Monogamy of correlations and entropy inequalities in the Bloch picture
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We investigate monogamy of correlations and entropy inequalities in the Bloch representation. Here, both can be understood as direct relations between different correlation tensor elements and thus appear intimately related. To that end we introduce the split Bloch basis, that is particularly useful for representing quantum states with low dimensional support and thus amenable to purification arguments. Furthermore, we find dimension dependent entropy inequalities for the Tsallis 2-entropy. In particular, we present an analogue of the strong subadditivity and a quadratic entropy inequality. These relations are shown to be stronger than subadditivity for finite dimensional cases.
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For any tripartite quantum state ρ_ABC with marginal states defined in the usual way, the marginal purities must obey d_A γ(ρ_AC) + d_B γ(ρ_BC) ≤ d_A d_B γ(ρ_ABC) + γ(ρ_C).
“From Theorem 2 in [81] for any tripartite quantum state ρ ABC with marginal states defined in the usual way, the marginal purities must obey”
From Simple formulation of no-cloning and no-hiding that admits efficient and robust verification (2024) · cites this paper as [81]
For any input system X and output systems A and B with equal dimensions d_X=d_A=d_B=d, the full quantum CUP set C* ⊆ [0,1]^2 is confined in the (u, ū) plane by u+ū ≤ 1 + 1/(d+1).
“Theorem B.3 (Partial cloning bound on full quantum CUP set C * ).Given any input system X and output systems A and B with equal dimensions d X = d A = d B = d.The associated full quantum CUP set C * ⊆ [0, 1] 2 is confined in the (u, ū) plane by”
From Simple formulation of no-cloning and no-hiding that admits efficient and robust verification (2024) · cites this paper as [81]
Theorem 1 (page unavailable) bounds correlations among tripartite states, but does not state a bound on a full quantum CUP set. Searches for partial cloning, CUP sets, and the claimed 1/(d+1) bound found no passage addressing that claim. (LLM, conf=0.73)
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- Authors
- Appel, P., Huber, M., & Klöckl, C.
- Affiliations
- Austrian Academy of Sciences (AT)
- Corresponding author
- Appel, Paul
- Venue
- Journal of Physics Communications
- Publisher
- IOP Publishing
- Published
- 2020-02-01
- Volume
- 4
- Issue
- 2
- Pages
- 025009
- ISSN
- 2399-6528 (ISSN-L)
- OpenAlex
- W2761001709
- Cited by
- 38
- References
- 47
- Citations by year
- 2025: 1 · 2024: 2 · 2023: 32 · 2020: 2 · 2018: 1
- FWCI
- 3.46
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- Locations
- Journal of Physics Communications (publishedVersion, cc-by)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Grantová Agentura České Republiky (GF17-33780L)
- Austrian Science Fund (I3053-N27)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Statistical Mechanics and Entropy
- Keywords
- entropy inequality, Bloch representation, Tsallis entropy, strong subadditivity, subadditivity, purification, correlation tensor
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