Sharif Digital Repository

One of the main challenges in the communication and storage of information is its evolution due to the environmental noises. There are various techniques in coding theory to decrease the probability of changing the message using redundancy. Among all of the possible codings, the maximum rate that can be achieved for reliable communication through a channel is called the capacity of that channel. In the classical information domain, this quantity has been investigated in the Shannon's second theorem and is equivalent to a finite convex optimization problem. This problem is much more complicated when dealing with quantum information and thus studying special common channels has been doubled in... 

In this thesis, we propose a new method for deriving the achievability results in quantum information theoretic problems. The calssical quan- tum decoupling lemma is an essential component in our method. Assume that each classical source is randomly binned at a finite rate. We find sufficient conditions on these rates such that the bin indices are nearly mutually independent of each other and of a quantum source Qn. Us- ing this theorem in conjunction with the calssical quantum Slepian Wolf (CQSW) result, this method suggest a new comprehensive framework for the achievability of network quantum information theoretic prob- lems. We’ve used the new method to redrive the Holevo bound, private... 

One of the most important problems of quantum information theory is to try to determine the channel capacity of noisy quantum channels. Alice would like to send Bob information over many uses of a noisy quantum communication link. As the line is usually noisy, this cannot be done perfectly, and so they must use suitable coding methods to minimize the error. Different coding methods yield different rates of information transition and different errors, the channel capacity is defined as the maximum rate at which information may be transferred with vanishing error in the limit of a large number of channel uses. There are a variety of different capacities, depending upon whether Alice and Bob... 

In this thesis, we study the divisibility of qutrit channels. First, we will review preliminaries and results in arbitrary dimensions and then results of divisibility of qubit channels. As deriving general results for Hilbert space dimension larger than two is complicated or impossible, in the following we analyze the divisibility of group-covariant channels and in particular study Z_2-covariant channels. Then we focus on qutrit channels. As there is no complete characterization of qutrit channels space, we study a subset of unital qutrit channels with the diagonal affine matrix. We call this set S and study the divisibility of its elements. First, we consider a three-parameter subset of S... 

One of the main aspects of resource theory is finding conditions that one state can map to another state with “allowed” operations. In quantum, allowed operations are a subset of quantum channels. In quantum thermodynamics, for example, one usually asks whether a state σ can be generated from an initial state ρ via a Gibbs-preserving channel which is a special case of [2]. In 1980 Alberti and Uhlmann [2]found a condition for the existence of a quantum channel that simultaneously transforms an input-pair of states into an output-pair. This problem is addressed in resource theory[1, 3], statistical comparison[4] and etc. Since then, this problem and its generalizations[8, 23, 22, 31, 7, 6]... 

One of the main tools of the developing quantum technology is making the desired quantum gates and processes in the presence of the environmental noises. In this thesis, we first derive a Markovian master equation which defines purely the time evolution of the dynamics (process matrix) of the open system rather than its state (density matrix). This master equation indeed describes the time evolution of the Choi-Jamiolkowsli matrix which is independent of the state of the system at all times including the initial state. The n, by using this master equation we provide a scheme to manipulate optimally and locally the dynamics of the open system by external coherent agents. Such scheme... 

One of the critical subjects in quantum information science is the transmission of quantum information. Like classical channels, the question of the capacity of quantum channels arises in the quantum information theory; however, in the case of quantum information theory, there are various notions of capacities that can be defined. In quantum channels, information is encoded into the quantum degrees of freedoms, and the channels are used for the transmission of classical and quantum information. Therefore, the classical capacity and quantum capacity of quantum channels are defined as the optimal rate of the transmission of classical and quantum information through quantum channels,... 

In recent studies, it has been shown that entanglement is not the only kind of genuinely quantum correlation. There exist models of quantum computation that provide exponential speed up over the best known classical algorithms and don’t have any quantum entanglement. These models show that in some cases separable state can be very useful in quantum computing models. Look for a property that causes the performance of these scenarios, quantum correlation being one of the most important concepts, including but not limited to entanglement. Local noise can produce quantum correlations on an initially classically correlated state, provided that it is not represented by a unital or semiclassical...