Certified measurement and control of an entanglement-breaking index on programmable hardware

Abstract

The entanglement-breaking index of a quantum channel, the number of self-compositions after which the channel destroys all entanglement with any reference, has to our knowledge never been measured. We show that a certified thermal collision feedback loop makes this integer both measurable and controllable on current programmable hardware, every load-bearing quantity delivered as an interval-arithmetic certificate. On the measurement side: a target list for the integer staircase n_EB(p) with decision-point negativities certified at margins 0.025 to 0.109; an exact per-round depolarising model in which the selected staircase survives realistic noise as certified integers; an exact, tight compilation of the round unitary (seven CNOTs all-to-all, five native arbitrary-angle gates, ten on heavy-hex); and a 33-million-draw gated search bounding the thermal valley's contrast by a wall with an interior maximum, a certified 2.85x10^-3 near floor 89. On the control side: the model composes rounds of differing bath polarisation exactly, so the valley becomes a pulsed valve, switching at a certified minimal pulse of exactly eight rounds; the optimal pulsed signal, a certified 3.43x10^-3, beats the static protocol, so the best valley measurement is intrinsically pulsed; and a coherent tilt of the bath Bloch vector lifts the signal to a certified 8.6x10^-3, three times the static ceiling, at zero population cost. Valley signatures certifiably die near per-round noise strength 10^-4, fixing the error-extrapolation burden. The staircase is a near-term experiment; the pulsed valley a precisely priced one.