Von Neumann Entropy from Unitarity

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Autoren

Externe Organisationen

  • Freie Universität Berlin (FU Berlin)
  • Perimeter Institute for Theoretical Physics
  • ETH Zürich
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Details

OriginalspracheEnglisch
Aufsatznummer210402
FachzeitschriftPhysical review letters
Jahrgang122
Ausgabenummer21
PublikationsstatusVeröffentlicht - 28 Mai 2019
Extern publiziertJa

Abstract

The von Neumann entropy is a key quantity in quantum information theory and, roughly speaking, quantifies the amount of quantum information contained in a state when many identical and independent (i.i.d.) copies of the state are available, in a regime that is often referred to as being asymptotic. In this Letter, we provide a new operational characterization of the von Neumann entropy which neither requires an i.i.d. limit nor any explicit randomness. We do so by showing that the von Neumann entropy fully characterizes single-shot state transitions in unitary quantum mechanics, as long as one has access to a catalyst - an ancillary system that can be reused after the transition - and an environment which has the effect of dephasing in a preferred basis. Building upon these insights, we formulate and provide evidence for the catalytic entropy conjecture, which states that the above result holds true even in the absence of decoherence. If true, this would prove an intimate connection between single-shot state transitions in unitary quantum mechanics and the von Neumann entropy. Our results add significant support to recent insights that, contrary to common wisdom, the standard von Neumann entropy also characterizes single-shot situations and opens up the possibility for operational single-shot interpretations of other standard entropic quantities. We discuss implications of these insights to readings of the third law of quantum thermodynamics and hint at potentially profound implications to holography.

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Von Neumann Entropy from Unitarity. / Boes, Paul; Eisert, Jens; Gallego, Rodrigo et al.
in: Physical review letters, Jahrgang 122, Nr. 21, 210402, 28.05.2019.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Boes, P, Eisert, J, Gallego, R, Müller, MP & Wilming, H 2019, 'Von Neumann Entropy from Unitarity', Physical review letters, Jg. 122, Nr. 21, 210402. https://doi.org/10.1103/PhysRevLett.122.210402
Boes, P., Eisert, J., Gallego, R., Müller, M. P., & Wilming, H. (2019). Von Neumann Entropy from Unitarity. Physical review letters, 122(21), Artikel 210402. https://doi.org/10.1103/PhysRevLett.122.210402
Boes P, Eisert J, Gallego R, Müller MP, Wilming H. Von Neumann Entropy from Unitarity. Physical review letters. 2019 Mai 28;122(21):210402. doi: 10.1103/PhysRevLett.122.210402
Boes, Paul ; Eisert, Jens ; Gallego, Rodrigo et al. / Von Neumann Entropy from Unitarity. in: Physical review letters. 2019 ; Jahrgang 122, Nr. 21.
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