The Information-Disturbance Tradeoff and the Continuity of Stinespring's Representation
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Stinespring's dilation theorem is the basic structure theorem for quantum channels: it states that any quantum channel arises from a unitary evolution on a larger system. Here we prove a continuity theorem for Stinespring's dilation: if two quantum channels are close in cb-norm, then it is always possible to find unitary implementations which are close in operator norm, with dimension-independent bounds. This result generalizes Uhlmann's theorem from states to channels and allows to derive a formulation of the information-disturbance tradeoff in terms of quantum channels, as well as a continuity estimate for the no-broadcasting theorem. We briefly discuss further implications for quantum cryptography, thermalization processes, and the black hole information loss puzzle.
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For any input system X and output systems A and B, the full quantum CUP set C* is confined such that (u, ū)=(1,x) implies x=0.
“Theorem B.2 (No-cloning bound on full quantum CUP set C * ).Given any input system X and output systems A and B. The associated full quantum CUP set C * is confined such that for”
From Simple formulation of no-cloning and no-hiding that admits efficient and robust verification (2024) · cites this paper as [5]
The channel tr_A • V is complementary to E and, from Theorem IV.1 and [5], must be completely depolarizing to some fixed state.
“The channel tr A • V is complementary to E and from Theorem IV.1 (and as a consequence of [5]) must therefore be completely depolarizing, tr A • V = D, to some fixed state.”
From Simple formulation of no-cloning and no-hiding that admits efficient and robust verification (2024) · cites this paper as [5]
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Orthey, A. C., Dieguez, P. R., Makuta, O., & Augusiak, R. (2025) · Physical Review A · doi:10.1103/physreva.111.012220 · Cited by 6 · see citing works
Nonperturbative gravity corrections to bulk reconstruction
Gesteau, E., & Kang, M. J. (2023) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/acef7d · Cited by 11 · see citing works
Measurement sharpness and disturbance tradeoff
Saberian, N., Akhtarshenas, S. J., & Shahbeigi, F. (2024) · Physical Review A · doi:10.1103/physreva.109.012201 · Cited by 6 · see citing works
BURES DISTANCE FOR COMPLETELY POSITIVE MAPS
Bhat, B. V. R., & Sumesh, K. (2013) · Infinite Dimensional Analysis Quantum Probability and Related Topics · doi:10.1142/s0219025713500318 · Cited by 6 · see citing works
Picture-perfect Quantum Key DistributionPreprint
Kissinger, A., Tull, S., & Westerbaan, B. (2017) · arXiv (Cornell University) · doi:10.48550/arxiv.1704.08668 · Cited by 6 · see citing works
Quantum Information and Convex Optimization
Reimpell, M. (2007) · Digitale Bibliothek Braunschweig (Verbundzentrale Göttingen (VZG)) · doi:10.24355/dbbs.084-200803130100-3 · Cited by 7 · see citing works
Estimation of correlations and nonseparability in quantum channels via unitarity benchmarking
Girling, M., Cîrstoiu, C., & Jennings, D. (2022) · Physical Review Research · doi:10.1103/physrevresearch.4.023041 · Cited by 5 · see citing works
Matrix product states and the decay of quantum conditional mutual information
Svetlichnyy, P., Mittal, S., & Kennedy, T. A. B. (2024) · Journal of Mathematical Physics · doi:10.1063/5.0152063 · Cited by 5 · see citing works
Precursor problem and holographic mutual information
Bao, N., & Kim, I. H. (2016) · CaltechAUTHORS (California Institute of Technology) · doi:10.48550/arxiv.1601.07616 · Cited by 6 · see citing works
Широков, М. Е. (2022) · Journal of Mathematical Physics · doi:10.1063/5.0102141 · Cited by 5 · see citing works
Strong$$^*$$ convergence of quantum channels
Широков, М. Е. (2021) · Quantum Information Processing · doi:10.1007/s11128-021-03087-z · Cited by 5 · see citing works
Bergamaschi, T. (2024) · Lecture notes in computer science · doi:10.1007/978-3-031-58734-4_14 · Cited by 6 · see citing works
