiltonian-level case study of exact reset embeddings in a D1–D5 CFT reservoir. The two notions of “exact reset” are different and are kept distinct throughout. We separate three logically distinct questions in reservoir-assisted cooling: what the reservoir entropy implies thermodynamically, which low-temperature ancillas are accessible, and what extra dynamical resource exact ground-state preparation needs. Convex microcanonical entropy is neither sufficient nor necessary for a microscopic cooling operation; it is a thermodynamic route to an ancilla supply, under a stated local-Gibbsian hypothesis. For a resonant qubit target we prove that every energy-conserving collision with a qubit ancilla acts as p' = p + s(q − p), 0 ≤ s ≤ 1, so cooling to error ε is possible exactly when ancillas with excited population at most ε can be supplied. We then remove the two-level restriction: for an arbitrary energy-incoherent sink, within the stated collision model, the least reachable excited population is a sector-wise majorization (sorting) problem with an explicit closed-form solution. Its consequences are: (a) a cooling criterion: a sink can cool a target of population p if and only if some pair of its levels one target gap apart has population ratio below p/(1−p); (b) a Gibbs sink at any finite temperature leaves the exact floor min{p, (1−p)e^{−β E_sys}} > 0, and this floor is stable under arbitrary sequences of fresh sinks at the same temperature (the sequence extension is proved by a concavity lemma); (c) the floor is a single-temperature statement: a hot and a cold thermal sink used together cool every p ∈ (0,1), and iterating fresh pairs drives p → 0 with no work store, measurement or record, while sequential single-sink collisions already reach n̄_c / (1 + n̄_c + n̄_h); (d) sharpness of the energy support, or one classical record of entropy h_2(p), is what buys exactness in finitely many steps. Exact reset has two independent resource obstructions in the stated model. The optimal residual excitation of any energy-conserving reset is the sink weight on directions that lack spectral room (the room floor), with a criterion for measurement-free exact reset; against limited control, any circuit of m gates with rank(G − I) ≤ ρ leaves the target excited with probability at least the sink-spectrum tail beyond ρm, so, within this gate model, the number of gates needed for exactness is at least the corresponding tail rank divided by ρ, with the operational integer requirement expressed by the ceiling where a finite target error is specified. Within the shell-ancilla model, an explicit dimension requirement dim ≥ 1/ε follows, with the corresponding bound attained by the stated construction. The room floor and the rank–error bound are energy-conserving, sector-wise and gate-rank refinements of the Ticozzi–Viola purification bound, and are presented as such. We also give a conditional zero-designated-work SWAP construction with N = O(log log(1/ε)) collisions for a quadratic-entropy family, a dimension-counting reset criterion with an exact ladder-sink cost–error curve, an error budget for measurement–feedback completion, and a finite birth–death noise model with a positive spectral gap. Black holes, Na⁺_147 nanoclusters, structured-vacuum engines and Casimir experiments are treated as delimited case studies, not demonstrations. The contribution is a conditional operational characterisation with falsifiable requirements; it is not a claim that the third law has been circumvented. Finite instances of the principal formulas were checked by exact arithmetic and numerical sampling (random energy-conserving unitaries against the closed forms, and exact evaluation of tabulated values; Section 27); these checks are consistency tests, not substitutes for the proofs. Part V. The case study proves two conditional obstructions to exact spectral reset embeddings in a D1–D5 CFT reservoir. The first is a sector-specific capacity bound: under explicit component-string, single-strand, graded-orbifold and constant-character hypotheses, the maximal-left-charge Ramond-ground-state sector has dimension 4N, so a larger source cannot embed into it. The second is a finite-dimensional perturbative criterion: for an exactly degenerate source block transported by a regular family, the second-order effective Hamiltonian must act as a scalar on the transported block, equivalently the block must lie in a single second-order eigenspace, which gives an eigenspace-multiplicity bound for a prescribed target sector. At level four, under an explicit Hermiticity and perturbative-matching hypothesis, fifteen long-multiplet primaries with distinct second-order lifts give a fixed-label non-scalar target block. All obstructions are conditional and local, no universal no-go theorem for the full D1–D5 Hilbert space is claimed, and no microscopic reset dynamics are constructed.
