Scales of time where the quantum discord allows an efficient execution of the DQC1 algorithm (Q2248357)

Summary: The power of one qubit deterministic quantum processor (DQC1) [\textit{E. Knill} and \textit{R. Laflamme}, ``Power of one bit of quantum information'', Phys. Rev. Lett.. 81, No. 25, 5672--5675 (1998; \url{doi:10.1103/PhysRevLett.81.5672 })] generates a nonclassical correlation known as quantum discord. The DQC1 algorithm executes in an efficient way with a characteristic time given by \(\tau=\mathrm{Tr}[u_n]/2^n\), where \(u_n\) is an \(n\) qubit unitary gate. For pure states, quantum discord means entanglement while for mixed states such a quantity is more than entanglement. Quantum discord can be thought of as the mutual information between two systems. Within the quantum discord approach the role of time in an efficient evaluation of \(\tau\) is discussed. It is found that the smaller the value of \(t/T\) is, where \(t\) is the time of execution of the DQC1 algorithm and \(T\) is the scale of time where the nonclassical correlations prevail, the more efficient the calculation of \(\tau\) is. A Mösbauer nucleus might be a good processor of the DQC1 algorithm while a nuclear spin chain would not be efficient for the calculation of \(\tau\).