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I want to know if a partial trace keeps the cyclic property of the trace. … $$ When is this partial trace cyclic? …

But how is the partial trace found and defined in terms of the matrix representation of the linear operator. … Does the input and output basis have to be the same to define partial trace similar to definition of trace ? …

If I have two operators A and B living in the Composite Hilbert Space $H_I \bigotimes H_{II} $ and I want to take the partial trace of $C=AB$ over the subspace $H_I$, i.e., $Tr_I[AB]$, is there any identity … Actually what I am interested in is the partial trace of the commutator $[A,B]$. …

For $d<7$ in a reasonable time (few seconds) I able to perform the partial trace $\rho_{AD}$ using the code proposed in http://www3.imperial.ac.uk/people/m.tame/research. … Do you know an efficient algorithm for calculating the partial trace of qudit which uses the fact that the matrix is sparse? …

If we evaluate $$\rho_{mm'}(x,x')=\delta_{m\sigma}\delta_{m'\sigma}\delta(x-z)\delta(x'-z)$$ and the partial trace involves $(\delta(x-z))^2$ which is ill-defined. … How to avoid this issue of getting a delta function squared when taking a partial trace over continuous degrees of freedom? …

In Quantum Processes Systems, and Information by Schumacher and Westmoreland we are given this property of the partial trace $$ Tr_R G^{RQ} = Tr_R \left( |\alpha^R,\phi^Q \rangle\langle\beta^R,\psi^Q| … \right) =\\ =Tr_R \left(|\alpha^R \rangle \langle \beta^R|\otimes|\phi^Q\rangle\langle \psi^Q| \right)=\\ =\langle\beta^R|\alpha^R\rangle |\phi^Q\rangle\langle\psi^Q|. $$ Can the partial trace still be …

How does one actually take the partial trace on a quantum computer/real experiment? Wikipedia says that this is a valid quantum operation but I can't see how to implement it. … So if I have a single copy of a quantum bipartite state, what quantum circuit should I use that spits out the partial trace? …

I'm having trouble understanding the physical information one might extract from partial traces, by interpreting the partial trace of a qubit as if the qubit was averaged out of the system. … If I partial trace qubit $c$, I end up with a separable mixed state. …

I am doing some simulations that requires me to take partial trace over a three qubit density matrix $\rho_{ABC}$. …

Why should taking the partial trace give the correct description of the system? … Taking the partial trace turns a pure density matrix into a mixed density matrix, but a pure state is always a pure state. …

I saw the following definition for the partial trace operator: $\rho_A=\sum_k \langle e_k|\rho_{AB}|e_k\rangle$, where $e_k$ is basis for the state space of system $B$. … trace. …

To find the reduced density matrix, $\rho_A$, of a composite quantum system with two subsystems A and B, I've seen that the procedure is to take the partial trace of the full density matrix, $\rho_{AB} …

Partial measurement and partial trace There is a connection between a measurement of a part of a system and tracing this subsystem out. … Therefore, there must be a difference between covariance matrix after a partial measurement and partial trace. What am I missing? …

also how to find the partial trace of $\rho$? … I am bit lost to find the partial trace from the formuale $\sum_{i=1,2} (I\otimes\langle e_i|)\rho(I\times\langle e_i|)$ is $I$ a $2\times 2$ Identity matrix? Thanks for the help. …

In fact the partial trace turns out to be the unique functions having this property. … Can someone explain why the partial trace is an unique function? …