The most general duality gates were introduced by Long, Liu and Wang and named allowable generalized quantum gates (AGQGs, for short). By definition, an allowable generalized quantum gate has the form ofs are unitary operators on a Hilbert space H and the coefficients c k 's are complex numbers with | d−1 k=0 c k | 1 and |c k | 1 for all k = 0, 1, . . . , d − 1. In this paper, we prove that an AGQG U = d−1 k=0 c k U k is realizable, i.e. there are two d by d unitary matrices W and V such that c k = W 0k V k0 (0 k d − 1) if and only if d−1 k=0 |c k | 1, in that case, the matrices W and V are constructed. realizability, allowable generalized quantum gate, Hilbert space, unitary operator, unitary matrix PACS: 03.67.Lx, 03.67.Ac
In this paper, we introduce and discuss the robustness of contextuality (RoC) R C (e) and the contextuality cost C(e) of an empirical model e. The following properties of them are proved. (i) An empirical model e is contextual if and only if R C (e) > 0; (ii) the RoC function R C is convex, lower semi-continuous and un-increasing under an affine mapping on the set EM of all empirical models; (iii) e is non-contextual if and only if C(e) = 0; (iv) e is contextual if and only if C(e) > 0; (v) e is strongly contextual if and only if C(e) = 1. Also, a relationship between R C (e) and C(e) is obtained. Lastly, the RoC of three empirical models is computed and compared. Especially, the RoC of the PR boxes is obtained and the supremum 0.5 is found for the RoC of all no-signaling type (2, 2, 2) empirical models. relative robustness, robustness of contextuality, contextuality cost, empirical model PACS number(s): 03.67.Mn, 03.65.Ta, 03.65.Ud, 03.65.Db Citation: H. X. Meng, H. X. Cao, and W. H. Wang, The robustness of contextuality and the contextuality cost of empirical models, Sci. China-Phys. Mech.
The aim of this paper is to discuss local quantum channels that preserve classical correlations. First, we give two equivalent characterizations of classical correlated states. Then we obtain the relationships among classical correlation-preserving local quantum channels, commutativity-preserving local quantum channels and commutativity-preserving quantum channels on each subsystem. Furthermore, for a two-qubit system, we show the general form of classical correlation-preserving local quantum channels.
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