Quantum Communication through an Unmodulated Spin Chain
Open accessAbstract
We propose a scheme for using an unmodulated and unmeasured spin chain as a channel for short distance quantum communications. The state to be transmitted is placed on one spin of the chain and received later on a distant spin with some fidelity. We first obtain simple expressions for the fidelity of quantum state transfer and the amount of entanglement sharable between any two sites of an arbitrary Heisenberg ferromagnet using our scheme. We then apply this to the realizable case of an open ended chain with nearest neighbor interactions. The fidelity of quantum state transfer is obtained as an inverse discrete cosine transform and as a Bessel function series. We find that in a reasonable time, a qubit can be directly transmitted with better than classical fidelity across the full length of chains of up to 80 spins. Moreover, our channel allows distillable entanglement to be shared over arbitrary distances.
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TL;DR
The paper proposes using an unmodulated, unmeasured spin chain as a channel for short-distance quantum communication by placing a qubit on one spin and retrieving it later on a distant spin. It derives simple fidelity and entanglement formulas and finds high-fidelity state transfer over chains up to 80 spins, plus distillable entanglement over arbitrarily large distances.
Key findings
- For an open-ended nearest-neighbor Heisenberg chain, perfect quantum state transfer occurs for \(N=2\) and \(N=4\) (\(F=1.000\) to 3 decimal places), near-perfect for \(N=8\) (\(F=0.994\)), and fidelity exceeds \(0.9\) for \(N=7,10,11,13,14\); an \(N=80\) chain exceeds the classical transmission fidelity \(2/3\) within \(T_{\max}=4000/J\).
- The channel can share distillable entanglement; for an 80-spin chain the maximum sharable entanglement is about \(E=0.45\). For very long chains with \(t_0=(N+0.8089N^{1/3})/2J\), \(E\) ranges from \(0.135\) for \(N=1000\) to \(1.35\times10^{-4}\) for \(N=10^{12}\), scaling as \(N^{-1/3}\).
- For a ring of \(2N\) spins with diametrically opposite sites, the maxima of entanglement coincide with those of the line, so a 4-spin ring allows perfect communication between diametrically opposite sites.
- General formulas are given for fidelity and entanglement in terms of the single transition amplitude \(f^N_{r,s}(t_0)=\langle r|\exp\{-iH_Gt_0\}|s\rangle\).
Methods
- Theoretical protocol on an arbitrary graph of \(N\) spins with ferromagnetic isotropic Heisenberg interactions, static magnetic fields, and couplings; the chain is initially cooled to its ground state \(|00\ldots0\rangle\), Alice replaces the sender spin with an unknown qubit, and Bob retrieves the receiver spin after a chosen time \(t_0\).
- For the linear open chain, the Hamiltonian uses \(J_{ij}=(J/2)\delta_{i+1,j}\) and \(B_i=B\); the transition amplitude is expressed via an inverse discrete cosine transform, and maximum \(|f^N_{N,1}(t_0)|\) is numerically evaluated for \(N=2\) to \(80\) over \(t_0\in[0,4000/J]\).
- For very long chains, a Bessel-function expansion and Airy-function approximation are used to choose a fixed \(t_0\); the ring case is treated via an inverse discrete Fourier transform.
Limitations
- The paper states no dedicated limitations section. It notes that the numerical search for \(t_0\) may return any of several times where the maxima of \(|f^N_{N,1}(t_0)|\) to 3 decimal places are attained, not necessarily the least time, and that direct state-transfer results hold only when directly transmitting over a distance; otherwise entanglement sharing can be distilled.
- Evident from the text: the scheme assumes an initial ground state, detachable sender and receiver spins, no individual access or modulation of channel spins, and a magnetic-field choice making the phase a multiple of \(2\pi\); the quantitative results are for ideal Heisenberg models, with direct-fidelity numerics only up to \(N=80\).
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- Findingown data§ Quantum Communication Through an Unmodulated Spin Chain · p. 3
For N=8, the open-ended chain gives near perfect quantum state transfer with fidelity F=0.994.