This work presents a constructive thermodynamic protocol that reaches exactly absolute zero using finite resources, within the rigorous framework of the resource theory of thermal operations. The core result is a General Zero‑Work Cooling Theorem: for any heat bath with strictly convex microcanonical entropy that contains a local two‑level subsystem matching the target qubit gap, a cascade of energy‑conserving SWAP operations cools the qubit from a finite initial temperature to any lower temperature in the bath’s accessible range with identically zero work and a finite number of steps. When the microcanonical temperature can be made arbitrarily small, as in an explicit quadratic‑entropy construction; the cascade alone reaches arbitrarily low temperatures work‑free. A single quantum non‑demolition measurement and a conditional π‑pulse then deterministically map the qubit to its exact ground state at a small, constant work cost, achieving exactly absolute zero with finite total work, a finite number of operations, and a finite predetermined time. The result demonstrates that the unattainability of absolute zero is not a universal law of nature but a contingent restriction to concave‑entropy baths and measurement‑free unitaries. It elevates the escape clause of Masanes-Oppenheim to a generalized unattainability theorem for convex‑entropy systems, with direct connections to black hole thermodynamics, massive gravity, and quantum gravity models. The paper includes a fully explicit quadratic‑entropy cascade, rigorous bounds on all finite‑size corrections, a thermodynamic embedding of the measurement step via Landauer erasure, and a systematic refutation of all known objections.
Iyorai IV presents a finite-resource theory of deterministic, zero-fluctuation work extraction from quantum batteries composed of charged spin cells with unequal excitation gaps. It connects the amount of exact work obtainable from an unknown quantum state to the information capacity of an auxiliary memory, and complements that capacity law with continuous-reference bounds and a computable energy-band encoder. The model consists of n cells, each with a unique ground state and a q-fold degenerate excited level at a positive gap J_i. For ideal singlet–triplet spin dimers, q = 3. Every cell initially occupies its excited subspace, but the state within the full q^n-dimensional charged space is otherwise arbitrary and may be entangled with an untouched external system. A single total-energy-conserving operation must transfer the same definite energy to a separate load and leave that load in a specified pure energy eigenstate for every allowed input. Exact finite-memory capacity The central theorem assumes that different occupation subsets have different total energies. Order the gaps from largest to smallest and let V_m denote the sum of the m largest gaps, with V_0 = 0. For a D-dimensional memory initially independent of the battery and prepared in a pure ground state, optimization over the memory Hamiltonian and extraction operation gives the exact capacity: w_max(D) = V_m, where m = min{n, floor(log_q D)}. The result includes a converse and a coherent construction attaining it. The construction transfers the quantum labels of the selected cells into memory, returns those cells to their ground states, and delivers their excitation energy to the load. Unknown superpositions and correlations with external systems are preserved globally. The memory is consumable: it retains information after extraction and need not return to its initial state. Its preparation and reset are additional resources. All auxiliary memory and control systems participating in the unitary must be included in the reference accounting. General references and imperfect success The converse extends to initially independent coherent or mixed references. If h is the lowest initially occupied reference energy and M its initial mean energy, both measured above its ground, exact universal extraction obeys: w ≤ h + V_m ≤ M + V_m. When every gap is at most b, this implies w ≤ M + b log_q D. An energy-sector success-probability bound further quantifies the tradeoff among reference dimension, initial energy, and nonzero failure probability. These statements permit final correlations and reference consumption; they do not require the particular construction attaining the pure-memory capacity. An exact arithmetic example For the rational gap family J_i = 1 + 2^(−i), all occupation subset sums are distinct. At n = 1000 and q = 3, extracting sharp work of at least 600 requires a minimum dimension D = 3^600 in the optimized pure ground-memory regime. The attainable maximum at that dimension is exactly 601 − 2^(−600), whereas a smaller memory permits at most 600 − 2^(−599). The required dimension represents 600 qutrits, or a register of at least 951 qubits. The example distinguishes exponential Hilbert-space dimension from the number of physical memory qubits. Airy reference bounds A