Equilibrium density operator, coherent states

Coherent States as Minimizing the Heisenberg Uncertainty Relation Statistical Equilibrium Density Operator of a Coherent State... 

N.4 STATISTICAL EQUILIBRIUM DENSITY OPERATOR OF A COHERENT STATE... 

As a consequence, one may inversely consider the equilibrium density operator pa as that of a coherent state at any temperature. 

A simple, non-selective pulse starts the experiment. This rotates the equilibrium z magnetization onto the v axis. Note that neither the equilibrium state nor the effect of the pulse depend on the dynamics or the details of the spin Hamiltonian (chemical shifts and coupling constants). The equilibrium density matrix is proportional to F. After the pulse the density matrix is therefore given by and it will evolve as in equation (B2.4.27). If (B2.4.28) is substituted into (B2.4.30), the NMR signal as a fimction of time t, is given by (B2.4.32). In this equation there is a distinction between the sum of the operators weighted by the equilibrium populations, F, from the unweighted sum, 7. The detector sees each spin (but not each coherence ) equally well. 

Experimental demonstration of fully coherent quantum feedback - This paper of 1999 by Nelson and co-workers describes a quantum circuit which implements a coherent quantum feedback by NMR [15]. The idea is to transmit a quantum state with its correlations from a quantum register to a target. A classical feedback can be used to control quantum states, but it involves a measurement step, which destroys quantum correlations. On the contrary, quantum feedback control is able to transmit full quantum states with correlations altogether. The experiment involves three spins (qubits) A, B, and C. The proposal is to use the quantum feedback control circuit to transmit the quantum correlations, initially between B and C, to A and C. Starting from the equilibrium state, a sequence of pulses applied over qubits B and C creates a density matrix proportional to the spin operators -1 + 21 if - Such a density matrix describes a thermal... 

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