Inequalities for complementarity in observed statistics

Distance-based approach to quantum coherence and nonclassicality

“…Furthermore, this also agrees with the general formalism of nonclassicality developed in Refs. [23,[48][49][50]. So, this well illustrates the results already commented in Sec.…”

Quantum conditional probabilities

“…In this spirit we may also naturally assume that the conditional probabilities take the form ν X (x|λ) = ν X (x|x ′ ) and ν Y (y|λ) = ν y (y|y ′ ), so that the statistics of X is derived exclusively in terms of the statistics of σ X , and equivalently, the statistics of Y is derived exclusively in terms of the statistics of σ Y . Moreover, we assume that the observed marginals p X (x) and p Y (y) in (20) contain complete statistical information about σ X and σ Y in the state ρ. To provide suitable expressions for the conditional probabilities, ν X (x|x ′ ) and ν y (y|y ′ ) we focus on the observed marginal statistics in (20) considering the case of eigenstates of σ X and σ Y , so we may conclude that…”

“…Moreover, we assume that the observed marginals p X (x) and p Y (y) in (20) contain complete statistical information about σ X and σ Y in the state ρ. To provide suitable expressions for the conditional probabilities, ν X (x|x ′ ) and ν y (y|y ′ ) we focus on the observed marginal statistics in (20) considering the case of eigenstates of σ X and σ Y , so we may conclude that…”

“…This is the idea of the formalism that we will follow in this work, that has been presented and extensively discussed in Refs. [14,15,16,17,18,19,20]. It is worth noting also that our work is not about the definition or construction of exact joint probabilities P (x, y), but about conditional probabilities once the noisy joint distribution p(x, y) has been obtained by practical means.…”

“…Usually this is in the form of observation processes that in classical physics would lead to a legitimate joint probability distribution, but that in quantum physics fail to provide it. This is the idea of the formalism that we will follow in this work, that has been presented and extensively discussed in references [14][15][16][17][18][19][20]. It is worth noting also that our work is not about the definition or construction of exact joint probabilities P(x, y), but about conditional probabilities once the noisy joint distribution p(x, y) has been obtained by practical means.…”