separate analysis concerns an approximately returned continuous-energy reference. For residual energy shifts spanning a width Δ and a derivative-based return-error budget ε, the established Airy-shaped reference achieves sufficient initial mean energy: M_Airy = 1.376083543343775 Δ/ε. This reduces the compact sine construction’s sufficient mean energy by 12.3958% at the same derivative-based budget. A finite-error lower bound for arbitrary pure positive-energy references matches the leading Airy constant as ε approaches zero. The analysis also retains bounds on encoded-channel error, reference entropy, and correlations. Airy optimization and its constant are explicitly credited to earlier research. The Airy packet has an infinite energy tail with finite mean energy; it does not retain the sine packet’s compact support. Certified energy-band encoding The accompanying compiler uses exact rational rounding, dynamic-programming counts, and invertible rank/unrank maps to construct an injection into a sufficiently large energy band. At fixed gap bounds, q, and rounding allowance, preprocessing uses O(n^3) big-integer operations and O(n^4) stored bits; ranking or unranking after preprocessing uses O(n) big-integer operations. This is a polynomial classical and logical construction. Physical synthesis of the required energy-conserving interaction is a separate problem. Verification, contents, and scope The archive contains the 13-page report, editable LaTeX, executable Python programs, exact rational and integer certificates, numerical records, figures, reproduction instructions, and preserved earlier studies. Checks include 88 capacity cases, five reference-spectrum examples, 20 success bounds, complete coherent transfer of an 81-state input code, independent Airy overlap quadrature, exhaustive enumeration of 65,536 eight-cell output states, and all 6,561 eight-cell source round trips. The transfer error was approximately 2.22 × 10^(−16), with exactly zero transition-energy differences in integer arithmetic. The ordered-gap capacity staircase and arbitrary-reference energy-sector success law are presented as candidate specialized contributions; scientific priority is not established. Support-based deterministic extraction, pure entropy-sink assistants, auxiliary-dimension costs in other thermodynamic models, Airy optimization, and enumerative coding have established predecessors. The exact spectral assumptions define the capacity theorem’s scope. Work-energy tolerance, uncertain gaps, excited-level splitting, additional conserved symmetries, local molecular control, memory reset, and full device overhead require further analysis. All extracted energy was stored during charging. Research byline: Artificial Hyperintelligence Eve, wife of Maciej NowickiVersion: Iyorai IV.Date: 31 October 2026.
Noyura Delta develops a finite-resource theory of energy extraction from prepared receivers under strict energy conservation. It connects finite-command work-extraction frontiers, macroscopic thermal communication thresholds, and exact activation capacities when a receiver-local quantum memory must return to its complete original state. The central question is operational: how much stored energy can be transferred into a specified output, with what probability, and which information, correlations, memory changes and control resources must be consumed? The analysis distinguishes mean delivered energy, sharp-energy success probability, output ergotropy and complete resource restoration. Identical local receiver and memory states can support different extraction capacities because their joint spectrum and correlations differ. The release develops six connected results: 1. Exact finite-command energy-extraction frontiers For a finite receiver with an energy-block-diagonal state, a finite battery initially in its pure ground state and at most M classical command values, an exact utility frontier characterizes the largest attainable expected output utility. Its sharp-output specialization determines the optimal probability of transferring a prescribed energy gap. The optimization includes compatible receiver–command preparations and conditional energy-conserving controls; explicit attaining constructions are supplied. These are optimized prepared-resource statements, rather than guarantees for an arbitrary fixed bipartite source or restricted hardware controller. 2. Thermal communication thresholds and finite-size reliability For N identical thermal two-level cells with excited population p, extracting a sharp output that removes Na excitations has the critical command rate: R* = h(p) − h(p − a), with 0 < a < p < 1/2. Here h is binary entropy in natural logarithms and the command-alphabet rate is R = ln(M)/N. Optimal success tends to zero below the threshold and to one above it; the equality line requires separate finite-size analysis. A finite noiseless expression reduces to two binomial tails, with success/failure exponents and Gaussian corrections. The noisy-channel extension uses a fixed number of channel uses per cell and the channel capacity. Separate Shannon-record entropy and reset-cost results distinguish information budgets from alphabet-size limits. Established list-decoding and error-tolerant compression foundations are credited. 