Reversible transformations from pure to mixed states, and the unique measure of information
arXiv:quant-ph/0212019 · doi:10.1103/PhysRevA.67.062104
Abstract
Transformations from pure to mixed states are usually associated with information loss and irreversibility. Here, a protocol is demonstrated allowing one to make these transformations reversible. The pure states are diluted with a random noise source. Using this protocol one can study optimal transformations between states, and from this derive the unique measure of information. This is compared to irreversible transformations where one does not have access to noise. The ideas presented here shed some light on attempts to understand entanglement manipulations and the inevitable irreversibility encountered there where one finds that mixed states can contain "bound entanglement".
10 pages, no figures, revtex4, table added, to appear in Phys. Rev. A
References in corpus (13)
- Mixed State Entanglement and Quantum Error Correction
- Concentrating Partial Entanglement by Local Operations
- Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels
- Entanglement Measures and Purification Procedures
- Conditions for a class of entanglement transformations
- Entanglement monotones
- A Thermodynamical Approach to Quantifying Quantum Correlations
- Thermodynamics and the Measure of Entanglement
- An improved bound on distillable entanglement
- The entanglement cost under operations preserving the positivity of partial transpose
- Information as a resource in distributed quantum systems
- Are the laws of entanglement theory thermodynamical?
- Irreversibility in asymptotic manipulations of entanglement
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