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We consider the problem of transmitting classical and quantum information reliably over an entanglement-assisted quantum channel. Our main result is a capacity theorem that gives a three-dimensional achievable rate region. Points in the…
In the first part of this thesis, we discuss the algebraic approach to classical and quantum physics and develop information theoretic concepts within this setup. In the second part, we discuss the uncertainty principle in quantum…
It is well known that quantum theory forbids the exact copying of an unknown quantum state. Therefore in broadcasting of classical information by a quantum channel an additional contribution to the error in the decoding is expected. We…
Recently the theory of communication developed by Shannon has been extended to the quantum realm by exploiting the rules of quantum theory. This latter stems on complex vector spaces. However complex (as well as real) numbers are just…
Quantum error correction (QEC) is one of the central concepts in quantum information science and also has wide applications in fundamental physics. The capacity theorems provide solid foundations of QEC. We here provide a general and highly…
The study of mutual entropy (information) and capacity in classica l system was extensively done after Shannon by several authors like Kolmogor ov and Gelfand. In quantum systems, there have been several definitions of t he mutual entropy…
In this thesis we analyse the type of states and ensembles which achieve the capacity for certain quantum channels carrying classical information. We first concentrate on the product-state capacity of a particular quantum channel, that is,…
Nyquist-Shannon sampling theorem, instrumental in classical telecommunication technologies, is extended to quantum systems supporting a unitary representation of a finite group $G$. Two main ideas from the classical theory having natural…
A renowned information-theoretic formula by Shannon expresses the mutual information rate of a white Gaussian channel with a stationary Gaussian input as an integral of a simple function of the power spectral density of the channel input.…
The coding theorem for the entanglement-assisted communication via infinite-dimensional quantum channel with linear constraint is extended to a natural degree of generality. Relations between the entanglement-assisted classical capacity and…
Coding theorems and (strong) converses for memoryless quantum communication channels and quantum sources are proved: for the quantum source the coding theorem is reviewed, and the strong converse proven. For classical information…
We consider the transmission of classical information through a degraded broadcast channel, whose outputs are two quantum systems, with the state of one being a degraded version of the other. Yard et al. proved that the capacity region of…
We consider state redistribution of a "hybrid" information source that has both classical and quantum components. The sender transmits classical and quantum information at the same time to the receiver, in the presence of classical and…
Shared entanglement is a resource available to parties communicating over a quantum channel, much akin to public coins in classical communication protocols. Whereas shared randomness does not help in the transmission of information, or…
With the recent development of quantum information theory, some attempts exist to construct information theory beyond quantum theory. Here we consider hypothesis testing relative entropy and one-shot classical capacity, that is, the optimal…
Quantum entanglement can be used in a communication scheme to establish a correlation between successive channel inputs that is impossible by classical means. It is known that the classical capacity of quantum channels can be enhanced by…
We derive upper bounds on the rate of transmission of classical information over quantum channels by block codes with a given blocklength and error probability, for both entanglement-assisted and unassisted codes, in terms of a unifying…
The dynamic capacity theorem characterizes the reliable communication rates of a quantum channel when combined with the noiseless resources of classical communication, quantum communication, and entanglement. In prior work, we proved the…
A strong converse theorem for the classical capacity of a quantum channel states that the probability of correctly decoding a classical message converges exponentially fast to zero in the limit of many channel uses if the rate of…
Establishing the strong converse theorem for a communication channel confirms that the capacity of that channel, that is, the maximum achievable rate of reliable information communication, is the ultimate limit of communication over that…