Quantum information with quantum-like bits

David S. Simon

Masataka Ohta

While Shannon introduced “binary digits, or more briefly bits” as units of information, a binary digit (and, thus, a bit) originally and still means a character of “0” or “1”, which may be represented by a binary symbol or storage cell. As a result, a bit often means a binary symbol or storage cell, which is inherited by a “qubit”, a quantum bit, introduced by Schumacher as “the fundamental units of quantum information”. Schumacher himself uses a bit, not a qubit, as a unit of quantum information and a qubit is a quantum binary symbol or storage cell.

Hongfang Li

The second quantum revolution blurs the distinction between information and matter. “It from (qu)bit or (Qu)bit from it” thus becomes a philosophical issue. According to the physicist Wen Xiaogang in MIT, quantum topological states of matter, formed by long-range entangled qubits, will show all particles, such as light and electrons, are unified by the long-range entanglement of qubits. That is, it from qubit, not bit. Quantum information unifies matter, i.e., quantum information = quantum matter. This represents a new way to view our world. However, the information-theoretical paradigm, which origins from Wheeler’s “it from bit”, can lead to informational immaterialism and instrumentalism. In perspective of the constructive structural realism, there exists a constructive co-dependent structural relationship between quantum information and quantum matter. Both qubit and it are fundamental structural elements for us constructing our understanding of the physical world.

Richard Jozsa

Robert B. Griffiths

Quantum, in contrast to classical, information theory, allows for different incompatible types (or species) of information which cannot be combined with each other. Distinguishing these incompatible types is useful in understanding the role of the two classical bits in teleportation (or one bit in one-bit teleportation), for discussing decoherence in information-theoretic terms, and for giving a proper definition, in quantum terms, of ``classical information.'' Various examples (some updating earlier work) are given of theorems which relate different incompatible kinds of information, and thus have no counterparts in classical information theory.

Michał Horodecki, G. Alber, Thomas Beth