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Equation 56 · The Bit Comes Back Before the Bearing

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ρrad(g)\rho_{\mathrm{rad}}(g)

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ρrad\rho_{\mathrm{rad}}

Symbol rho_rad

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gg

Symbol g

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subscript

subscript

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What the covariance also does, though, is forbid the radiation from leaking coherence between different eigenspaces of J^\hat J to an observer who has not independently fixed a frame. Kitaev, Mayers, and Preskill made the resource cost explicit: a superselection rule restricting accessible operations to those commuting with a group can be simulated away entirely if the two parties already share a suitable reference system, and cannot be worked around at all if they do not [ 11 ] . Absent such a shared frame, whatever the radiation reveals about g has to be extracted from the asymmetry of ρrad(g)\rho_{\mathrm{rad}}(g) relative to the group — a quantity that scrambling, left to its own devices, does…
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What the covariance also does, though, is forbid the radiation from leaking coherence between different eigenspaces of J^\hat J to an observer who has not independently fixed a frame. Kitaev, Mayers, and Preskill made the resource cost explicit: a superselection rule restricting accessible operations to those commuting with a group can be simulated away entirely if the two parties already share a suitable reference system, and cannot be worked around at all if they do not [ 11 ] . Absent such a shared frame, whatever the radiation reveals about g has to be extracted from the asymmetry of ρrad(g)\rho_{\mathrm{rad}}(g) relative to the group — a quantity that scrambling, left to its own devices, does not have any particular reason to concentrate quickly. The qubit’s logical content survives scrambling because nothing about being “close to |0⟩\rangle versus |1⟩\rangle ” is protected by a conservation law. The compass’s heading survives scrambling constrained by exactly the law that makes it meaningful in the first place, and that is a slower kind of survival.

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