Quantum channels, complex Stiefel manifolds, and optimization
Russkikh, I., Volkov, B. O., & Pechen, A. N. (2025) · Quantum Information Processing · doi:10.1007/s11128-025-04782-x · Cited by 4 · see citing works
An Operational Environment for Quantum Self-Testing
Christandl, M., Houghton-Larsen, N. G., & Mančinska, L. (2022) · Quantum · doi:10.22331/q-2022-04-27-699 · Cited by 4 · see citing works
Finite-Dimensional Stinespring Curves Can Approximate Any Dynamics
Ende, F. V. (2024) · Open Systems & Information Dynamics · doi:10.1142/s1230161224500045 · Cited by 3 · see citing works
Coherent information of a quantum channel or its complement is generically positive
Singh, S., & Datta, N. (2022) · Quantum · doi:10.22331/q-2022-08-11-775 · Cited by 4 · see citing works
Maximum and Minimum Causal Effects of Physical Processes
Chiribella, G., & Goswami, K. (2025) · PRX Quantum · doi:10.1103/prxquantum.6.020335 · Cited by 3 · see citing works
Relation between the state distinction power and disturbance in quantum measurements
Hamamura, I., & Miyadera, T. (2019) · Journal of Mathematical Physics · doi:10.1063/1.5109446 · Cited by 3 · see citing works
Dequantization Via Quantum Channels
Andersson, A. (2016) · Letters in Mathematical Physics · doi:10.1007/s11005-016-0874-2 · Cited by 3 · see citing works
The Fidelity Alternative and Quantum Measurement SimulationPreprint
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Simple formulation of no-cloning and no-hiding that admits efficient and robust verification
Girling, M., Cîrstoiu, C., & Jennings, D. (2024) · Physical Review Research · doi:10.1103/physrevresearch.6.023090 · Cited by 2 · see citing works
“The most commonly encountered form of incompatibility refers to measurements – position and momentum cannot be simultaneously measured with the same precision – leading to formulations of no information without disturbance [5].”
Fault-Tolerant Quantum Computation with Constant Overhead for General Noise
Christandl, M., Fawzi, O., & Goswami, A. (2025) · PRX Quantum · doi:10.1103/k4cm-pp9p · Cited by 2 · see citing works
Conditional disclosure of secrets with quantum resources
Asadi, V. R., Kuroiwa, K., Leung, D., May, A., Pasterski, S., & Waddell, C. (2025) · Quantum · doi:10.22331/q-2025-10-16-1885 · Cited by 2 · see citing works
Measurement-Disturbance Tradeoff Outperforming Optimal CloningPreprint
Knips, L., Dziewior, J., Hashagen, A.-L. K., Meinecke, J. D. A., Weinfurter, H., & Wolf, M. M. (2018) · arXiv (Cornell University) · doi:10.48550/arxiv.1808.07882 · Cited by 2 · see citing works
Are quantum cryptographic security claims vacuous?Preprint
Renes, J. M., & Renner, R. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2010.11961 · Cited by 2 · see citing works
Nonperturbative gravity corrections to bulk reconstruction
Gesteau, E., & Kang, M. J. (2021) · arXiv · doi:10.48550/arxiv.2112.12789 · Cited by 6
- Authors
- Kretschmann, D., Schlingemann, D., & Werner, R. F.
- Affiliations
- University of Cambridge (GB)
- Institute for Scientific Interchange (IT)
- Technische Universität Braunschweig (DE)
- ORCID
- Werner, Reinhard F.
- Venue
- IEEE Transactions on Information Theory
- Published
- 2008-04
- Volume
- 54
- Issue
- 4
- Pages
- 1708-1717
- ISSN
- 0018-9448 (ISSN-L)
- OpenAlex
- W2102077152
- Cited by
- 122
- References
- 43
- Citations by year
- 2026: 6 · 2025: 9 · 2024: 10 · 2023: 6 · 2022: 9 · 2021: 5 · 2020: 7 · 2019: 5 · 2018: 10 · 2017: 8 · 2016: 7 · 2015: 4 · 2014: 7 · 2013: 5 · 2012: 2
- FWCI
- 10.04
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- IEEE Transactions on Information Theory (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Funders
- European Commission
- Deutscher Akademischer Austauschdienst
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Keywords
- quantum channels, quantum cryptography, thermalization, black hole information loss
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
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