“N = 8 gives near perfect ( F = 0 . 994).”
Quote in the paperSubstantial claim- The authors state this as an assumption: The spin chain is initially cooled to its ground state |0...0>, with each spin in the spin-down state aligned along the -z direction.
- The authors state this as an assumption: The sender and receiver spins are detachable from the chain.
- The authors state this as an assumption: The magnetic fields B_i can be chosen such that γ is a multiple of 2π for any given t0.
- Findingown data§ Quantum Communication Through an Unmodulated Spin Chain · p. 3
For open-ended chains up to N=21, fidelities are lower when N is divisible by 3 compared to N+1 and N+2.
“Till N = 21 we observe that the fidelities are lower when N is divisible by 3 in comparison to the fidelities for N +1 and N +2.”
Quote in the paperNot a substantial claim- The authors state this as an assumption: The spin chain is initially cooled to its ground state |0...0>, with each spin in the spin-down state aligned along the -z direction.
- The authors state this as an assumption: The sender and receiver spins are detachable from the chain.
- The authors state this as an assumption: The magnetic fields B_i can be chosen such that γ is a multiple of 2π for any given t0.
- Findingcitation§ Quantum Communication Through an Unmodulated Spin Chain · p. 4
For benzene molecules with J_ij = δ_{i⊕1,j}/4 + δ_{i⊕2,j}/(12√3) + δ_{i⊕3,j}/32, the fidelity F for r-s=3 at t0=130 is 0.793.
“Benzene molecules (with NMR probes possible) with J ij = δ i ⊕ 1 ,j 4 + δ i ⊕ 2 ,j 12 √ 3 + δ i ⊕ 3 ,j 32 , still have | ˜ m 〉 R as eigenstates [16]. F can thus be calculated by an IDFT to be 0 . 793 for r -s = 3 at t 0 = 130.”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [16] G. J. Bowden, J. Math. Chem. 31 , 363 (2002).
Not checked in the free run.
- Findingown data§ Quantum Communication Through an Unmodulated Spin Chain · p. 3
For N=4, the open-ended chain gives perfect quantum state transfer with fidelity F=1.000 to 3 decimal places.
“N = 4 gives perfect ( F = 1 . 000) quantum state transfer to 3 decimal places”
Quote in the paperNot a substantial claim- The authors state this as an assumption: The spin chain is initially cooled to its ground state |0...0>, with each spin in the spin-down state aligned along the -z direction.
- The authors state this as an assumption: The sender and receiver spins are detachable from the chain.
- The authors state this as an assumption: The magnetic fields B_i can be chosen such that γ is a multiple of 2π for any given t0.
- Findingreasoning§ Quantum Communication Through an Unmodulated Spin Chain · p. 3
For an open-ended chain with nearest-neighbor interactions of equal strength and uniform magnetic field, the transition amplitude f^N_{r,s}(t0) is given by an inverse discrete cosine transform.
“where, v m = a m cos { π 2 N ( m -1)(2 r -1) } e -iE m t 0 and IDCT s ( v m ) = ∑ N m =1 a m v m cos { π 2 N ( m -1)(2 s -1) } is the s th element of the inverse discrete cosine transform of the vector { v m } .”
Quote in the paperSubstantial claim- The authors state this as an assumption: The spin chain is initially cooled to its ground state |0...0>, with each spin in the spin-down state aligned along the -z direction.
- The authors state this as an assumption: The sender and receiver spins are detachable from the chain.
- The authors state this as an assumption: The magnetic fields B_i can be chosen such that γ is a multiple of 2π for any given t0.
- Findingown data§ Quantum Communication Through an Unmodulated Spin Chain · p. 3
For open-ended chains, the fidelity exceeds 0.9 for N=7,10,11,13 and 14.
“The fidelity also exceeds 0 . 9 for N = 7 , 10 , 11 , 13 and 14.”