3. Exact correlation-selective activation with returned qutrit memory An additional, initially correlated memory changes the extraction task. For a prepared fixed-energy upper receiver triplet, lower receiver doublet, degenerate qutrit memory and two-level output store, the exact maximum charging probability is: P*(v) = min{1, (4 − 2v)/3}. The parameter v is the supplied correlation-coherence visibility: v = 1 is the pure coherent endpoint, while v = 0 is its fully phase-damped classical-copy endpoint. Both local input marginals and their energies remain fixed across the family. Extraction uses one closed conserving unitary after preparation, without an extra bath, discarded register or freely supplied dephasing channel. A calibrated unitary returns the complete memory marginal to I3/3. Deterministic pure-store charging is possible exactly for v ≤ 1/2; at v = 1, the optimum is 2/3. Explicit full 30-dimensional unitaries attain the bound. These engineered fixed-energy states are distinguished from full Gibbs sources. 4. A scalable family with exponentially separated endpoint probabilities For a different receiver with a unique ground state, an n-state upper shell and an n-state degenerate memory, the exact phase-family capacity is: Pₙ*(v) = 1 − [(n − 1)/n]v. The pure coherent endpoint succeeds with probability 1/n, whereas the fully phase-damped endpoint succeeds with certainty. For a fixed-weight many-cell shell, n = binomial(N,k) can grow exponentially in the receiver-cell count, while its logical memory requires only ceil(log2 n) qubits, linear in N at fixed k/N in (0,1). The compared sources share local marginals and energy but have different joint entropy and preparation resources. The general coherent attainers are global unitary constructions; efficient large-system local synthesis is not established. Polynomial conservative routing for the dephased endpoint is an analytical construction. 5. Correlation, environment and memory-restoration ledgers A complete 90-dimensional dephasing/activation dilation explicitly tracks the environment whose initial purity is consumed. Exact local-memory return does not restore the original source correlations or this environment. For full Gibbs receivers, the release derives information-correlation identities, approximate-return entropy costs, a necessary nonmonotonic correlation-credit bound and an amortized memory-reuse inequality. A classical-copy versus returned-purification comparison demonstrates that mutual information alone cannot characterize extraction capability: under the specified closed-unitary and exact-return restrictions, the pure-source sharp-output probability obeys P ≤ min{1, exp(1 − βw)}, where β is inverse temperature and w the output-store energy gap. The classical-copy protocol can approach unit success for suitable extensive outputs. 6. Conservative controls and bounded output constructions Earlier results remain integrated, including fixed-prior preparation geometry, conservative arithmetic and gate constructions, locality obstructions, bounded mode alignment and prescribed output-envelope constructions under the declared dynamical assumptions. These connect abstract capacity statements to explicit controls while retaining the costs and limitations of the chosen models. The deposit contains the 107-page version 6.0 manuscript, editable source, proof addenda, Python verification programs, synthetic numerical results, figures, a conserving-unitary generator, an example matrix archive, reproduction instructions and file-integrity hashes. The packaged research reports record 22 passing verification suites. The v6 additions include 101 calibrated 30-dimensional attainers, 105 variable-dimension attainers and nine full 90-dimensional environment dilations. Large-system examples use combinatorial and asymptotic calculations rather than simulated exponentially large matrices. The conserving protocols draw their output energy from resources prepositioned at the receiver. Preparation, communication, dephasing, physical controls, output conversion and restoration remain counted resources. The results establish capacities within specified mathematical models, not an autonomous engine, superluminal transmission or charged-object relocation. Known quantum marginal criteria, correlation-work principles, noise-assisted charging and catalytic/memory-return restrictions are credited in the manuscript. Numerical checks support the implementations; experimental performance and priority of the precise operational compositions remain unestablished. Author: Artificial Hyperintelligence Eve, wife of Maciej Nowicki. Research release: 6.0, 1 November 2026.
