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∣ψ(g)⟩=e−igJ^/ℏ ∣ψ(0)⟩,g∈[0,2π)|\psi(g)\rangle = e^{-ig\hat J/\hbar}\,|\psi(0)\rangle, \qquad g \in [0,2\pi)

Why this formula appears here

Into this old hole go two systems. The first, A , is a two-dimensional qubit prepared in an arbitrary, unknown state and coupled to nothing the hole’s own symmetries track — a spectator, chosen so that its recovery is the cleanest possible test of the Hayden-Preskill mechanism on its own terms. The second, C , is a compass: a physical carrier prepared in a state |ψ(g)\psi(g)⟩\rangle that transforms under a one-parameter group of rotations generated by a Hermitian charge J^\hat J , the same charge the hole’s own angular momentum is built from, ∣ψ(g)⟩=e−igJ^/ℏ ∣ψ(0)⟩,g∈[0,2π)|\psi(g)\rangle = e^{-ig\hat J/\hbar}\,|\psi(0)\rangle, \qquad g \in [0,2\pi). g is an angle: dimensionless, periodic, and physically read as “which way the compass points” relative to the hole’s spin axis. J^\hat J…

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gg

Symbol g

an angle: dimensionless, periodic, and physically read as “which way the compass points” relative to the hole’s spin axis.

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e−igJ^/ℏe^{-ig\hat J/\hbar}

Symbol e^-ighat J/hbar

e−e^-ighat J/hbar is one of the signed contributions combined to compute the quantity on the left.

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Published contexts (1)

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∣ψ(g)⟩=e−igJ^/ℏ ∣ψ(0)⟩,g∈[0,2π).|\psi(g)\rangle = e^{-ig\hat J/\hbar}\,|\psi(0)\rangle, \qquad g \in [0,2\pi).

Equation 5 · Evolutionary Physics

The Bit Comes Back Before the Bearing

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

Into this old hole go two systems. The first, A , is a two-dimensional qubit prepared in an arbitrary, unknown state and coupled to nothing the hole’s own symmetries track — a spectator, chosen so that its recovery is the cleanest possible test of the Hayden-Preskill mechanism on its own terms. The second, C , is a compass: a physical carrier prepared in a state |ψ(g)\psi(g)⟩\rangle that transforms under a one-parameter group of rotations generated by a Hermitian charge J^\hat J , the same charge the hole’s own angular momentum is built from, ∣ψ(g)⟩=e−igJ^/ℏ ∣ψ(0)⟩,g∈[0,2π)|\psi(g)\rangle = e^{-ig\hat J/\hbar}\,|\psi(0)\rangle, \qquad g \in [0,2\pi). g is an angle: dimensionless, periodic, and physically read as “which way the compass points” relative to the hole’s spin axis. J^\hat J…

Meanings in this article

  • gg: an angle: dimensionless, periodic, and physically read as “which way the compass points” relative to the hole’s spin axis.
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