From Detector Pulses to Delayed Readout: A Preregisterable Benchmark for Periodic, Quasiperiodic, and Floquet-Controlled Optical-Memory Buffers under Collider-Like Disturbances
A downstream memory cannot freeze, replay, or increase the information content of a high-energy collision after detector transduction. We prove this claim using contractivity of trace distance under completely positive trace-preserving maps: once two collision states have become indistinguishable in the detector record, no later optical buffer can restore their distinguishability. The scientifically admissible question is therefore narrower: can an alreadytransduced, bandwidth-matched optical pulse be stored and retrieved more effectively in a periodic, quasiperiodic, or explicitly driven memory medium under controlled disturbances? We formulate a preregisterable bench-scale benchmark with matched optical depth, input spectrum, control power, and disturbance history. The memory is treated as an open quantum channel governed by Maxwell–Bloch or Lindblad dynamics; performance is assessed by retrieval efficiency, waveform or state fidelity, added noise, storage time, bandwidth, and time-bandwidth product. We distinguish quasiperiodic localization from topological protection and prove a Floquet no-go: for a single scalar cosine drive, the leading van Vleck commutator vanishes, so a first-order Floquet gap cannot be inferred. A nonzero first-order correction requires at least two noncommuting drive quadratures. A reproducible nine-site single-excitation design study compares periodic, quasiperiodic, and matched-random detuning patterns under equal loss and dephasing. For the predeclared normalized integrated return probability over 0 ≤ t ≤ 20J−1, the uniform baseline is 0.247. The best scanned median values are 0.379 for periodic modulation, 0.391 for quasiperiodic modulation, and 0.384 for a matched-random null. Their replicate intervals overlap strongly. The toy model therefore shows that static modulation can suppress coherent leakage in some regimes, but it does not establish quasiperiodic specificity, topological protection, an LHC advantage, or a quantum-memory implementation. The admissible near-term result is a blinded comparative bench test, not “frozen collision dynamics” and not an LHC detector upgrade. Frozen claim boundary. This manuscript does not claim that a quantum buffer stores the original collision state; that delayed readout increases detector time resolution; that an Aubry–André potential is automatically topological; that localization necessarily improves coherence; that a scalar Floquet drive opens a leading-order gap; that NV centres are qualified for an LHC radiation environment; or that the synthetic design study predicts laboratory performance. It establishes no-go results, a controlled open-system benchmark, and a matched-null simulation that defines what must be demonstrated before stronger claims are admissible.
A downstream memory cannot freeze, replay, or increase the information content of a high-energy collision after detector transduction. We prove this claim using contractivity of trace distance under completely positive trace-preserving maps: once two collision states have become indistinguishable in the detector record, no later optical buffer can restore their distinguishability. The scientifically admissible question is therefore narrower: can an alreadytransduced, bandwidth-matched optical pulse be stored and retrieved more effectively in a periodic, quasiperiodic, or explicitly driven memory medium under controlled disturbances? We formulate a preregisterable bench-scale benchmark with matched optical depth, input spectrum, control power, and disturbance history. The memory is treated as an open quantum channel governed by Maxwell–Bloch or Lindblad dynamics; performance is assessed by retrieval efficiency, waveform or state fidelity, added noise, storage time, bandwidth, and time-bandwidth product. We distinguish quasiperiodic localization from topological protection and prove a Floquet no-go: for a single scalar cosine drive, the leading van Vleck commutator vanishes, so a first-order Floquet gap cannot be inferred. A nonzero first-order correction requires at least two noncommuting drive quadratures. A reproducible nine-site single-excitation design study compares periodic, quasiperiodic, and matched-random detuning patterns under equal loss and dephasing. For the predeclared normalized integrated return probability over 0 ≤ t ≤ 20J−1, the uniform baseline is 0.247. The best scanned median values are 0.379 for periodic modulation, 0.391 for quasiperiodic modulation, and 0.384 for a matched-random null. Their replicate intervals overlap strongly. The toy model therefore shows that static modulation can suppress coherent leakage in some regimes, but it does not establish quasiperiodic specificity, topological protection, an LHC advantage, or a quantum-memory implementation. The admissible near-term result is a blinded comparative bench test, not “frozen collision dynamics” and not an LHC detector upgrade. Frozen claim boundary. This manuscript does not claim that a quantum buffer stores the original collision state; that delayed readout increases detector time resolution; that an Aubry–André potential is automatically topological; that localization necessarily improves coherence; that a scalar Floquet drive opens a leading-order gap; that NV centres are qualified for an LHC radiation environment; or that the synthetic design study predicts laboratory performance. It establishes no-go results, a controlled open-system benchmark, and a matched-null simulation that defines what must be demonstrated before stronger claims are admissible.
