Abstract
We present uncertainty relations based on Wigner–Yanase–Dyson skew information with quantum memory. Uncertainty inequalities both in product and summation forms are derived. It is shown that the lower bounds contain two terms: one characterizes the degree of compatibility of two measurements, and the other is the quantum correlation between the measured system and the quantum memory. Detailed examples are given for product, separable and entangled states.
Highlights
The uncertainty principle is an essential feature of quantum mechanics, characterizing the experimental measurement incompatibility of non-commuting quantum mechanical observables in the preparation of quantum states
Inspired by the works [32,35], in this paper, we study the uncertainty relations based on Wigner–Yanase–Dyson skew information in the presence of quantum memory, which generalize the results in [32] to the case of Wigner–Yanase–Dyson skew information, and the results in [35], which generalize to the case with the presence of quantum memory
It is shown that the lower bound contains two terms: one is the quantum correlation Dα (ρ AB ), and the other is ∑ Lα,ρ A, k which characterizes the degree of compatibility of the two measurements, just as for the meaning of log2 1c in the entropy uncertainty relation [15]
Summary
The uncertainty principle is an essential feature of quantum mechanics, characterizing the experimental measurement incompatibility of non-commuting quantum mechanical observables in the preparation of quantum states. In [32], an uncertainty relation based on Wigner–Yanase skew information I (ρ, H ) has been obtained with quantum memory, where I (ρ, H ) = 12 Tr [(i [ ρ, H ])2 ] = Tr (ρH 2 ) − Tr ( ρH ρH ) We present uncertainty inequalities both in product and summation forms, and show that the lower bounds contain two terms: one concerns the compatibility of two measurement observables, and the other concerns the quantum correlations between the measured system and the quantum memory.
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