A probabilistic and information theoretic interpretation of quantum evolutions

Abstract

In quantum mechanics, outcomes of measurements on a state have a probabilistic interpretation while the evolution of the state is treated deterministically. Here we show that one can also treat the evolution as being probabilistic in nature and one can measure `which unitary' happened. Likewise, one can give an information-theoretic interpretation to evolutions by defining the entropy of a completely positive map. This entropy gives the rate at which the informational content of the evolution can be compressed. One cannot compress this information and still have the evolution act on an unknown state, but we demonstrate a general scheme to do so probabilistically. This allows one to generalize super-dense coding to the sending of quantum information. One can also define the ``interaction-entanglement'' of a unitary, and concentrate this entanglement.

9 pages

References in corpus (5)

• Statistical distinguishability between unitary operations
• Storing quantum dynamics in quantum states: stochastic programmable gate for U(1) operations
• Quantum entanglement of unitary operators on bi-partite systems
• Non-local Operations: Purification, storage, compression, tomography, and probabilistic implementation
• Are there phase transitions in information space?

Cited by in corpus (9)

• On the quantum, classical and total amount of correlations in a quantum state
• Not So SuperDense Coding - Deterministic Dense Coding with Partially Entangled States
• Local Distinguishability of Multipartite Unitary Operations
• A Coding Theorem for Bipartite Unitaries in Distributed Quantum Computation
• Quantifying Superpositions Between Quantum Evolutions
• Generalizing Entanglement
• Violation of smooth observable macroscopic realism in a harmonic oscillator
• Asymptotic Compressibility of Entanglement and Classical Communication in Distributed Quantum Computation
• Entropy, Convex Optimization, and Competitive Quantum Interactions