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Eran Kopel

Publications and source records attributed to Eran Kopel.

5 recordsLinked to original sources
arXiv2026

Certified targets for measuring and controlling an entanglement-breaking index on programmable hardware

The entanglement-breaking index of a quantum channel is the number of self-compositions after which the channel destroys all entanglement with any reference system. For qubit channels it is decided by a partial transpose, and to our knowledge it has never been measured. We give a certified design for measuring and controlling it on programmable hardware, using one round of a collision model: a message qubit meets two fresh thermal ancillas. The ancilla states are diagonal, so the bath polarisation p is programmed exactly by classical sampling; the round is affine on the Bloch vector, so composite channels are computed exactly, and every quantity called certified is a two-sided enclosure or a proven integer in 256-bit ball arithmetic. We certify a target list for the integer staircase n_EB(p), with decision margins between 0.025 and 0.109 at twelve points, show that it survives per-round depolarising noise of strength 5e-3 as certified integers, and give exact and tight gate counts (seven CNOTs all-to-all, five native arbitrary-angle gates, ten CNOTs on heavy-hex). A gated search of 33 million circuits shows that the contrast of thermal valleys, circuits whose index dips below its infinite-temperature value on an interior window of p, has an interior maximum near index 90 at a certified 2.85e-3, below what standard tomography resolves. Exact composition over rounds of different polarisation then turns a valley into a switch: a centred pulse of exactly eight rounds restores entanglement, a 53-round pulse beats the static protocol by a certified margin, a certified depth-three valley is walked down its staircase by pulse duration, and a 1.2 per cent coherent tilt of the ancilla opens the switch and triples the static signal at fixed population. Valley signatures die at per-round noise near 1e-4. Certificates, code, search output and an independent re-derivation script are deposited.

quant-ph↗
arXiv2026

A sharp norm inequality for entanglement-breaking channels

For a channel $Φ$ on $M_d$ written in the generalised Bloch parameterisation $r \mapsto Ar+c$, we prove that entanglement breaking implies $\|A\|_*^2 + \frac{d(d-1)}{2}|c|^2 \le (d-1)^2$, where $\|\cdot\|_*$ denotes the nuclear norm. The bound is attained in every dimension by the completely dephasing channel, and at $d=2$ by an explicit family with $c\neq0$. The qubit case reads $\|A\|_*^2+|c|^2\le1$ and extends to full rank a rank-two condition of Ruskai. The proof sharpens Ruskai's bound $\|A\|_*\le1$ by retaining the POVM completeness relation $\sum_k f_k=0$, which her argument discards; this recentres $A$ from a second moment into a cross-covariance, and is the entire content of the improvement.

quant-ph↗
arXiv2026

The quantum lifetime of a future-referential feedback loop: certified index, architecture floor, and thermal bonus

A quantum feedback loop that returns information from a forward simulation to an earlier internal time induces a completely positive trace-preserving map on a message register; iterating that map eventually destroys its ability to carry entanglement. The entanglement-breaking index N = n_EB(Phi), the round at which this happens, is studied here along two axes: the interaction and the bath. On the interaction axis we prove that strict contraction onto a full-rank fixed point forces N finite in every dimension, via an explicit separable ball around the limiting Choi state; the qubit closed form overshoots the exact answer by the factor ln(2 sqrt 3) / ln 3 = 1.1309... on isotropic unital channels, and across 3997 sampled channels index and stability gap are one clock, N [1 - rho(A)] in [0.60, 1.50]. On the bath axis, replacing the zero-temperature ancilla by a thermal one at polarisation p = tanh(hbar omega / 2 k_B T) makes every channel quantity an exact quadratic polynomial in p, and the same one-sided certificates (no eigensolver) establish N = 3 at the reference circuit at every temperature, uniformly on a parameter box. The infinite-temperature index is an architecture floor with closed form and exact measure (46.427% of circuits break entanglement in one round however hot the bath). The floor is not a bound: certified circuits dip below it in interior temperature windows, unit-quantised in depth; over 4.1 million circuits their rate follows a Gaussian cutoff in epsilon = 1 - ||A||_2 with exponent 2.02 [1.90, 2.16], and 12 million more certified circuits show valleys surviving to epsilon = 0.125. Certified endpoints make comparisons exact: temperature moves the index by at most 21/14 = 3/2; the interaction moves it by 1213/3.

quant-ph↗
arXiv2026

How many labels can a biological oscillator carry? A quality-factor screen for proposed information carriers

How many distinguishable labels can a biological oscillator carry? Proposals invoking collective vibrational modes, endogenous electromagnetic fields, microtubule excitations and oscillatory phase codes are each debated on grounds particular to themselves, with no shared standard for comparison. We show that spectral distinguishability alone bounds the number of labels by the quality factor, M <= Q = 2 pi nu tau. This follows from the relation between linewidth and coherence time, so it is independent of substrate, of mechanism, and of any position on quantum effects in biology, and it can be evaluated from two published quantities. Applied to a recently proposed 30 GHz intracolumnar microwave field in cortex, it gives Q = 0.19: the linewidth exceeds the carrier five-fold. The obvious rescue, that a driven emitter can be spectrally narrower than its gain medium, requires a resonant cavity, and the model's own geometry forbids one. An independent bound on metabolic power is exceeded by five to nine orders of magnitude. Six further criteria follow from the same standpoint, including a two-sided persistence window requiring a label to be both readable and rewritable. Screening eleven carriers, only the low-frequency neural rhythms pass. High-frequency molecular carriers are eliminated by brevity, not by the fragility the debate has assumed.

q-bio.NC↗
arXiv2026

Certified coherent, informative, and non-entanglement-breaking fixed points of future-referential quantum feedback

We study quantum processes in which information extracted from a forward simulation is returned as input to an earlier internal time of the simulated dynamics: externally the protocol is an ordinary causally ordered circuit, but internally it is future-referential. Contracting a process tensor with a leakage instrument and a controller induces a completely positive trace-preserving map on a message register, and we classify its fixed points by five operational properties: stability, informativeness, feedability, coherence, and preservation of quantum correlations. Four results separate notions that informal discussions of "information from the future" often conflate. A two-parameter unitary-dilation family yields a closed-form, globally attractive, coherent fixed point (Proposition 1), yet is entanglement breaking whenever future records are perfectly distinguishable (Lemma 1). Releasing that orthogonality, a four-parameter partial-swap family admits a nonempty open non-entanglement-breaking region (Proposition 2), with an explicit Choi partial-transpose neighborhood of half-width $0.0163π$ (Proposition 3). Combining outward-rounded interval enclosures with perturbation bounds tracking the channel and its stationary-state drift, we certify an explicit parameter square of half-width $0.0013π$ on which the feedback channel is simultaneously strictly contractive (margin $\ge 0.237$), coherent ($\ge 0.416$), informative about the designated future variable ($\ge 0.172$ bits), and non-entanglement-breaking (NPT margin $\ge 0.188$) (Proposition 4). Direct evaluation shows all four properties persisting over a region an order of magnitude larger, so the certified square is a proof of principle rather than a phase boundary. All enclosures and margins are confirmed by a machine-verified ball-arithmetic certificate, and the complete code and certificate accompany the paper.

quant-ph↗