Discording Power of Quantum Evolutions

Fernando Galve¹, Francesco Plastina^2,3, Matteo G. A. Paris^4,5, and Roberta Zambrini¹

¹FISC (UIB-CSIC), Instituto de Física Interdisciplinar y Sistemas Complejos, UIB Campus, E-07122 Palma de Mallorca, Spain

²Dipartimento di Fisica, Università della Calabria, I-87036 Arcavacata di Rende (Cosenza), Italy

³INFN—Gruppo collegato di Cosenza

⁴Dipartimento di Fisica dell’Università degli Studi di Milano, I-20133 Milano, Italy 5CNISM, UdR Milano Statale, I-20133 Milano, Italy

We introduce [1] the discording power of a unitary transformation, which assesses its capability to produce quantum discord, and analyze in detail the generation of discord by relevant classes of two-qubit gates. Our measure is based on the Cartan decomposition of two-qubit unitaries and on evaluating the maximum discord achievable by a unitary upon acting on classical-classical states at fixed purity. We find that there exist gates which are perfect discorders for any value of purity μ, and that they belong to a class of operators that includes the √SWAP. Other gates, even those universal for quantum computation, do not possess the same property: the CNOT, for example, is a perfect discorder only for states with low or unit purity, but not for intermediate values. The discording power of a two-qubit unitary also provides a generalization of the corresponding measure defined for entanglement to any value of the purity.

[1] Phys. Rev. Lett. 110, 010501 (2013)