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Phys. 269, 223 (2007). 14. A. Kalev and I. Hen, No-broadcasting theorem and its classical counterpart, Phys. Rev. Lett. 100, 210502 (2008). 15. D. Kretschmann, D. Schlingermann, and R. F. Werner, The information-disturbance tradeoff and the continuity of Stinespring’s representation, IEEE Trans. Inform. Theory 54, 1708 (2008). 16. N. Li and S. Luo, Total versus quantum correlations in quantum states, Phys. Rev. A 76, 032327 (2007). 17. S. Lloyd, Capacity of the noisy quantum channel, Phys. Rev. A 55, 1613 (1997).

This decoherence is also the central phenomenon relating the quantum world to the classical realm. Given a mixed state ρ, which is mathematically represented by a non-negative operator with unit trace on a Hilbert space, and a quantum operation E, which is described by a trace-preserving completely positive linear mapping on quantum states,20 in order to quantify the decoherence caused by the quantum operation, one naturally asks how the output state E(ρ) is different from the input state ρ, and furthermore, how the relations with their respective outside environments are changed.

Optim. 10, 275–286 (1983) 16. I. Lasiecka and R. Triggiani, Differential and algebraic Riccati equations with applications to boundary/pioint control problems, Lecture Notes in Control and Inform. , vol. 165, Springer-Verlag, Berlin, Heidelberg, New York, 1991. 17. I. Lasiecka and R. Triggiani, Control Theory for Partial Differential Equations: Continuous and Approximation Theories. II. Abstract hyperboliclike systems over a finite time horizon, Encyclopedia of Mathematics and its Applications, 75.

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