Towards a unification of physics and information theory

A common framework for quantum mechanics, thermodynamics and information theory is presented. It is accomplished by reinterpreting the mathematical formalism of Everett’s manyworlds theory of quantum mechanics and augmenting it to include preparation according to a given ensemble. The notion of directed entanglement is introduced through which both classical and quantum communication over quantum channels are viewed as entanglement transfer. This point is illustrated by proving the Holevo bound and quantum data processing inequality relying exclusively on the properties of directed entanglement. Within the model quantum thermodynamics is treated in such a way as to eliminate the problem of Maxwell’s demon altogether, and a simple proof of the second law is given. We present a novel interpretation of quantum mechanics which we argue to be more conducive to the development of quantum information theory and quantum thermodynamics. Our motivation is both practical and one of principles. On the practical side, we find the standard Copenhagen formalism to be unsatisfactory in various ways. For example, there are many different reasons for a quantum system Q to be described by some mixed density operator ρQ. It could be prepared from some ensemble of pure states, it could be a result of an unobserved measurement performed on a pure state, it could be entangled with some other physical system, or it could be some combination of these three. A related issue is that classical and quantum communication over quantum channels appear to be rather independent problems [1]. Another dichotomy is that two protagonists may share information about a physical event through communication rather than through common observation, yet these are treated very differently. As for quantum thermodynamics, it suffers from an inadequately defined thermodynamic entropy which allows for the existence of Maxwell’s demon [2], a hypothetical being capable of violating the second law of thermodynamics as long as it has a sufficiently large memory at its disposal. Regarding principles, we would like to view the laws of physics in information theoretical terms. This attitude may be traced to Wheeler’s motto ”It from Bit” [3], and Wigner’s observation that physics merely describes correlations between events [4]. The two are unified by the statement that the totality of conceptual experience can be described in terms of correlated random variables; this will allow us to make contact with Shannon’s information theory [5] in which random variables are the carriers of information. For instance, two protagonists sharing the same physical world is no more than classical correlations between the states of their knowledge regarding that world. Similarly, the observation of definite physical laws is no more than classical correlations between states ∗Electronic address: [email protected]