Version 8.1 develops a state–channel–task framework for quantum correlations, with anexplicit pedagogical and diagnostic layer.The framework contains three distinct structures.First, the set-inclusion hierarchy describes exact mathematical relations among classicalcorrelations, separable states, entangled states, steerable states and Bell-nonlocal states:Cclass ⊂ Csep, CBell ⊂ Csteer ⊂ Cent = S \ Csep. (1)Second, operational robustness is defined as a state–channel functional rather than as auniversal ordering of resources. For a resource measure M, noise channel Eθ and initial stateρ0, the survival function isPM(θ) = Pr[M(Eθ(ρ0)) > Mmin] . (2)Third, task utility is defined through an explicitly specified performance functional involvingsensitivity, precision, resource cost, robustness and experimental overhead.Version 8.1 additionally integrates a distance-to-boundary analysis, an explicit correc-tion note on the misstated inclusion Csteer ⊂ Cent, a verification protocol based on the chainSCHSH > 2 ⇒ Rsteer > 0 ⇒ N > 0, and illustrative reference tables with explicit disclaimers.The framework rejects the interpretation that a single universal hierarchy of robustness canbe inferred from set inclusion.No experimental result is claimed.
Version 8.1 develops a state–channel–task framework for quantum correlations, with anexplicit pedagogical and diagnostic layer.The framework contains three distinct structures.First, the set-inclusion hierarchy describes exact mathematical relations among classicalcorrelations, separable states, entangled states, steerable states and Bell-nonlocal states:Cclass ⊂ Csep, CBell ⊂ Csteer ⊂ Cent = S \ Csep. (1)Second, operational robustness is defined as a state–channel functional rather than as auniversal ordering of resources. For a resource measure M, noise channel Eθ and initial stateρ0, the survival function isPM(θ) = Pr[M(Eθ(ρ0)) > Mmin] . (2)Third, task utility is defined through an explicitly specified performance functional involvingsensitivity, precision, resource cost, robustness and experimental overhead.Version 8.1 additionally integrates a distance-to-boundary analysis, an explicit correc-tion note on the misstated inclusion Csteer ⊂ Cent, a verification protocol based on the chainSCHSH > 2 ⇒ Rsteer > 0 ⇒ N > 0, and illustrative reference tables with explicit disclaimers.The framework rejects the interpretation that a single universal hierarchy of robustness canbe inferred from set inclusion.No experimental result is claimed.
Version 6.1 develops the Quantum Correlations Stack into a complete multi-resource researcharchitecture.The framework integrates six principal resource families:1. quantum coherence;2. quantum discord;3. quantum steering;4. contextuality;5. entanglement;6. Bell nonlocality.Version 6.1 introduces and preserves a formal separation between:witness ̸= estimator ̸= certification ̸= selection ̸= application utility. (1)Each resource is represented by an estimated state, uncertainty, certification status, imple-mentation cost, latency, robustness, and application utility.A resource-state vector is defined asR = (RC , RD, RS, RV , RE, RB, uC , uD, uS, uV , uE, uB). (2)The selection problem is extended from scalar optimization to constrained multiobjectiveoptimization:R⋆ ∈ arg minR∈HcertF(R; A), (3) where Hcert contains only resources that pass preregistered certification criteria.The Pareto frontier is explicitly retained so that the architecture does not artificiallymanufacture a unique winner from an arbitrary weighting scheme.The framework additionally specifies:• resource certification;• witness-based evidence versus full resource estimation;• uncertainty propagation;• multiplicity control;• classical and quantum reference states;• resource-conversion accounting;• FMEA risk analysis;• Go/No-Go criteria;• configuration locking;• digital audit trails;• economic-cost separation;• independent reproduction;• computational reference implementation.No experimental result is claimed.
Version 6.1 develops an integrated research framework for a modular particle detector usingmultiple quantum correlation resources.The architecture does not posit one universal quantum resource. Instead, it defines a resourcestackH = {C, D, S, V, E}, (1)together with an adaptive controller operating on measured resource estimates, uncertaintyintervals, detector conditions, and environmental covariates.The V6.1 architecture introduces five major extensions: 1. leakage-resistant experimental data partitioning;2. explicit calibration and domain-shift correction;3. uncertainty-aware adaptive resource selection;4. multi-objective classification and energy inference;5. hierarchical reproducibility and falsification criteria.The detector is represented as a conditional measurement system:p(Y | P, Z, Q, Θ), (2)where P denotes particle state, Z environmental conditions, Q the quantum subsystem, andΘ the locked experimental configuration.The adaptive controller selects a resource or resource subset using a preregistered utilityfunction:r⋆ = arg minr∈HLr. (3)Unlike a simple point-estimate controller, V6.1 explicitly propagates uncertainty and allowsan abstention state when the available evidence does not justify a classification.The primary validation framework evaluates classification, energy reconstruction, backgroundrejection, calibration, calibration transfer, robustness, and independent replication.Version 6.1 additionally integrates an explicit sensor platform layer, an event-conditioningchannel, a multi-resource feature vector, and a readout-and-timing block.No experimental result is claimed.
