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What is reduced density matrix of On Subsystem 1?

It is known as the reduced density matrix of on subsystem 1. It is easy to check that this operator has all the properties of a density operator. Conversely, the Schrödinger–HJW theorem implies that all density operators can be written as for some state .

What are the properties of the density matrix?

A very useful property of the density matrix is that when taking the trace Tr Tr of its square ρ2 ρ 2, we obtain a scalar value γ γ that is good measure of the purity of the state the matrix represents. For normalized states, this value is always less than or equal to 1, with the equality occurring for the case of a pure state:

What is the reduced matrix of a matrix?

The reduced matrix is defined as the partial trace of the density matrix. Let A, B be finite dimensional Hilbert spaces, and let there be a T such that T ∈ L ( A ⊗ B) (i.e., T is a linear operator on A ⊗ B ), then the partial trace of T, represented as T r B [ T] in L ( A), is defined by:

Are reduced density matrices pure or mixed?

Reduced density matrices obtained from the density matrix ρAB representing a composite state of the subsystems A and B, are always pure or mixed depending upon whether ρAB is separable or entangled. Both ρA and ρB are always mixed even if ρAB is pure, provided A and B are entangled.

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