There have been some exciting developments in quantum information theory in the presence of closed timelike curves (CTCs). In general theory of relativity we define CTC by a world line which connects back on itself. However an important doubt always remains on formulation of a consistent theory of quantum mechanics in presence of CTCs. Such a formalism was developed by Deutsch who proposed a model of quantum theory in the presence of CTCs [22] We have seen the presence of closed time like curves can affect the computational power like factorization of composite numbers efficiently with the help of a classical computer, solving NP-complete problems and other abilities to perform information processing tasks of a system. These include perfectly distinguishibility of nonorthogonal quantum states, having possible implications for the security of quantum cryptography . In the presence of CTCs, information flow of quantum states , purifications of mixed states , and nonlocal boxes have also been addressed.

The problem of complementarity or mutually exclusive aspects of quantum phenomena is fromthe birth of quantum mechanics, soon after, Heisenberg discovered the uncertainty principle for the momentum and the position. A year later, Bohr proposed the concept of complementarity [53]. Even in the domain of quantum information theory, the idea of complementarity exist in different forms like the complementarity between the local and non-local information of quantum systems, dual physical processes.

Quantum superposition and entanglement is the key that makes quantum information processing radically different from classical counterpart. The same properties also stops us to do certain tasks which otherwise possible in the classical world . It all started with the no-cloning theorem which states that there does not exist any quantum operation which can perfectly duplicate a pure state . Pati and Braunstein later showed that we cannot delete either of the two quantum states with fidelity 1 . There are many other no-go theorems like no-flipping , no-self replication, no-partial erasure no-splitting and no- partial swapping which together tells us the indivisibility of the information content present in a quantum system.