Perfect transfer of arbitrary states in quantum spin networks
Open accessAbstract
We propose a class of qubit networks that admit perfect state transfer of any two-dimensional quantum state in a fixed period of time. We further show that such networks can distribute arbitrary entangled states between two distant parties, and can, by using such systems in parallel, transmit the higher-dimensional systems states across the network. Unlike many other schemes for quantum computation and communication, these networks do not require qubit couplings to be switched on and off. When restricted to $N$-qubit spin networks of identical qubit couplings, we show that $2\phantom{\rule{0.2em}{0ex}}{\mathrm{log}}_{3}N$ is the maximal perfect communication distance for hypercube geometries. Moreover, if one allows fixed but different couplings between the qubits then perfect state transfer can be achieved over arbitrarily long distances in a linear chain. This paper expands and extends the work done by Christandl et al., Phys. Rev. Lett. 92, 187902 (2004).
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Perfect QST without dynamical controls is possible if couplings between spins are non-uniform.
“However, it has been suggested [12] that perfect QST, without dynamical controls, is possible if we allow the couplings between the spins to be non-uniform.”
From Quantum speed limit for perfect state transfer in one dimension (2006) · cites this paper as [12]
The linear spectrum is the simplest solution to Eq. (5).
“Perhaps the simplest solution to the Eq. (5) is the linear spectrum [12].”
From Quantum speed limit for perfect state transfer in one dimension (2006) · cites this paper as [12]
The optimal solution for perfect state transfer is the one proposed in Ref.[12,22] (the linear spectrum), which is the same as the set of couplings describing spin precession in a static magnetic field.
“We prove that the optimal solution is the one simulating the precession of a spin in a static magnetic field.”
From Quantum speed limit for perfect state transfer in one dimension (2006) · cites this paper as [12]
Under the constraint that evolution time is the same (∆_min ≥ ̃∆_min ≡ 1), the range of any nonlinear spectrum must be at least greater than that of the linear spectrum by one, ∆E ≥ ̃∆E +1 = N, as the ratio between any two ∆_k's must be a rational number.
“Under the constraint that the evolution time to be the same, i.e. ∆ min ≥ ˜ ∆ min ≡ 1, the range of any nonlinear spectrum must be at least greater then that of the linear spectrum by one, ∆ E ≥ ˜ ∆ E +1 = N , as the ratio between any two ∆ k 's must be a rational number [12].”
From Quantum speed limit for perfect state transfer in one dimension (2006) · cites this paper as [12]
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Cites
The Feynman Lectures on Physics
Feynman, R. P., Leighton, R. B., Sands, M., & Treiman, S. B. (1964) · Physics Today · doi:10.1063/1.3051743 · Cited by 2,944 · see citing works
The Feynman Lectures on Physics
Leech, J. W. (1966) · Physics Bulletin · doi:10.1088/0031-9112/17/10/010 · Cited by 1,896 · see citing works
Approximate formulas for some functions of prime numbers
Rosser, J. B., & Schoenfeld, L. (1962) · Illinois Journal of Mathematics · doi:10.1215/ijm/1255631807 · Cited by 1,596 · see citing works
Quantum Communication through an Unmodulated Spin Chain
Bose, S. (2003) · Physical Review Letters · doi:10.1103/physrevlett.91.207901 · Cited by 1,407 · see citing works
Quantum computation and decision trees
Farhi, E., & Gutmann, S. (1998) · Physical Review A · doi:10.1103/physreva.58.915 · Cited by 1,215 · see citing works
Perfect State Transfer in Quantum Spin Networks
Christandl, M., Datta, N., Ekert, A., & Landahl, A. J. (2004) · Physical Review Letters · doi:10.1103/physrevlett.92.187902 · Cited by 1,179 · see citing works
Self-citationSelected Topics in Graph Theory 2
Beineke, L. W., & Wilson, R. J. (1983) · Opus: Research & Creativity (Indiana University – Purdue University Fort Wayne) · Cited by 653 · see citing works
An Example of the Difference Between Quantum and Classical Random Walks
Childs, A. M., Farhi, E., & Gutmann, S. (2002) · Quantum Information Processing · doi:10.1023/a:1019609420309 · Cited by 481 · see citing works
Mirror Inversion of Quantum States in Linear Registers
Albanese, C., Christandl, M., Datta, N., & EKERT, A. K. (2004) · Physical Review Letters · doi:10.1103/physrevlett.93.230502 · Cited by 265 · see citing works
Self-citationPropagation of quantum information through a spin system
Osborne, T. J., & Linden, N. (2004) · Physical Review A · doi:10.1103/physreva.69.052315 · Cited by 236 · see citing works
Niven, I. (1956) · doi:10.5948/9781614440116 · Cited by 224 · see citing works
Electron wavepacket propagation in a chain of coupled quantum dots
Nikolopoulos, G. M., Petrosyan, D., & Lambropoulos, P. (2004) · Journal of Physics Condensed Matter · doi:10.1088/0953-8984/16/28/019 · Cited by 129 · see citing works
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Research works printed but not linked: 3
- [13]C. Moore and A. Russell, Randomization and Approximation Techniques: 6th International Workshop, (RANDOM 2002), Lecture Notes in Computer Science (Springer-Verlag, 2002), vol. 2483, p. 164.