Six frozen interference predictions, independent calibration and a count-preserving memory test g∗=(1,c∗,2c∗2−1,c∗2,1,c∗2),c∗=cos8π. Can a retained reference recover interference that two fresh references cannot? This prospective protocol freezes the signed coherence for six histories: null, single, shared forward, fresh forward, shared echo and fresh echo. The forward and echo memory contrasts are respectively minus and plus sin2(π/8)=0.1464466094…. The paper derives the complete reference-partition map, specifies 24 history/phase settings, preserves every raw attempt including loss, and separates source coefficients from independent apparatus calibration. It fixes a disjoint training sample, 2.4 million validation attempts, simultaneous finite-sample rejection and equivalence criteria, and held-out scores against explicitly declared comparators. A second, independently timestamped laboratory capsule is required before validation data are acquired. What the test establishes. A qualified joint pass validates this QTT optical construction and its reference-memory pattern in the specified apparatus. The matched controlled-unitary quantum-mechanical model predicts the same pattern with the same calibration and no additional fitted parameters. Therefore this benchmark does not distinguish QTT from matched QM or independently establish an absolute clock. Any predictive advantage over a fitted memory-free reduction or history-specific harmonic fit is reported separately. Design-stage preregistration. The deposit includes the full paper, frozen machine-readable predictions, analysis code, independent algebra and mutation checks, synthetic operating checks, and exact reconstruction checksums. No new laboratory result is reported. The earlier 95.76% injected-template retention motivates count-preserving processing; it is neither a natural-signal detection nor an experimental correction factor. QTT source dependency: Balanced-Rail Optical Intertwining Theorem. The necessary mathematics is reproduced here. Related physical reference qualification: Physical-Terminal Reference Framework. The current PDF is the default preview; the ZIP contains the complete reconstruction package.
In this study, we examine whether periodic driving of a model with a quasiperiodic potential can generate interesting Floquet phases that have no counterparts in the static model. Specifically, we consider the Aubry-Andr\'e model, which is a one-dimensional time-independent model with an on-site quasiperiodic potential V0 and a nearest-neighbor hopping amplitude that is taken to have a staggered form. We add a uniform hopping amplitude that varies in time either sinusoidally or as a square pulse with a frequency $\ensuremath{\omega}$. Unlike the static Aubry-Andr\'e model, which has a simple phase diagram with only two phases (only extended or only localized states), we find that the driven model has four possible phases for the Floquet eigenstates: a phase with gapless quasienergy bands and only extended states, a phase with multiple mobility gaps separating different quasienergy bands, a mixed phase with coexisting extended, multifractal, and localized states, and a phase with only localized states. The multifractal states have generalized inverse participation ratios that scale with the system size with exponents that are different from the values for both extended and localized states. In addition, we observe intricate reentrant transitions between the different kinds of states when $\ensuremath{\omega}$ and V0 are varied. The appearance of such transitions is confirmed by the behavior of the Shannon entropy. Many of our numerical results can be understood from an analytic Floquet Hamiltonian derived using a Floquet perturbation theory that uses the inverse of the driving amplitude as the perturbation parameter. In the limit of high frequency and large driving amplitude, we find that the Floquet quasienergies match the energies of the undriven system, but the Floquet eigenstates are much more extended. We also study the spreading of a one-particle wave packet, and we find that it is always ballistic but the ballistic velocity varies significantly with the system parameters, sometimes showing a nonmonotonic dependence on V0 that does not occur in the static model. Finally, we compare the results for the driven model, which has a static staggered hopping amplitude, with a model that has a static uniform hopping amplitude, and we find some significant differences between the two cases. All of our results are found to be independent of the driving protocol, either sinusoidal or square pulse. We conclude that the interplay of the quasiperiodic potential and driving produces a rich phase diagram that does not appear in the static model.
