Harnessing Quantumness of States using Discrete Wigner Functions under (non)‐Markovian Quantum Channels

Abstract

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. The study of Wigner negativity and its evolution under different quantum channels can provide insight into the stability and robustness of quantum states under their interaction with the environment, which is essential for developing practical quantum computing systems. The variation of DWF negativity of qubit, qutrit, and two‐qubit systems under the action of (non)‐Markovian random telegraph noise (RTN) and amplitude damping (AD) quantum channels is investigated. Different negative quantum states that can be used as a resource for quantum computation and quantum teleportation are constructed. The success of quantum computation and teleportation is estimated for these states under (non)‐Markovian evolutions.

Protecting quantum correlations of negative quantum states using weak measurement under non-Markovian noise

“…This section briefly reviews negative quantum states [67][68][69], and the non-Markovian noisy quantum channels. Additionally, a physical model for protecting quantum correlations and universal quantum teleportation protocols of two-qubit quantum states using weak measurement and quantum measurement reversal in the non-Markovian environment is also canvased.…”

“…The negative quantum states are obtained by considering the MUBs and striations to find the phase space point operators A α ʼs. The state corresponding to the normalized eigenvector of the minimum eigenvalue of A α is known as the first negative quantum state, i. e. , NS 1 state [67]. Analogously, the second and third negative quantum states are represented by NS 2 state and NS 3 state, corresponding to the normalized eigenvectors of second and third negative eigenvalues of A α , respectively, and so on.…”

“…In this paper, in order to find suitable two-qubit states, apart from the Bell states, for universal quantum teleportation, we study the impact of weak measurement (WM) and quantum measurement reversal (QMR) [54][55][56][57][58]61] on the quantum correlations [15][16][17][18][19][20][21][22][23][24] and UQT requirements [13,14,28,29] of the negative quantum states of two-qubit systems proposed in [67]. The influence of both non-Markovian non-unital (specified by non-Markovian amplitude damping (AD)) and unital (specified by non-Markovian random telegraph noise (RTN)) channels are taken into consideration.…”