Questions tagged [trace]
For questions about trace, the sum of elements on the main diagonal of a square matrix, which can concern matrices, operators, or functions.
7
questions
1
vote
2answers
58 views
Does $\mathrm{Tr}(\rho\sigma) > 0$ prove that a state $\sigma$ is separable?
As an example I have the density matrix:
$\rho = \frac{1}{3}(| \phi^+ \rangle\langle\phi^+| + | 00 \rangle\langle 00|+| 11 \rangle\langle11| )$
And the two-qubit state is:
$\frac{1}{3}(| \phi^- \...
2
votes
3answers
139 views
Why does the trace of density operators need to be one?
Usually, the textbook starts with a few assumptions of what density operator $\rho$ has.
One of them is $Tr(\rho) = 1$.
Why is that?
5
votes
2answers
81 views
Understanding partial trace
I want to confirm my understanding of a partial trace.
Essentially, we have a system that $H_a \otimes H_b$. When we trace out system $b$, what we are doing is basically reducing the system down to as ...
2
votes
1answer
52 views
How is $\sum_i\langle i|M|i\rangle$ correlated to $\mathrm{tr}(M)$?
In the book Quantum computation and quantum information, it says to evaluate $tr(A|\psi\rangle\langle\psi|)$ using Gram-Schmidt procedure to extend $|\psi\rangle$ to an orthonormal basis $|i\rangle$ ...
0
votes
1answer
56 views
How does the term $|\psi\rangle\langle\psi|$ come from while calculating the expectation value? [duplicate]
Suppose there're two systems $A$ and $B$, if we're in a pure state $|\psi\rangle\in\mathbb{H}_a\otimes\mathbb{H}_b$, let $\hat A$ be an operator acts on $\mathbb{H}_a$, and $|\psi\rangle=\sum_{i,j}\...
1
vote
2answers
62 views
How do I trace out the second qubit to find the reduced density operator? [duplicate]
I'm doing an exercise to trace out the second qubit to find the reduced density operator for the first qubit:
$tr_2|11\rangle\langle00| = |1\rangle\langle0|\langle0|1\rangle$
I'm just wondering if I ...
1
vote
1answer
48 views
Prove that for a general tri-partite state $\rho_{ABE}$, $H(AB) = H(E)$
How do I prove that for a general tri-partite state $\rho_{ABE}$, the following holds:
$$
H(\rho_{AB}) = H(\rho_{E}), H(\rho_{AE}) = H(\rho_{B}),
$$
where, $H$ is the Von Neumann entropy. Would ...
