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Results tagged with trace
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user 46073
Use this tag when having questions concerning expressions with the trace of a matrix/operator.
1
vote
1
answer
223
views
An identity for nested commutators
Let $A,B$ be Hermitian operators on an arbitrary Hilbert space. Define nested commutators of $B$ with respect to $A$ as $\text{Ad}_{A}(B) = \left[A,B\right]$, $\text{Ad}_{A}^{2}(B) = \left[A,\left[A,B …
- 799
7
votes
2
answers
10k
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Reasoning Check: Trace of squared mixed-state density matrix
It's often written in the QI literature that, for a density operator $\rho$, if $\text{Tr}\left[\rho^{2}\right] < 1$, then $\rho$ describes a mixed state. However, I haven't seen any proofs of this ex …
- 799