To explore the properties of a two-qubit mixed state, we consider quantum teleportation. The fidelity of a teleported state depends on the resource state purity and entanglement, as characterized by concurrence. Concurrence and purity are functions of state parameters. However, it turns out that a state with larger purity and concurrence, may have comparatively smaller fidelity. By computing teleportation fidelity, concurrence and purity for two-qubit X-states, we show it explicitly. We further show that fidelity changes monotonically with respect to functions of parameters -other than concurrence and purity. A state with smaller concurrence and purity, but larger value of one of these functions has larger fidelity. These functions, thus characterize nonlocal classical and/or quantum properties of the state that are not captured by purity and concurrence alone. In particular, concurrence is not enough to characterize the entanglement properties of a two-qubit mixed state.
We exhibit the intriguing phenomena of "Less is More" using a set of multipartite entangled states. We consider the quantum communication protocols for the exact teleportation, superdense coding, and quantum key distribution. We find that sometimes less entanglement is more useful. To understand this phenomena we obtain a condition that a resource state must satisfy to communicate a n-qubit pure state which has m terms. We find that an appropriate partition of the resource state should have a von-Neumann entropy of log 2 m. Furthermore, it is shown that some states may be suitable for exact superdense coding, but not for exact teleportation.
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