The geometric quantum discord of a two-qudit state has been studied in many papers; however, its exact analytical value in the explicit form is known only for a general two-qubit state, a general qubit-qudit state, and some special families of two-qudit states. Based on the general Bloch vectors formalism [E. R. Loubenets et al., J. Phys. A: Math. Theor. 54, 195301 (2021)], we find the explicit exact analytical value of the geometric quantum discord for an arbitrary two-qudit state of any dimension via the parameters of its correlation matrix and the Bloch vectors of its reduced states. This general analytical result includes all the known exact results on the geometric quantum discord only as particular cases and proves rigorously that the lower bound on the geometric discord presented in [S. Rana et al., Phys. Rev. A 85, 024102 (2012)] constitutes its exact value for each two-qudit state. Moreover, our general result allows us to find for an arbitrary two-qudit state, pure or mixed, the upper and lower bounds on its geometric quantum discord, expressed via the Hilbert space characteristics of this state.
This paper investigates the properties of the Gorini–Kossakowski–Sudarshan–Lindblad (GKSL) equation within the camel-like framework, with a focus on quantum correlations in the context of open quantum systems. Here, we compute quantum correlations such as quantum discord and quantum steering, analyzing their behavior under decoherence and environmental interaction for three sets of quantum states. Our results indicate that the sign of the entanglement entropy's derivative serves as an indicator of the system's drift toward classical or quantum information exchange—an insight with important implications for quantum error correction and dissipation processes in quantum thermal machines. \\ Moreover, we parametrize quantum states using both single-parameter and Bloch-sphere representations. The Bloch-sphere analysis is particularly developed by examining the topology of the quantum states as elements on the
S2 sphere, yielding a gradient map and a topological basin map which illustrate how quantum states evolve under the camel-like framework and how this can be partitioned into basins on the Bloch sphere, by stability/instability against decoherence. The decoherence-unstable regions form a Braiding ring around the Bloch sphere at the circle defined by
θ=43π. Notably, these unstable states on the Braiding ring form attraction points for the evolution of states by a constructed Lyapunov function, which gives an illustration of the complex interplay between geometry and dynamics and which shapes the topological geometry on the Bloch sphere. This deeper analysis underscores that quantum dynamics are governed not only by local energetics but also by the global structure of the state space. Moreover, we also derive a testable rudimentary experimental setup from the camel-like entropy, which describes the unitary evolution of pure states on the Bloch surface and add the analytical solutions of selected quantum states.
We show that two qubits, initially in a fully classical state, can develop significant quantum correlations as measured by the quantum discord (QD) under the action of a local memoryless noise (specifically we consider the case of a Markovian amplitude-damping channel). This is analytically proven after deriving in a compact form the QD for the class of separable states involved in such a process. We provide a picture in the Bloch sphere that unambiguously highlights the physical mechanism behind the effect regardless of the specific measure of quantum correlations adopted.