In quantum renormalization group studies, the process is starting with dividing of the hamiltonian into block and block-block part, and then the projection operator is found by using ground state functions of block hamiltonian. My question is about that how can we write reduced density matrix of the block by taking partial trace over some of the qubits (if there are more than two particles in a block). How can we choose the qubits remained after partial trace and is there any physical reason of this choice?
The answer to the first part of the question is that the procedure is the same in principle as in any decimation procedure; that the degrees of freedom are qubits instead of classical spins doesn't change anything.
The answer to the second part of the question is, once more, that the choice doesn't matter and can't matter. How it's done is just like in any other application of the decimation procedure.
People seem to think that qubits are exotic objects-the renormalization group transformations don't care what the degrees of freedom are.
Because the developments of the 1970s are relevant for dealing with the systems studied in the last 15 years, also. What changed is experimental control, not the theory.
A qubit is the same thing as a field, whose target space is the 2-sphere. So a field theory of such objects is nothing more or less than a nonlinear sigma model, with target space the 2-sphere. That many people don’t recognize this fact doesn’t mean it isn’t true, just that people, that work now in quantum computing, apparently, don’t learn field theory. They should.
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