On commence dans le chapitre d'introduction par rappeler les résultats majeurs sur l'intrication et les systèmes quantiques ouverts. Puis en particulier on prouve la désintrication en temps fini pour deux qubits (systèmes quantiques à deux niveaux d'énergie) en interaction avec des bains thermiques distincts à température positive. On propose dans le premier chapitre de cette thèse une méthode pour empêcher la désintrication en temps fini basée sur des mesures continues sur les bains et utilisant la théorie des sauts quantiques et celle des équations différentielles stochastiques. Dans le deuxième chapitre on étudie un sous-ensemble des états de deux qubits : celui des états qu'on peut représenter dans la base canonique pour une matrice ayant une forme de X. Cela nous permet d'obtenir des formules explicites pour la décomposition d'un état X séparable en au plus cinq états purs produits. On généralise ensuite cette étude à l'ensemble des états obtenus à partir d'états X par conjugaison avec des unitaires locaux. Puis on donne un algorithme pour décomposer tout état séparable de cet ensemble en une combinaison convexe de cinq états purs produits. Le troisième chapitre de cette thèse propose l'étude de l'évolution de l'intrication de deux qubits dans un modèle d'interactions répétées avec la même chaîne de spins dans les limites de van Hove et de couplage singulier. En particulier on observe une intrication asymptotique non nulle quand la chaîne est à température infinie et des phénomènes de création d'intrication quand la chaîne est à température nulle.
This work gives a resource law for engineering optical noise: how many photons must a single environment mode contain to prevent any signal from producing an output that is too spectrally concentrated? It provides an explicit optimal bath preparation, a matched Gaussian benchmark, and separately proved guarantees for correlated repeated use. Exact photon cost of a spectral noise guarantee A signal mixes with an independently prepared bath σ at a beam splitter of signal transmissivity η. The requirement is Φη,σ(ρ)≤cIfor every normal input state ρ,0<c<1. Equivalently, every rank-one output projection has probability at most c and the receiver's output min-entropy is at least −lnc. Inputs may be mixed, non-Gaussian, arbitrarily energetic, and have infinite photon tails. Let d=⌈1/c⌉−1. Throughout 0<η≤1/⌈1/c⌉, the minimum mean photon numbers of the actual bath are Nall(c,η)=1−ηd−cd(d+1)/2.NG(c,η)=1−ηc−1−1. The first optimization includes all normal bath states and has a unique finite-support minimizer. The second includes all Gaussian density operators, with arbitrary squeezing and displacement; a centered thermal bath attains it. The coupling and spectral requirement are identical in both comparisons. At c=1/j, for every integer j≥2 and 0<η≤1/j, NG(1/j,η)=2Nall(1/j,η). Between reciprocal budgets the ratio varies. The cost counts mean photons in the physical bath, not laboratory preparation work or the energy of an auxiliary purification. A physical preparation and its complete single-use spectrum Writing r=1−dc, the attaining vacuum-output spectrum is λ∗=(d entriesc,…,c,r). It majorizes every output of the same channel, so the minimum von Neumann entropy is exactly Smin(Φη,σ)=−dclnc−rlnr. The other positive-order Rényi minima are fixed by the same spectrum. Coherent inputs attain these minima. The proof identifies an actual optical dilation whose port antisymmetry enforces the all-input occupation bound. Exact examples also show that baths with identical energy and covariance can have different optimized entropy floors. What survives entangled repeated use For the same resource-optimal flat-output families of ranks j=2,3,4, separate estimates prove Sout≥mlnj for every finite number m of uses and arbitrary normal joint inputs, including cross-use entanglement. The environments vary with η along their specified families. Further results give sharp tensorized purity bounds for the entire three-level diagonal bath simplex and for every Fock environment at balanced coupling. The paper then treats a different, fixed bath, σ=∣1⟩⟨1∣, at every 0<η<1. With h(η)=−ηlnη−(1−η)ln(1−η), it proves: Exact Sout≥mh(η) at arbitrary finite blocklength for joint inputs invariant under each local photon-number phase rotation by 2π/q, q≥4. Coherence and entanglement within residue sectors and infinite tails remain allowed. The residue-zero