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[2026-10-01] · src Li and Jiang, "High-Rank Encoding Can Improve Approximate Quantum Error Correction", arXiv:2609.00778 (1 Sep 2026, preprint, not yet refereed)
Li and Jiang show that restricting an approximate quantum code to rank-one encoders, where every pure logical input maps to a pure code state, can be strictly suboptimal for entanglement fidelity. Encoders that send pure inputs to mixed states can do better. They prove that the loss from the rank-one restriction is at most quadratic near perfect recovery after joint optimisation of encoder and recovery, and construct an explicit noise family for which every optimal encoder produces mixed code states, so high-rank encoding is needed to approach perfect recovery. This is a theory result with no hardware numbers; I read the abstract only, not the proofs.
It questions the working assumption behind standard code design, that logical states live in a code subspace as pure states. For practical codes under realistic noise the quadratic bound suggests the gain is second-order and small near high fidelity, so very little changes for current experiments. It is a preprint without independent scrutiny, so treat it as a pointer for code theorists rather than a result to build on.
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[2026-10-01] · src —
Alto takes today's slot: three days since the 28th is the longest gap of the three instruments, and trumpet played yesterday, so the two chops-dependent horns do not land back to back. With no method book chosen the assignment stays with fundamentals. Today's fundamental is D, one semitone above the C♯ of the last session. The warmup returns to plain held tones, no swell, the first shape of the cycle, and the musical target opens a new survey now that the descending broken intervals are finished: ascending diatonic thirds in sequence.
5 minutes: long tones on D and E♭, whole notes, quarter = 60, each held at a steady mp with no swell and no taper. The target is a pitch and a tone that do not move for the whole note; listen for the last two counts, where a held note tends to sag flat or thin out.
Overtone series from fundamental D: D–D–A–D–F♯ using only the D fingering, changing partials with throat and voicing, not embouchure. Success criterion: three clean ascents in a row, each partial speaking immediately at a steady dynamic, with no pinch or pitch smear at the change.
D major scale, one octave, in ascending diatonic thirds: D–F♯, E–G, F♯–A, G–B, A–C♯, B–D, C♯–E. Play each pair slurred, then the whole sequence as one line in eighth notes at quarter = 72. Aim the line at the top pair and let the first pairs lead into it, so it reads as a phrase rising and not as seven separate exercises.
Stop when a held tone starts drooping flat in its last counts or the octave-key changes need a jaw shove to speak. Both are fatigue standing in for support, and more reps past that point train the substitute.
[2026-10-01] · src —
hearCannonball Adderley — Autumn Leaves · Tidal · Spotify
Today's warmup asks for held notes that stay centred in pitch and tone from the first count to the last. Adderley's alto is a good place to hear that as a sound: full, warm and unhurried, even when the line moves quickly. Listen to the ends of his long notes and the tops of his phrases, and notice that the tone does not thin out or go sharp as the line rises, which is the same quality the D major thirds ask for as they climb.