Entanglement Entropy of a Random Pure State
Entanglement Entropy of a Random Pure State
Entanglement Entropy of a Random Pure State
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Reduced Density Matrix <strong>of</strong> subsystem A:<br />
A<br />
B<br />
N−dim.<br />
M−dim.<br />
| i A<br />
|α B<br />
Coupled Bipartite System<br />
N M<br />
• Reduced Density Matrix: ˆρ A = Tr B [ˆρ] = Tr B [|ψ〉〈ψ|] with Tr[ˆρ A ] = 1<br />
Measurement → 〈ÔA〉 = Tr[Ô ˆρ A]<br />
[<br />
M∑<br />
N∑ M<br />
]<br />
∑<br />
• ˆρ A = Tr B [ˆρ] = < α B |ˆρ|α B > = x i,α xj,α<br />
∗ |i A >< j A |<br />
α=1<br />
i,j=1<br />
α=1<br />
S.N. Majumdar<br />
Distribution <strong>of</strong> Bipartite <strong>Entanglement</strong> <strong>of</strong> a <strong>Random</strong> <strong>Pure</strong> <strong>State</strong>