Manuscript Hawk05-C@1 · Hawk05-C.tex · example · ba0719f1

Example: One excitation does not give an extensive tent

Conserved-sector scrambling: a direct-sum Page calculation · lines 1504–1532

Hawk05-C@1#ex:onecharge

For $N$ qubits with total excitation number one and a cut after $k$ qubits, the sector has dimension $N$ . For $0 < k < N$ , its two blocks have dimensions

(r_{0}, b_{0}) = (1, N - k), (r_{1}, b_{1}) = (k, 1) .

The coherent reduction has rank at most two and entropy at most one bit. The exact mean is

E S (R_{k}) = \frac{H _{N} - \frac{N - k}{N} H _{N - k} - \frac{k}{N} H _{k}}{ln 2} .

The record mean is

E H (Y_{\leq k}) = \frac{H _{N} - \frac{N - k}{N} H _{N - k} - \frac{k}{N} H _{1}}{ln 2} .

The endpoint coherent entropy is zero, but the curve is not $min (k, N - k)$ bits.

Displayed formulas in this passage

unlabeled · line 1509
$(r_{0}, b_{0}) = (1, N - k), (r_{1}, b_{1}) = (k, 1) .$
unlabeled · line 1515
$E S (R_{k}) = \frac{H _{N} - \frac{N - k}{N} H _{N - k} - \frac{k}{N} H _{k}}{ln 2} .$
unlabeled · line 1523
$E H (Y_{\leq k}) = \frac{H _{N} - \frac{N - k}{N} H _{N - k} - \frac{k}{N} H _{1}}{ln 2} .$

Example: One excitation does not give an extensive tent

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