Reversible transformations from pure to mixed states and the unique measure of information

By Michal Horodecki, Pawel Horodecki, Jonathan Oppenheim. 2002

232 citations recorded by the source corpus.

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 with 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'.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/b4432c81d15c21b1b5053a301c791d1b7da056c8

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

The resource theory of informational nonequilibrium in thermodynamics (2013, background): “These have been called noisy operations in (Horodecki et al., 2003a,b), where this resource theory was first studied1.”
The classical-quantum boundary for correlations: Discord and related measures (2011, background): “A system is classical, (only has classical correlations), if the same amount of work that can be extracted from the total system as one, Wt, can also be extracted from the subsystems after suitable LOCC operations, Wl.”
The role of quantum information in thermodynamics—a topical review (2015, background): “In this setting, thermodynamics inherits directly from the theory of noisy operations [79].”
Fundamental limitations for quantum and nanoscale thermodynamics (2011, background): “We know [19] that then any mixture of unitary transformations can be performed on the system R 2 S E , provided K is large with respect to K ′ E , and we shall choose K, and the size of the total system, in such a way, that this is so, and at the same time K ′ E can be large too, which we will need ”
Geometry of Quantum States: Index (2007, background): “15 An early version of this result [461] had to assume an ancilla of a large size.”
Measures and dynamics of entangled states (2005, background): “There are attempts to find a distinct set of axioms that leads to a unique measure [56].”
A mathematical theory of resources (2014, unknown): “The quantum resource theory of nonuniformity [27, 25] is deﬁned in terms of the following partitioned process theory.”
Quantum coherence and geometric quantum discord (2017, background): “Stimulated by the work of Horodecki et al. (2003a) and Gour et al. (2015), a resource theory of purity was established by Streltsov et al. (2018).”
An improved Landauer principle with finite-size corrections (2013, methodology): “tial correlations with Mthat the process Ucan access. As a further extension of the setup from Section 2.1, instead of only unitary interactions U, one may allow for so-called \noisy operations" [HHO03], i.e. unitaries using an additional completely mixed ancilla system, or more generally any u”
The resource theory of stabilizer quantum computation (2013, background): “[26] Michał Horodecki, Paweł Horodecki, and Jonathan Oppenheim.”
Quantum resource theories (2018, methodology): “The latter provided one of the first explicit constructions of a QRT that is different than entanglement theory, although the framework for a QRT of information had already been investigated in a series of earlier papers (Horodecki et al., 2003a, 2005b; Oppenheim et al., 2002).”