Time evolution of the quantum correlation of the hybrid qubit-qutrit system in multilocal and global dephasing under the effect of a classical noises environment is presented. We considered the qutrit in z direction and the qubit x direction. In addition, our system presents two configurations: the different and the common environment and our discussion involves three types of noises: A Static Noise (SN), Random Telegraph Noise (RTN) and Ornstein- Uhlenbeck noise (OU). By using the density matrix approach to determine the evolution of the state of the system, the found that the static noise is fatal for the quantum entanglement, the quantum correlation and for RTN and OU noises the quantum entanglement, the quantum correlation decreases monotonically with a sufficiently long time. Therefore, we can say that, entanglement and the quantum correlation are more robust to the noise precisely those Random telegraph noise and Ornstein-Uhlenbeck noise.

Quantum Computers are provisioned as very high performance computers using quantum mechanical aspects for information processing. Quantum Information Theory and Quantum Computing topics are popular topics in academia aiming the construction of theoretical background of Quantum Computers. The information processing units for Quantum Computers are defined as qubits but for some problems three level (trinary) systems may be applied as well. We call these three level systems as qutrits. The scope of this work is the analysis of well-defined entanglement measures Negativity and Relative Entropy of Entanglement (REE) for two qutrit (3- level/trinary) quantum systems. In this manner, for randomly generated 1000 two qutrit and 1000 two qubit states the mentioned measures are calculated and these values are compared. These comparisons are analyzed and for quantum state ordering problem, some interesting results are reported.

Communication, compression of information, transmission of information through noisy channels, interconnecting different information systems, cryptography, gate construction –– these areas all depend on classical information theory. We show that, in classical terms, semantic aspects of communication are not at all irrelevant to the engineering problem, contrary to Shannon, and affect the message intended to be transmitted. This is revisited and captured by an analogy to trust, in that they are essential to the channel (for proper use), but cannot be transferred (under risk of flaws) through that same channel. Information is also described by, at least, a tri-state system — not by binary logic. The trust analogy semantics can be coded as the Curry-Howard relationship, connecting computer code with structural logic, by way of different categories. Two-state and Boolean logic (aka Shannon semantics) was used classically before, with Shannon theory, but without trust analogy semantics – found to be a sine qua non condition. This is now familiar in classical gate construction with physical systems with, e.g., Verilog and SystemVerilog. The applications to computation and quantum theory are further explored. The most fundamental entity in today`s theory of information is proposed to use at least three logical states, not bits, in all applications, including: cyber-physical systems, devices, in computation, and in quantum theory.