Harnessing Quantumness of States using Discrete Wigner Functions and Protecting it using Weak Measurement from Non-Markovian Quantum Noise

The negativity of the discrete Wigner functions (DWFs) is a measure of non-classicality and is often used to quantify the degree of quantum coherence in a system. Studying Wigner's negativity and its evolution under different noisy non-Markovian quantum channels provides insight into the stability and robustness of quantum states. The variation of DWF negativity of qubit, qutrit, and two-qubit systems under the action of (non)-Markovian random telegraph noise and amplitude damping noise is investigated. Different negative quantum states that can be used as a resource for quantum computation and quantum teleportation are constructed. Quantum computation and teleportation success is estimated for these states under (non)-Markovian evolutions. Weak measurement (WM) and quantum measurement reversal (QMR) protect against quantum states' collapse and are used to preserve and enhance quantum correlations and universal quantum teleportation protocol.

We study the quantum correlations, maximal fidelity, and fidelity deviation of the two-qubit negative quantum states developed using DWFs with (without) WM and QMR. We evolve the states via the above-mentioned non-Markovian channels to consider the effect of the noisy environment. To benchmark the performance of negative quantum states, we compare our results with the two-qubit maximally entangled Bell state. Interestingly, we observe that some negative quantum states perform better with WM and QMR than the Bell state for different cases under evolution via noisy quantum channels.