Negative entropy and information in quantum mechanics

TL;DR

A framework for a quantum mechanical information theory is introduced that is based entirely on density operators, and gives rise to a unified description of classical correlation and quantum entanglement.

Abstract

A framework for a quantum mechanical information theory is introduced that is based entirely on density operators, and gives rise to a unified description of classical correlation and quantum entanglement. Unlike in classical (Shannon) information theory, quantum (von Neumann) conditional entropies can be negative when considering quantum entangled systems, a fact related to quantum non-separability. The possibility that negative (virtual) information can be carried by entangled particles suggests a consistent interpretation of quantum informational processes.

Figures (2)

• Figure 1: (a) Entropy Venn diagram for a bipartite system $AB$. (b) Diagram for two qubits with $S(A)=S(B)=1$: (I) independent 50/50 mixtures of states $|0\rangle$ and $|1\rangle$; (II) maximally classically (anti)correlated qubits, i.e., a 50/50 mixture of $|01\rangle$ and $|10\rangle$; (III) fully entangled EPR state with wavefunction $2^{-1/2} (|01\rangle - |10\rangle)$, or any Bell state in general.
• Figure 2: Physical spacetime diagrams and quantum information dynamics diagrams for (a) quantum teleportation and (b) superdense coding.