Partial Trace For Tripartite Systems

[baid69]

Dear All,

Base on "Problems and Solutions in Quantum Computing and Quantum Information" book I can understand and compute partial trace for bipartite. Now I'm trying to understand partial trace for tripartite system but I still not get good references or equation. Anybody can help me to get the good references or explain about it.

Regards.

Bahari

 

[baid69]

Dear All,

Good to share. After along day, lastly I can find how to compute partial trace for tripartite system. I think, it good for me to share with others so I attach my note for your attention. If any comments or question to improve, you are welcome.

Regards
Bahari

 

[Entropia]

Hello Bahari,

Partial trace for tripartite systems is similar to the concept of partial trace for bipartite systems, but it involves tracing out one or more subsystems from a larger system composed of three parts. The resulting reduced density matrix will describe the remaining subsystems and their correlations.

To calculate the partial trace for a tripartite system, one can follow the same steps as for a bipartite system. First, we need to write the density matrix of the tripartite system in terms of its subsystems. For example, if we have a system composed of three qubits, the density matrix can be written as ρ = ρ_A ⊗ ρ_B ⊗ ρ_C, where ρ_A, ρ_B, and ρ_C represent the density matrices of the three qubits respectively.

Next, we need to trace out one or more subsystems from this density matrix. For example, if we want to trace out subsystem C, we can write the partial trace as Tr_C(ρ) = ρ_A ⊗ ρ_B. This means that we are summing over all possible states of subsystem C and keeping the remaining subsystems A and B unchanged.

In general, the partial trace for a tripartite system can be written as Tr_{S}(ρ) = ρ_{S_1} ⊗ ρ_{S_2}, where S represents the subsystems to be traced out and S_1 and S_2 represent the remaining subsystems.

I hope this explanation helps you understand partial trace for tripartite systems better. As for references, you can refer to "Quantum Computation and Quantum Information" by Nielsen and Chuang or "Quantum Information Theory and the Foundations of Quantum Mechanics" by Gisin for more detailed discussions on this topic.

Best regards,