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Separable quantum state

{title2=$\rho^{T_B}$}
{wiki}

In a fixed product basis, the partial transpose on subsystem $B$ sends
$$
|i\rangle\langle j|\otimes|k\rangle\langle\ell|
\longmapsto
|i\rangle\langle j|\otimes|\ell\rangle\langle k|.
$$
It preserves Hermiticity and trace but need not preserve positivity on entangled inputs.


Partial transpose

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 323 / 2 / ii / Solution

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 323 / 2 / v / Solution

Swap operator

Partial transpose ( $ρ^{T_{B}}$ )

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Partial transpose (ρTB​)

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Partial transpose ( $ρ^{T_{B}}$ )

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