When quantum information initially stored in a local qubit disappears, it need not be lost: it may have moved into nearby degrees of freedom or become inaccessible to shallow local control. We introduce finite-window recoverability as an operational channel benchmark that separates these possibilities. It compares optimal recovery from the target site, recovery by a bounded-depth decoder on a finite window, and the unrestricted optimum for that window. Its operational component, local variational recovery, uses local state preparation, window-local control, and target-qubit Pauli readout to certify recoverable memory beyond the target and quantify how much of the same-window advantage is accessible to shallow control. In a disordered kicked-Ising Floquet chain, a depth-6 decoder on a five-site window realizes Q0opt<Q2shallow<Q2opt across the crossover regime, with positive certified gain for most disorder realizations and substantial shallow-accessibility fractions. The signal differs from target-site persistence and reconstructed coherent-information increments. Positive radius-2 gain also persists when the task is embedded in longer open chains using an independent tensor-network backend. Guided by this hierarchy, we test a carrier-deletion task in which the original target register is reset after the dynamics. A depth-8 decoder repairs the input from a radius-3 surrounding halo with held-out median Favg=0.758, above the single-qubit classical benchmark 2/3, and outperforms optimal one-, two-, and three-site halo-subwindow counterfactuals. These results establish finite-window recovery as a local-control benchmark for off-site quantum memory, diagnosing both where local quantum information remains and whether bounded-depth control can refocus it.
We derive a causal law of observer-indexed entropy retrieval: retrieved reference information grows toward the supply available to a finite observer. A recorded admission-and-readout instrument produces orthogonal operational sectors from arbitrary coherent radiation; exact diary fidelity and decoupling give the flagged family, while branch errors bound its approximate realization. An exact quantum transfer channel yields the remaining-gap law and its continuous Lindblad evolution. The channel has an explicit unitary collision realization: admitted reference information moves from radiation to memory, while the capture record remains diary-blind. Its memory marginal is the Choi state of an erasure channel, giving an intrinsic positive-coherent-information boundary at retrieved fraction r = 1/2. A strip-holomorphic modular speed limit bounds how rapidly the channel can activate, with the hyperbolic tangent selected uniquely at extremality. The integrated retrieval dose is invariant under a change of clock, making the Kerr lapse cancellation one geometric instance of a general result. At fixed supply and kinetic rate under an affine clock, the transfer and activation laws compose into a closed proper-time retrieval trajectory on the equality branch, identify that trajectory as the sharp fastest-retrieval envelope, and fix the earliest admissible retrieval horizon. In the continuum formulation, Araki relative entropy defines retrieval on restricted observable algebras, and a split Type-I factor provides the regulated density-operator representation. The experimental program follows the same causal sequence through retrospective analysis and staged intervention. Tier 0A determines whether archived analog-horizon data retain the shot-level, timing, protocol, and processing information needed to ask the retrieval question. Tier 0B then tests whether qualifying data contain observer-, protocol-, readout-, or analysis-operator-indexed correlation structure that standard pooling or filtering suppresses. A positive Tier 0B result identifies retrieval-relevant structure and motivates Tier 1; it does not by itself confirm the complete law. The prospective Tier 1 BEC program targets the held-out g²(t₁,t₂) surface, bandwidth scaling, and protocol dependence. Independent activation readout tests the modular bound and tanh rigidity. Reference-tagged supply and memory test cumulative dose, composite-hazard recovery, degraded-channel ordering, and two-memory allocation. The v2 verification artifact provides synthetic benchmarks and numerical consistency checks at bond dimensions D = 4 and D = 8 for the transfer law, inverse recovery, finite-resolution robustness, and matched adversarial alternatives. Standard RT/HRT geometry and a separate accessibility functional place the retrieval dynamics within holographic language. The retrieval law closes the observer-local path between global encoding and retained access. Information conservation, radiation encoding, causal collection, finite-observer retrieval, formal reconstruction, and comprehension are distinct physical operations. The black-hole information problem contains a proper-time access dynamics that global entropy accounting alone does not determine. Physical complexity enters through encoding, supply, clock, activation, transfer, retention, and observation. Those layers locate each source of retrieval failure instead of idealizing it away. The theory orders the encoding, supply, and retrieval clocks; distinguishes late supply from early supply through their overlap with future transfer dose; and gives an exact finite-lifetime retrieval criterion. Here rᵢ(τ) is the normalized reference information retained by observer i, eᵢ(τ) is the causally available supply, kᵢ(τ) is the composite access hazard, and τ_char is the characteristic activation scale.
