Task, antecedents and operational scope

Task, antecedents and operational scope

This paper develops phase-sensitive source–readout constructions within Shadow Theory’s pre-existing programme [9]. A source distinction may be invisible in separate mode intensities yet accessible to a phase-sensitive interaction. To turn that observation into a physical statement one must specify the source stock, interaction, committed records, null/loss outputs and admitted decoder. We study the common-sign phase distinction in two degenerate one-excitation modes. The preparation controller is unread by the reader, failed trials are not replaced by freshly sampled sources, and all complete instruments act with identity on an arbitrary inert reference. Unambiguous discrimination and optical filtering are established techniques. Uzdin–Gat’s norm-action bound supplies a close unitary-resource antecedent; Chefles–Barnett’s state-separation and symmetric-state discrimination results supply the underlying pure-state geometry. The added results here solve the specified independently lossy stable-flag control problem, a source-uncertainty minimax and a restricted common-conversion/imperfect-matching filter problem. These antecedents are credited explicitly [1–6, 10]. No worldwide priority claim is made. Ordinary quantum probabilities and the prescribed preparation/control laws remain premises.

Trial, outputs and notation. One trial here uses one original source preparation and retains its conclusive, null and loss branches. A conclusive-rate guarantee and conditional error therefore describe a decision problem with inconclusive outcomes. They are not a fixed-copy deadline task in which every record must receive a sign. In particular, the preparation visibility and transfer ceiling below have different physical meanings from the detector visibility and erasure efficiency of a repeated equatorial-reader model. Identifying them requires a derived common instrument, not equality of their symbols. A coherent direct-sum output, a classically recorded instrument and its pointer-only marginal are also different channels. We state which is used in each norm or resource claim; none of these choices gives the decoder access to an otherwise unread retained bath or reference.

The Hamiltonians, uncertainty sets and control theorems below specify the apparatus and access conditions for the stated tasks. Specifying and optimizing one reader does not establish a unique underlying source, and retaining a loss bath does not automatically grant permission to measure it. Reduced detector equivalence and complete retained-output comparison are separate claims, treated explicitly in the technical companion.

Organization. Section 2 treats bounded coherent conversion and the distinct bounded-hazard model. Section 3 develops preparation uncertainty and fixed upstream attenuation. The remaining sections separate a calibrated entrance filter from common conversion, then quantify departures from exact matching. The companion contains absorbing-reader banks, detector comparison, finite references and calibration/monitoring interfaces under their own stated contracts.