Details
| Original language | English |
|---|---|
| Article number | 010325 |
| Journal | PRX Quantum |
| Volume | 3 |
| Issue number | 1 |
| Publication status | Published - Mar 2022 |
| Externally published | Yes |
Abstract
The variance of (relative) surprisal, also known as varentropy, so far mostly plays a role in information theory as quantifying the leading-order corrections to asymptotic independent and identically distributed (IID) limits. Here, we comprehensively study the use of it to derive single-shot results in (quantum) information theory. We show that it gives genuine sufficient and necessary conditions for approximate state transitions between pairs of quantum states in the single-shot setting, without the need for further optimization. We also clarify its relation to smoothed min and max entropies, and construct a monotone for resource theories using only the standard (relative) entropy and variance of (relative) surprisal. This immediately gives rise to enhanced lower bounds for entropy production in random processes. We establish certain properties of the variance of relative surprisal, which will be useful for further investigations, such as uniform continuity and upper bounds on the violation of subadditivity. Motivated by our results, we further derive a simple and physically appealing axiomatic single-shot characterization of (relative) entropy, which we believe to be of independent interest. We illustrate our results with several applications, ranging from interconvertibility of ergodic states, over Landauer erasure to a bound on the necessary dimension of the catalyst for catalytic state transitions and Boltzmann's H theorem.
ASJC Scopus subject areas
- Materials Science(all)
- Electronic, Optical and Magnetic Materials
- Computer Science(all)
- Mathematics(all)
- Mathematical Physics
- Physics and Astronomy(all)
- Mathematics(all)
- Applied Mathematics
- Engineering(all)
- Electrical and Electronic Engineering
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In: PRX Quantum, Vol. 3, No. 1, 010325, 03.2022.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Variance of Relative Surprisal as Single-Shot Quantifier
AU - Boes, Paul
AU - Ng, Nelly H.Y.
AU - Wilming, Henrik
PY - 2022/3
Y1 - 2022/3
N2 - The variance of (relative) surprisal, also known as varentropy, so far mostly plays a role in information theory as quantifying the leading-order corrections to asymptotic independent and identically distributed (IID) limits. Here, we comprehensively study the use of it to derive single-shot results in (quantum) information theory. We show that it gives genuine sufficient and necessary conditions for approximate state transitions between pairs of quantum states in the single-shot setting, without the need for further optimization. We also clarify its relation to smoothed min and max entropies, and construct a monotone for resource theories using only the standard (relative) entropy and variance of (relative) surprisal. This immediately gives rise to enhanced lower bounds for entropy production in random processes. We establish certain properties of the variance of relative surprisal, which will be useful for further investigations, such as uniform continuity and upper bounds on the violation of subadditivity. Motivated by our results, we further derive a simple and physically appealing axiomatic single-shot characterization of (relative) entropy, which we believe to be of independent interest. We illustrate our results with several applications, ranging from interconvertibility of ergodic states, over Landauer erasure to a bound on the necessary dimension of the catalyst for catalytic state transitions and Boltzmann's H theorem.
AB - The variance of (relative) surprisal, also known as varentropy, so far mostly plays a role in information theory as quantifying the leading-order corrections to asymptotic independent and identically distributed (IID) limits. Here, we comprehensively study the use of it to derive single-shot results in (quantum) information theory. We show that it gives genuine sufficient and necessary conditions for approximate state transitions between pairs of quantum states in the single-shot setting, without the need for further optimization. We also clarify its relation to smoothed min and max entropies, and construct a monotone for resource theories using only the standard (relative) entropy and variance of (relative) surprisal. This immediately gives rise to enhanced lower bounds for entropy production in random processes. We establish certain properties of the variance of relative surprisal, which will be useful for further investigations, such as uniform continuity and upper bounds on the violation of subadditivity. Motivated by our results, we further derive a simple and physically appealing axiomatic single-shot characterization of (relative) entropy, which we believe to be of independent interest. We illustrate our results with several applications, ranging from interconvertibility of ergodic states, over Landauer erasure to a bound on the necessary dimension of the catalyst for catalytic state transitions and Boltzmann's H theorem.
UR - http://www.scopus.com/inward/record.url?scp=85126566779&partnerID=8YFLogxK
U2 - 10.1103/PRXQuantum.3.010325
DO - 10.1103/PRXQuantum.3.010325
M3 - Article
AN - SCOPUS:85126566779
VL - 3
JO - PRX Quantum
JF - PRX Quantum
IS - 1
M1 - 010325
ER -