This thesis reports on the realization of Floquet topological systems with ultracold atoms in an optical honeycomb lattice. Using periodically driven quantum systems, topological phases of matter can be simulated by an effective, static Hamiltonian related to the time-evolution at integer multiples of the driving period, which is known as Floquet engineering. However, periodic driving can also give rise to genuinely time-dependent settings without static counterparts. One example is the anomalous Floquet phase in two dimensions, in which all bulk bands have a Chern number of zero but nevertheless robust chiral edge modes appear, which would be precluded by the bulk-edge correspondence in a static system. In an optical honeycomb lattice, anomalous Floquet systems can be created by continuous, periodic modulation of the laser intensities. This driving scheme results in different topological regimes, three of which are investigated, including the anomalous Floquet phase and a Haldane-like phase. Periodically driven systems feature periodic quasienergies and can be characterized in terms of winding numbers, which count the number of chiral edge modes in each quasienergy gap. By interferometric measurements of the quasienergy gaps between the first two Floquet bands, the topological phase transitions, emerging as gap closings, are located. For periodically driven systems, a modified bulk-edge correspondence can be formulated. In particular, the change of the winding number at a phase transition is related to the sign change of the local Berry curvature. The Berry curvature at the gap closing points is probed by Hall deflection measurements to obtain the winding numbers in each of the topological regimes, revealing the existence of chiral edge modes also in a setting with smooth boundaries as used in the experiments. The measured quasienergy gaps and transverse deflections are quantitatively well described by a numerical calculation of the Floquet bandstructure that includes coupling to higher bands during the driving period. To derive the spectrum of the modulated lattice in a geometry with edges, a tight-binding description of the system is discussed. Circular phase modulation of the honeycomb lattice can also give rise to an anomalous Floquet system when inversion symmetry is broken. The topological phase diagrams and the experimental feasibility are compared for both modulation schemes. Due to the vanishing Chern numbers, the bulk states in the anomalous Floquet regime can be fully localized by a disorder potential. This could prevent heating in interacting, periodically driven systems, resulting in a many-body localized bulk coexisting with thermalizing edge states. The experimental realization of disorder and strong interactions, as well as independent probes of the edge states are investigated. Bloch band geometry can be extended to multiband systems, using Wilson lines. The possible symmetry protection of their eigenvalues is discussed, along with measurements in the optical honeycomb lattice. Moreover, the onset of heating in weakly-interacting, periodically driven systems, triggered by parametric instabilities, is studied experimentally in a one-dimensional lattice.
Reliable quantum-state engineering in periodically driven devices requires more than reproducing their excitation spectrum: the environment must resolve the transitions of the driven system. We show that two dissipative descriptions of the same parametrically coupled qubits can yield closely similar period-averaged populations yet qualitatively different asymptotic entanglement. Both retain the complete periodically driven Hamiltonian, the same microscopic bath couplings, and the same physical observables; they differ in the dynamical representation used to resolve the dissipative channels and the corresponding system operators: the static dressed basis in the partial harmonic decomposition approach (PHDA) and the Floquet basis, including all relevant drive sidebands, in Floquet-Born-Markov (FBM) theory. The population maps preserve the same resonance skeleton and remain closely similar over broad low-to-moderate drive regions, while clearer differences emerge as the modulation becomes stronger. Phase-resolved single- and two-qubit coherence observables reveal a substantially stronger redistribution of amplitudes and phases. Concurrence amplifies this hidden state-level discrepancy: Floquet-resolved dissipation selects stronger and more extended Bell-like entangled regions and a larger overlap with a fixed Bell-like reference, while PHDA generally underestimates the entanglement and its thermal persistence. A channel-resolution test verifies the secular, completely positive FBM construction throughout the relevant parameter domain. Our results establish population agreement as an insufficient benchmark for open Floquet quantum-state engineering and identify coherence-sensitive observables as the decisive validation test.