Abstract
We present an analytical solution for classical correlation, defined in terms of linear entropy, in an arbitrary system when the second subsystem is measured. We show that the optimal measurements used in the maximization of the classical correlation in terms of linear entropy, when used to calculate the quantum discord in terms of von Neumann entropy, result in a tight upper bound for arbitrary systems. This bound agrees with all known analytical results about quantum discord in terms of von Neumann entropy and, when comparing it with the numerical results for 106 two-qubit random density matrices, we obtain an average deviation of order 10−4. Furthermore, our results give a way to calculate the quantum discord for arbitrary n-qubit GHZ and W states evolving under the action of the amplitude damping noisy channel.
Highlights
Eq (7) gives the analytical formula for the classical correlation in terms of linear entropy for a general d ⊗ 2 quantum state
We have seen that the upper bound of quantum discord based on von Neumann entropy, obtained from the optimal measurements for the classical correlation based on linear entropy, is often exact
The analytical formula for classical correlation based on linear entropy has been explicitly derived, from which an analytical tight upper bound of quantum discord based on von Neumann entropy is obtained for arbitrary qudit-qubit states
Summary
Eq (7) gives the analytical formula for the classical correlation in terms of linear entropy for a general d ⊗ 2 quantum state. We show that for the case of a bipartite qudit-qubit state, the classical correlation based on linear entropy is maximized over projective measurements (see proof in the appendix). The quantum discord based on von Neumann entropy has an upper bound: Q (ρ AB)
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