Information Theory of Quantum-Mechanical Channels

Michael A. Nielsen

Quantum information theory is the study of the achievable limits of information processing within quantum mechanics. Many different types of information can be accommodated within quantum mechanics, including classical information, coherent quantum information, and entanglement. Exploring the rich variety of capabilities allowed by these types of information is the subject of quantum information theory, and of this Dissertation. In particular, I demonstrate several novel limits to the information processing ability of quantum mechanics. Results of especial interest include: the demonstration of limitations to the class of measurements which may be performed in quantum mechanics; a capacity theorem giving achievable limits to the transmission of classical information through a two-way noiseless quantum channel; resource bounds on distributed quantum computation; a new proof of the quantum noiseless channel coding theorem; an information-theoretic characterization of the conditions under which quantum error-correction may be achieved; an analysis of the thermodynamic limits to quantum error-correction, and new bounds on channel capacity for noisy quantum channels.

Mark M. Wilde

Mark M. Wilde

Jiahui Du, Michel Kadoch, Boxiang Chao

In classical information theory (represented by Shannon's framework), the study of information transmission typically presupposes a fixed "channel" endowed with absolute attributes. This assumption implicitly holds that the properties of the channel are determinate and observer-independent, remaining unchanged regardless of perspective or the state of the channel itself. However, contemporary physics---particularly the development of quantum mechanics---fundamentally challenges the very notion of "absoluteness." As Carlo Rovelli has emphasized in one of his core arguments, quantum mechanics compels us to abandon the conception of states and properties as "absolute" and "observer-independent." The insistence on such absoluteness is precisely what underlies many of the paradoxes and interpretative difficulties that plague quantum theory. Rovelli extends this general philosophical critique of "absoluteness" consistently into the domain of information theory, thereby provoking a profound re-examination and critique of the classical presupposition of the "absolute channel." From this relational perspective, information should not be conceived as an abstract entity existing independently of physical relations, but rather as an observable measure of relative relations between systems. Accordingly, the reconstruction of classical information theory on the basis of relational ontology---namely, the reconstruction of information theory itself---is not only a demand of theoretical coherence but also a necessary step in responding to the challenge of quantum reality and in building a more universal theory of information.

Bingju Zhou, Xiaojuan Liu, Qingping Zhou +1 more

Based on the quantum information theory, we have investigated the entropy squeezing of a moving two-level atom interacting with the coherent field via the quantum mechanical channel of the two-photon process. The results are compared with those of atomic squeezing based on the Heisenberg uncertainty relation. The influences of the atomic motion and field-mode structure parameter on the atomic entropy squeezing and on the control of noise of the quantum mechanical channel via the two-photon process are examined. Our results show that the squeezed period, duration of optimal entropy squeezing of a two-level atom and the noise of the quantum mechanical channel can be controlled by appropriately choosing the atomic motion and the field-mode structure parameter, respectively. The quantum mechanical channel of two-photon process is an ideal channel for quantum information (atomic quantum state) transmission. Quantum information entropy is a remarkably accurate measure of the atomic squeezing.

Lev B. Levitin