Quantum-information distributors: Quantum network for symmetric and asymmetric cloning in arbitrary dimension and continuous limit
Open accessAbstract
We show that for any Hilbert-space dimension, the optimal $\stackrel{\ensuremath{\rightarrow}}{1}2$ universal quantum cloner can be constructed from essentially the same quantum circuit, i.e., we find a universal design for universal cloners. In the case of infinite dimensions (which includes continuous variable quantum systems) the universal cloner reduces to an essentially classical device. More generally, we construct a universal quantum circuit for distributing qudits in any dimension which acts covariantly under generalized displacements and momentum kicks. The behavior of this covariant distributor is controlled by its initial state. We show that suitable choices for this initial state yield both universal cloners and optimized cloners for limited alphabets of states related by generalized phase-space displacements.
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The two-parameter isometry set U_AB(α, β) generates all possible complementary channel pairs, up to local unitaries.
“However, the two parameter isometry set with U AB = U AB (α, β ) (for α, β ∈ R) (with circuit as in Fig. 3 below) generates all possible complementary channel pairs, up to local unitaries [60].”
From Simple formulation of no-cloning and no-hiding that admits efficient and robust verification (2024) · cites this paper as [60]
The Introduction (p. 2) describes real parameters α and β controlling information transferred to two output systems, and Section III (p. 5) presents a circuit for that distributor. The paper does not establish that this two-parameter construction generates all possible complementary channel pairs up to local unitaries; its stated scope is a covariant information distributor. (LLM, conf=0.85)
Experimental — accuracy not yet measuredFor d_X = d_A = d_B = 2, all isometries can be expressed in the form V(α, β, γ) with 0 ≤ α, β, γ ≤ π.
“For d X = d A = d B = 2, all isometries can be expressed in the above form, where 0 α, β, γ π [60].”
From Simple formulation of no-cloning and no-hiding that admits efficient and robust verification (2024) · cites this paper as [60]
Section II (p. 3) says the paper’s formalism reduces to the qubit case when N = 2. Section III (p. 6) describes a QID input state with real parameters α and β, but the passages found do not address whether all three-qubit isometries have a form V(α, β, γ) or specify the claimed angle ranges. I searched for isometries, γ, and a three-angle qubit parameterization. (LLM, conf=0.75)
Experimental — accuracy not yet measured
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Cites
A single quantum cannot be cloned
Wootters, W. K., & Zurek, W. H. (1982) · Nature · doi:10.1038/299802a0 · Cited by 5,406 · see citing works
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Research works printed but not linked: 5
- [2]See for example: M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000), in press.
- [8]S. Albeverio and S. M. Fei, European Phys. J. B 14 , 669 (2000) [see also quant-ph/9912038 ]. · arXiv
- [14]P. Deuar and W. J. Monroe, Phys. Rev. A 61 , 010396(R) (2000); see also Los Alamos arXive quant-ph/0008032 (2000). · arXiv
- [19]Wan-Li Li, Chuan-Feng Li, Yun-Feng Huang, YongSheng Zhang, Yong Jiang, and Guang-Can Guo, Los Alamos arXive quant-ph/0006032 (2000). · arXiv
- [34]P. A. M. Dirac, The Principles of Quantum Mechanics 4 th edition (Clarendon Press, Oxford, 1964).
Cited by
Sorted by citations
Quantum information with continuous variables
Braunstein, S. L., & van Loock, P. (2005) · Reviews of Modern Physics · doi:10.1103/revmodphys.77.513 · Cited by 3,858 · see citing works
Self-citationUniversal state inversion and concurrence in arbitrary dimensions
Rungta, P., Bužek, V., Caves, C. M., Hillery, M., & Milburn, G. J. (2001) · Physical Review A · doi:10.1103/physreva.64.042315 · Cited by 848 · see citing works
Self-citationWitnessing incompatibility of quantum channels
Carmeli, C., Heinosaari, T., Miyadera, T., & Toigo, A. (2019) · Journal of Mathematical Physics · doi:10.1063/1.5126496 · Cited by 30 · see citing works
Universal asymmetric quantum cloning revisited
Hashagen, A.-L. (2017) · Quantum Information and Computation · doi:10.26421/qic17.9-10-2 · Cited by 9 · see citing works
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
- Authors
- Braunstein, S. L., Bužek, V., & Hillery, M.
- Affiliations
- Bangor University (GB)
- The University of Queensland (AU)
- Hunter College (US)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2001-04-18
- Volume
- 63
- Issue
- 5
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2164854511
- Cited by
- 108
- References
- 1
- Citations by year
- 2025: 4 · 2024: 2 · 2023: 1 · 2022: 5 · 2021: 2 · 2020: 1 · 2019: 2 · 2018: 6 · 2017: 1 · 2016: 5 · 2015: 2 · 2014: 5 · 2013: 5 · 2012: 4
- FWCI
- 9.31
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Keywords
- quantum cloning, quantum information distribution, qudits, continuous-variable quantum systems, momentum kick, quantum networks
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