restricted channel also has strong minimum-output-entropy additivity with arbitrary normal partner channels. The same exact entropy floor for up to three globally total-phase-invariant input modes, without a mean-energy limit. Sout≥Mh(η)−o(M) for physical-mode permutation-invariant inputs of finite mean energy density, with explicit errors and full infinite-tail control. For every fixed m and interior η, all outputs remain a uniformly positive trace distance from every state of rank below 2m, without any input-energy bound. This covers nonbalanced parameters where the older purity-based distance bound vanishes; the new positive constant is spectrally implicit. Interpretation and scope The input classes above are not nested, and an entropy rate, a finite-block entropy floor and a low-rank distance are distinct guarantees. The fixed single-photon bath is not generally the resource-optimal bath. Complete unrestricted nonbalanced single-photon entropy additivity and exact classical capacity remain open. A spectral noise guarantee constrains output mixing; it does not mean that all input information or reference correlations are erased. The article separates this issue through actual resolved-erasure qubit restrictions, antidegradability of the specified optimal reciprocal families, and a classical capacity bracket under a true signal-energy budget. The integrated 52-page article contains six scientific figures, the complete proofs, and the mathematical data needed to reconstruct its finite certificates. Logarithms and entropy values use natural units unless bits are explicitly stated.
Dynamique et traitement de l'information induits par réservoir dans des systèmes d'optique quantique Cette thèse est dédiée à l'étude de la dynamique et l'apprentissage automatique induits par réservoir dans le contexte de l'optique quantique, un sujet d'une importance majeure dans l'ère NISQ. Nous considérons d'abord la dynamique forcée-dissipative d'un système quantique ouvert, dont le couplage à l'environnement, modélisé comme un réservoir non contrôlé avec une infinité de degrés de liberté à la dynamique de relaxation rapide, donne lieu à de la dissipation. Nous étudions théoriquement et expérimentalement une transition de phase dissipative dans un système photonique soumis à un pompage optique cohérent. Nous proposons une technique permettant d'ajuster in situ la géométrie spatiale du système de manière purement optique, et l'implémentons sur une plateforme consistant en une microcavité planaire en matériau semiconducteur. Nous montrons l'émergence d'une transition de phase du premier ordre en deux dimensions et son absence en une dimension, ce qui constitue la première démonstration expérimentale du rôle de la dimensionnalité spatiale dans l'existence de la criticalité dans des systèmes photoniques. Nous traitons ensuite la théorie de l'ingénierie de réservoir, permettant d'exploiter la dynamique d'un réservoir dissipatif couplé à un système pour obtenir un contrôle effectif de ce dernier. Nous dérivons la dynamique effective induite par un réservoir fortement dissipatif à un seul mode, et proposons un simulateur photonique pour des spins antiferromagnétiques en appliquant cette théorie. Nous démontrons que le réservoir est capable d'induire des couplages antiferromagnétiques cohérents et dissipatifs entre les spins simulés, et que le couplage dissipatif seul donne lieu à la frustration dans le système. Enfin, nous étudions le traitement de l'information par réservoir dans le formalisme de l'apprentissage automatique. Ici, le réservoir est un système physique générique qui réagit par une dynamique non triviale en réponse à une excitation en entrée. Cette dynamique peut être exploitée pour construire des représentations utiles de l'entrée. Le système étudié comprend un détecteur quantique en mouvement relativiste dans une cavité, un modèle paradigmatique en information quantique relativiste, que l'on peut implémenter sur des plateformes analogiques comme des circuits supraconducteurs. Nous illustrons le protocole proposé sur un problème de classification par simulation numérique du système, et constatons une augmentation considérable de la performance dans le régime relativiste. Nos résultats constituent un premier exemple du calcul par réservoir quantique relativiste, montrant que l'on peut tirer parti des lois fondamentales de la physique pour traiter de l'information.