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Timeverse x Quantum Measurement

Phase-Addressed Scheduling of Measurement Interactions (A Control-Plane Framework Compatible with Standard POVMs)

Status: Theoretical Framework (v1)
DOI: 10.5281/zenodo.18637000

Abstract

As quantum processors and quantum networks scale, measurement operations become increasingly sensitive to non-stationary drift, phase noise, and fragile long-horizon time synchronization. We propose phase-addressed measurement scheduling: a control-plane framework in which measurement interactions are triggered inside cycle-anchored phase windows of a shared reference phase φ(t) ∈ [0,1) ≅ S1, rather than targeted by absolute timestamps or fixed qubit-index order.

The proposal does not modify quantum mechanics, the Born rule, or POVM-based measurement theory. It constrains when standard measurement instruments are applied, using wrap-safe phase windows and an explicit cycle index to avoid periodic ambiguity (``same phase / wrong cycle''). We formalize phase-window execution in standard notation, provide analytic toy models clarifying when phase-addressing can reduce the impact of quasi-periodic and correlated measurement drift, and propose experimentally testable protocols on superconducting and photonic platforms. The framework connects naturally to phase-coordination stacks (Q-Address, TAQA, HS-Bloch) using tick-canonical semantics for unambiguous verification and audit contexts.

Scope, Claims, and Positioning

  • In scope: deterministic representation of a cyclic reference phase; cycle anchoring; wrap-safe phase windows; phase-addressed triggering of standard measurement interactions; conditions of benefit; test protocols.
  • Out of scope: modifications to quantum dynamics, collapse postulates, POVM formalism, or the Born rule.
  • Claim level: this is a theoretical and architectural proposal with analytic toy models and experimentally testable predictions. No performance numbers are claimed here without hardware validation.

Security scope: Phase-addressed scheduling is not security by itself. Authenticity, integrity, canonical encoding, and anti-replay require an external security profile. Timeverse/Q-Address/TSAE fields are treated as public context, not secrets.

Motivation

In distributed settings (quantum networks, multi-controller labs), long-horizon absolute timestamp synchronization can be fragile without continuous coupling or frequent recalibration. This motivates scheduling mechanisms that are robust to long-horizon offset growth and that remain verifiable under bounded short-horizon estimation error.

Phase-Addressed Scheduling (informal): Replace absolute-time targeting of measurement interactions with cycle-anchored phase-window triggering on a shared cyclic reference phase φ(t)∈S1.

Reference Phase, Cycle Anchoring, and Phase Windows

Phase Window:

For a target phase center φ0∈[0,1) and half-width tolerance Δ∈(0,1/2), a (wrap-safe) phase-acceptance window is W(φ0,Δ) = {t: distS1(φ(t),φ0) ≤ Δ}.

Cycle Anchoring:

A phase-window instruction is cycle-anchored by specifying an intended cycle index n⋆, requiring execution only when n(t)=n⋆ and t∈W(φ0,Δ).

Cycle anchoring prevents ambiguity in periodic schedules. In implementation-oriented stacks, φ membership is verified using a fixed-point ticks per cycle encoding to avoid floating-point boundary ambiguity.

Measurement Model (No Change to Quantum Mechanics)

Let ρ(t) denote the quantum state at time t. Measurement at time t is represented by a quantum instrument or POVM {E(t)m}m. Outcome probabilities remain standard: p(m|t)=Tr[E(t)mρ(t)].

Interpretation: The proposal is a timing and scheduling constraint on when measurement interactions occur. It is compatible with standard quantum measurement theory.

Phase-Addressed Scheduling Rule (Control-Plane View)

A generic phase-addressed measurement instruction is: `MEASURE(n⋆,φ0,Δ; micro-slot)`, where `(n⋆,φ0,Δ)` define the macro timing constraint and the `micro-slot` defines local ordering or offsets inside the accepted window. This aligns with Q-Address and TAQA.

Toy Models: When Phase Windows Help

  • Quasi-periodic measurement drift: If drift is correlated with the reference phase, phase-gating makes the drift a constant offset, enabling easier calibration.
  • Trade-off: Smaller windows increase phase conditioning but reduce throughput.
  • White noise: If noise is uncorrelated with phase, this method offers no guaranteed improvement.

Experimental Protocols (Proposed)

  • Superconducting processors: Test whether readout error shows reproducible dependence on φ(t).
  • Photonic links: Validate that cycle-anchored windows enable robust coordination for entanglement distribution.

Conclusion

We proposed phase-addressed measurement scheduling: a cycle-anchored, wrap-safe phase-window method for triggering standard measurement interactions. The approach does not modify the POVM formalism or the Born rule; it introduces a control-plane reference phase φ(t)∈S1 and explicit cycle anchoring. The method composes naturally with tick-canonical verification and quality and freshness gates in phase-coordination stacks (Q-Address, TAQA, HS-Bloch).

References