# Tag Info

### Is acting with a positive map on a state not part of a larger system allowed?

Any map which is not Completely Positive, Trace Preserving (CPTP), is not possible as an "allowed operation" (a more-or-less complete account of how some system transforms) in quantum mechanics, ...
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### For 2x2 and 2x3 systems, is the partial transpose the only positive but not CP operation?

The partial transpose is not the only positive but not completely positive operation that is possible on 2x2 and 2x3 systems. Trivially, any completely positive operation (such as a local unitary) ...
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### Why is $\rho$ NPT if and only if $\rho^{\otimes N}$ is NPT?

The short answer is that $(\rho^{\otimes N})^{T_B}=(\rho^{T_B})^{\otimes N}$. More explicitly, if $\rho=\sum_{ii'jj'}\rho_{ii',jj'}|i\rangle\!\langle i'|\otimes |j\rangle\!\langle j'|$, then we can ...
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### Does a partial transpose always have real eigenvalues?

Yes, the partial transpose takes Hermitian matrices to Hermitian matrices and consequently the eigenvalues of the partial transpose of a Hermitian matrix are all real. Proof For concreteness, suppose ...
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### Is there an easy way to calculate the eigenvalues of the partial transpose of a given matrix?

In this specific case, absolutely! Note that $$|\psi\rangle=|\phi_A\rangle|\phi_B\rangle,$$ such that $$\rho=|\phi_A\rangle\langle\phi_A|\otimes |\phi_B\rangle\langle\phi_B|.$$ Now, it is the case ...
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