- [14]J. R. Norris, Markov Chains (Cambridge University Press, 1999), chap. 1.7-1.8.
- [17]T. J. Osborne (2003), quant-ph/0312126. · arXiv
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Lewenstein, M., Sanpera, A., Ahufinger, V., Damski, B., Sen(De), A., & Sen, U. (2007) · Advances in Physics · doi:10.1080/00018730701223200 · Cited by 2,104 · see citing works
Universal quantum computation using the discrete-time quantum walk
Lovett, N. B., Cooper, S., Everitt, M., Trevers, M., & Kendon, V. (2010) · Physical Review A · doi:10.1103/physreva.81.042330 · Cited by 510 · see citing works
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Perez-Leija, A., Keil, R., Kay, A., Moya-Cessa, H., Nolte, S., Kwek, L.-C., Rodríguez-Lara, B. M., Szameit, A., & Christodoulides, D. N. (2013) · Physical Review A · doi:10.1103/physreva.87.012309 · Cited by 182 · see citing works
Self-citationQuantum speed limit for perfect state transfer in one dimension
Yung, M.-H. (2006) · Physical Review A · doi:10.1103/physreva.74.030303 · Cited by 128 · see citing works
Localization and its consequences for quantum walk algorithms and quantum communication
Keating, J. P., Linden, N., Matthews, J. C. F., & Winter, A. (2007) · Physical Review A · doi:10.1103/physreva.76.012315 · Cited by 123 · see citing works
Memory-keeping effects and forgetfulness in the dynamics of a qubit coupled to a spin chain
Apollaro, T. J. G., Di Franco, C., Plastina, F., & Paternostro, M. (2011) · Physical Review A · doi:10.1103/physreva.83.032103 · Cited by 106 · see citing works
Universal state transfer on graphs
Cameron, S., Fehrenbach, S., Granger, L., Hennigh, O., Shrestha, S., & Tamon, C. (2014) · Linear Algebra and its Applications · doi:10.1016/j.laa.2014.05.004 · Cited by 26 · see citing works
Tailoring quantum walks in integrated photonic lattices
Raymond, A., Cathala, P., Morassi, M., Lemaître, A., Raineri, F., Ducci, S., & Baboux, F. (2025) · Optics Express · doi:10.1364/oe.571522 · Cited by 1 · see citing works
“Indeed, discrete fractional Fourier transforms can be realized in waveguide arrays through engineered coupling profiles that mimic the J x operator algebra [48–50].”
- Authors
- Christandl, M., Datta, N., Dorlas, T. C., Ekert, A., Kay, A., & Landahl, A. J.
- Affiliations
- University of Cambridge (GB)
- Dublin Institute For Advanced Studies (IE)
- National University of Singapore (SG)
- Hewlett-Packard (United States) (US)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2005-03-14
- Volume
- 71
- Issue
- 3
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2077488909
- Cited by
- 512
- References
- 12
- Citations by year
- 2026: 18 · 2025: 30 · 2024: 21 · 2023: 24 · 2022: 24 · 2021: 29 · 2020: 26 · 2019: 30 · 2018: 17 · 2017: 16 · 2016: 20 · 2015: 18 · 2014: 18 · 2013: 27 · 2012: 29
- FWCI
- 29.50
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- National University of Singapore (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Deutscher Akademischer Austauschdienst
- Engineering and Physical Sciences Research Council
- 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 many-body systems
- Keywords
- perfect state transfer, quantum spin networks, qubit networks, entanglement distribution, quantum communication, linear chains, higher-dimensional quantum states
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