Bell’s inequality is investigated in parity-time ($\mathcal{PT}$) symmetric quantum mechanics, using a recently developed form of the inequality by Maccone, with two $\mathcal{PT}$-qubits in the unbroken phase with real energy spectrum. It is shown that the inequality produces a bound that is consistent with the standard quantum mechanics even after using Hilbert space equipped with $\mathcal{CPT}$ inner product and therefore, the entanglement has identical structure with standard quantum mechanics. Consequently, the no-signaling principle for a two-qubit system in $\mathcal{PT}$-symmetric quantum theory is preserved.

In this work, we investigate the dynamics of quantum correlations captured by entropic and geometric measures of discord under the influence of dissipative channels for widely used two qubit X state with maximally mixed marginals. Identifying the phenomena of the preservation, sudden change and revival of quantum correlation quantifiers, we determine their hierarchy of robustness under memory-less decoherence channels. We find the analytical expressions of decoherence probabilities at which sudden change occur when the first qubit is subjected to the decoherence channels for multiple times. We deduce the exact analytical expression for the preservation time, the duration for which quantum correlations remain unaffected by noise. We also find the time duration between the two sudden change phenomena of trace distance discord, and show its inverse proportionality to the number of times a channel operates on the state. The constraint relations of decoherence probabilities corresponding to the sudden change region and preservation phenomena are obtained when both the qubits are subjected to locally independent quantum channels for multiple times. Our investigation provides physical insights and possible practical implementation of the discord measures in noisy environments.