Details
| Original language | English |
|---|---|
| Article number | 210402 |
| Journal | Physical review letters |
| Volume | 122 |
| Issue number | 21 |
| Publication status | Published - 28 May 2019 |
| Externally published | Yes |
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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In: Physical review letters, Vol. 122, No. 21, 210402, 28.05.2019.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Von Neumann Entropy from Unitarity
AU - Boes, Paul
AU - Eisert, Jens
AU - Gallego, Rodrigo
AU - Müller, Markus P.
AU - Wilming, Henrik
N1 - Funding Information: We acknowledge funding from Deutsche Forschungsgemeinschaft (GA 2184/2-1, CRC 183, EI 519/14-1, EI 519/9-1, FOR 2724), the European Research Council (TAQ), and the Studienstiftung des deutschen Volkes. H. W. further acknowledges contributions from the Swiss National Science Foundation via the NCCR QSIT as well as Project No. 200020_165843. This research was supported in part by Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported by the Government of Canada through the Department of Innovation, Science and Economic Development Canada and by the Province of Ontario through the Ministry of Research, Innovation and Science.
PY - 2019/5/28
Y1 - 2019/5/28
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85066439367&partnerID=8YFLogxK
U2 - 10.1103/PhysRevLett.122.210402
DO - 10.1103/PhysRevLett.122.210402
M3 - Article
C2 - 31283324
AN - SCOPUS:85066439367
VL - 122
JO - Physical review letters
JF - Physical review letters
SN - 0031-9007
IS - 21
M1 - 210402
ER -