Alladi Ramakrishnan Hall

Fidelity Fluctuations in Quantum Teleportation

Arkaprabha Ghosal

Bose Institute, Kolkata

Quantum systems can be utilized as potential resources for
information processing tasks, where one obtains a measurable quantum advantage over classical strategies. Quantum Teleportation (QT) is a task that requires shared entanglement between a sender and a receiver who are allowed to perform only Local Operations and Classical Communications (LOCC). Perfect QT requires a maximally entangled state. On the other hand, QT becomes imperfect whenever the shared entangled state is noisy. Thus it becomes necessary to appropriately characterize the noisy state as a resource for QT. The standard figure of merit for QT is the average teleportation fidelity. The maximal fidelity is defined as the maximal value of the average fidelity achievable within the standard protocol and
local unitary strategies, and any protocol that achieves the aximal value is said to be optimal. A two-qubit state is said to be useful for QT if and only if the maximal value of the average fidelity is greater than 2/3, which is the classical bound. Recently it was pointed out that average fidelity is not sufficient to fully characterize a noisy resource since all input states may not be teleported with the same fidelity. Hence, for imperfect QT, fidelity values are distributed about the average value. The fidelity deviation measures fluctuations in fidelity values by computing the standard deviation. Here, we evaluate the exact expression for the fidelity deviation in the fidelity maximizing protocol with an arbitrary shared two-qubit state. Furthermore, we obtain the necessary and sufficient conditions for any given two-qubit state to be useful and universal for QT. By useful and universal we mean all input states are teleported equally well with maximal fidelity greater than 2/3. We then appropriately characterize optimal two-qubit states for QT in terms of maximal fidelity and fidelity deviation for a given state property, namely, purity, Bell nonlocality, and entanglement. The optimal two-qubit states by their definition possess the largest maximal fidelity and zero fidelity deviation for a given value of the property under consideration.