Quantum metrology exploits physical resources whose parameter sensitivity can exceed that ofconventional measurement strategies under appropriate conditions. However, a resource that isoptimal under one noise, temperature, drift, preparation, or detection regime need not remainoptimal under another.Version 6.1 proposes an adaptive hierarchy metrology architecture in which a predefined set ofprotocol families is available: H = {C, D, S,E}.The central methodological correction of Version 6.1 is that coherence, discord, steering, andentanglement are not themselves identified with quantum Fisher information. Instead, each resourcecorresponds to a physically specified preparation–encoding–noise– measurement protocol. Theresulting parameterized density operator defines the quantum Fisher information (QFI), while theactual measurement defines the classical Fisher information (CFI).The adaptive system therefore estimates, for each candidate protocol,FQr(θ|z), FCr(θ|z), Ir(θ|z) = FCr(θ|z)τr,where r denotes the protocol family, z denotes the measured operating context, and τr is thetotal wall-clock cost per useful trial.The primary optimization target is the information rate, not raw QFI.Selection is uncertainty-aware. Rather than choosing the resource with the largest pointestimate, the system may use lower confidence bounds, switching penalties, feasibility constraints,and hysteresis:rt = arg maxr∈Ft[LCB1−α (Ir|zt) − Pswitch(r, rt−1)] .Version 6.1 additionally introduces an overhead-aware net advantage quantity:Anet =Iadaptmaxr Ifixed,r·11 + ηoverhead,where ηoverhead accounts for characterization, switching, computational, and dead-time coststhat may not be entirely captured by the per-shot cycle-time τr.The test remains locked against target-outcome leakage: the primary adaptive policy may usecalibration and context variables, but it must not use the target measurement outcomes of theheld-out test block to modify the selection rule.The system is evaluated against fixed-resource baselines under equalized wall-clock budgets andheld-out operating conditions. Primary analysis uses paired information-rate comparisons withhierarchical uncertainty estimation.The framework includes preregistered thresholds, falsification criteria, robustness analysis,selection regret, switching stability, shadow-mode validation, missing-data rules, reproducibilityrequirements, audit logs, synthetic reference implementations, and a staged experimental validationplan.
Quantum correlations are fragile under noise, motivating quantitative measures that track not only their presence but also their degradation during physical evolution. We develop a robustness framework for the hierarchy of Bell nonlocality, EPR steering, and entanglement, establishing an ordering of the corresponding robustness measures and relating robustness to noise-induced transition times. We further formulate the instantaneous robustness decay along Lindblad dynamics as a directional derivative determined by both the evolution and the robustness functional. Applications to isotropic depolarizing noise and amplitude damping illustrate, respectively, the resulting resource transition times and the directional dependence of steering robustness. The framework provides an approach to characterizing the degradation and lifetime of bipartite quantum correlations under noisy dynamics.
The diverse range of resources which underlie the utility of quantum states in practical tasks motivates the development of universally applicable methods to measure and compare resources of different types. However, many of such approaches were hitherto limited to the finite-dimensional setting or were not connected with operational tasks. We overcome this by introducing a general method of quantifying resources for continuous-variable quantum systems based on the robustness measure, applicable to a plethora of physically relevant resources such as optical nonclassicality, entanglement, genuine non-Gaussianity, and coherence. We demonstrate in particular that the measure has a direct operational interpretation as the advantage enabled by a given state in a class of channel discrimination tasks. We show that the robustness constitutes a well-behaved, bona fide resource quantifier in any convex resource theory, contrary to a related negativity-based measure known as the standard robustness. Furthermore, we show the robustness to be directly observable-it can be computed as the expectation value of a single witness operator-and establish general methods for evaluating the measure. Explicitly applying our results to the relevant resources, we demonstrate the exact computability of the robustness for several classes of states.
This record contains version 0.5 of the Epsilon–Theta (ET) Framework Meta-Specification: a framework-level specification for baseline-relative deviation analysis in finite bipartite Bell scenarios. The ET framework defines a residual-first language for comparing observed Bell data with an explicit baseline probability model. Its primary object is the full observable residual table, from which scalar radii, compressed static summaries, Bell-functional projections, no-signalling diagnostics, and temporal diagnostics may be derived under declared conventions. The framework separates two complementary layers of analysis. The epsilon layer describes static, baseline-relative deviations in conditional probability tables. The theta layer provides a generic contract for temporal, order-dependent, or higher-order diagnostics, such as memory, drift, block dependence, and settings-time confounding, under declared calibration protocols. This Meta-Spec defines the framework-level contract: scope, baseline modes, residual-first principle, conformance classes, reporting requirements, calibration discipline, extension rules, and the relationship between the general framework and named scenario packs. It does not define a universal compressed residual vector, universal Bell functional, or universal temporal statistic. Those objects are intentionally delegated to scenario-specific packs. The document is not a new physical theory, not a new Bell inequality, and not a replacement for Bell-valid significance analyses, loophole-specific experimental audits, device-independent security proofs, or quantum-set compatibility tools. Instead, ET is intended as a complementary reporting, diagnostic, and sensitivity framework for declared classes of baseline-relative observable departures. The canonical 2x2x2 binary-outcome scenario is specified separately in the ET-CS-222 scenario pack and its companion supplements. Future versions of the Meta-Spec may extend the framework-level contract to additional Bell-scenario families, such as multipartite, network, or adaptive settings.