The Nature and Location of Quantum Information

Abstract

Quantum information is defined by applying the concepts of ordinary (Shannon) information theory to a quantum sample space consisting of a single framework or consistent family. A classical analogy for a spin-half particle and other arguments show that the infinite amount of information needed to specify a precise vector in its Hilbert space is not a measure of the information carried by a quantum entity with a $d$-dimensional Hilbert space; the latter is, instead, bounded by log d bits (1 bit per qubit). The two bits of information transmitted in dense coding are located not in one but in the correlation between two qubits, consistent with this bound. A quantum channel can be thought of as a "structure" or collection of frameworks, and the physical location of the information in the individual frameworks can be used to identify the location of the channel. Analysis of a quantum circuit used as a model of teleportation shows that the location of the channel depends upon which structure is employed; for ordinary teleportation it is not (contrary to Deutsch and Hayden) present in the two bits resulting from the Bell-basis measurement, but in correlations of these with a distant qubit. In neither teleportation nor dense coding does information travel backwards in time, nor is it transmitted by nonlocal (superluminal) influences. It is (tentatively) proposed that all aspects of quantum information can in principle be understood in terms of the (basically classical) behavior of information in a particular framework, along with the framework dependence of this information.

Latex 29 pages, uses PSTricks for figures

References in corpus (3)

• Quantum Nonlocality without Entanglement
• Information Flow in Entangled Quantum Systems
• Choice of Consistent Family, and Quantum Incompatibility

Cited by in corpus (8)

• Efficient implementation of bipartite nonlocal unitary gates using prior entanglement and classical communication
• Atemporal diagrams for quantum circuits
• Types of quantum information
• Channel kets, entangled states, and the location of quantum information
• Practical scheme for quantum dense coding between three parties using microwave radiation in trapped ions
• A Consistent Quantum Ontology
• Information Content of Systems as a Physical Principle
• Epistemic Restrictions in Hilbert Space Quantum Mechanics