Quote in the paperNot a substantial claim- The authors state this as an assumption: The spin chain is initially cooled to its ground state |0...0>, with each spin in the spin-down state aligned along the -z direction.
- The authors state this as an assumption: The sender and receiver spins are detachable from the chain.
- The authors state this as an assumption: The magnetic fields B_i can be chosen such that γ is a multiple of 2π for any given t0.
- Findingown data§ Quantum Communication Through an Unmodulated Spin Chain · p. 3
For an 80-spin open-ended chain, the maximum sharable entanglement E is about 0.45.
“If one first shares entanglement through the channel, then the amount of entanglement E is about 0 . 45 for an 80 spin chain.”
Quote in the paperSubstantial claim- The authors state this as an assumption: The spin chain is initially cooled to its ground state |0...0>, with each spin in the spin-down state aligned along the -z direction.
- The authors state this as an assumption: The sender and receiver spins are detachable from the chain.
- The authors state this as an assumption: The magnetic fields B_i can be chosen such that γ is a multiple of 2π for any given t0.
- Findingown data§ Quantum Communication Through an Unmodulated Spin Chain · p. 3
For open-ended chains with N from 2 to 80, the maximum fidelity of quantum state transfer over t0 in [0,4000/J] exceeds the classical fidelity threshold 2/3 for N=80.
“The plot also shows that a chain of N as high as 80 exceeds the highest fidelity for classical transmission of the state i.e., 2 / 3 [12] in the time interval probed by us.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [12] M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Rev. A 60 , 1888 (1999). source
Not checked in the free run.
- The authors state this as an assumption: The spin chain is initially cooled to its ground state |0...0>, with each spin in the spin-down state aligned along the -z direction.
- The authors state this as an assumption: The sender and receiver spins are detachable from the chain.
- The authors state this as an assumption: The magnetic fields B_i can be chosen such that γ is a multiple of 2π for any given t0.
- Interpretationcitation§ Quantum Communication Through an Unmodulated Spin Chain · p. 2
The spin chain acts as an amplitude damping quantum channel.
“The spin chain then acts as an amplitude damping quantum channel [8, 9].”
Quote in the paperSubstantial claim0 of 2 sources checked- cites [8] source
Not checked in the free run.
- cites [9] M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information , Cambridge University Press, 2000. source
Not checked in the free run.
- The authors state this as an assumption: The spin chain is initially cooled to its ground state |0...0>, with each spin in the spin-down state aligned along the -z direction.
- The authors state this as an assumption: The sender and receiver spins are detachable from the chain.
- The authors state this as an assumption: The magnetic fields B_i can be chosen such that γ is a multiple of 2π for any given t0.
- Interpretationcitation§ Quantum Communication Through an Unmodulated Spin Chain · p. 4
A 4-spin ring allows perfect communication between diametrically opposite sites.
“An immediate implication is that a 4 spin ring allows perfect communication between diametrically opposite sites (because a 2 spin line does [11]).”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [11] D. Loss and D. P. DiVincenzo, Phys. Rev. A 57 , 120 (1998). source
Not checked in the free run.
- The authors state this as an assumption: The spin chain is initially cooled to its ground state |0...0>, with each spin in the spin-down state aligned along the -z direction.
- The authors state this as an assumption: The sender and receiver spins are detachable from the chain.
- The authors state this as an assumption: The magnetic fields B_i can be chosen such that γ is a multiple of 2π for any given t0.
- Interpretationreasoning§ Quantum Communication Through an Unmodulated Spin Chain · p. 2
Because the total spin-z operator commutes with the Hamiltonian, the state |s> only evolves to states |j> with one flipped spin.
“As [ H G , ∑ N i =1 σ i z ] = 0, the state | s 〉 only evolves to states | j 〉”
Quote in the paperSubstantial claim - Interpretationreasoning§ Quantum Communication Through an Unmodulated Spin Chain · p. 4
For a ring of 2N spins with diametrically opposite sites, the maxima of entanglement E coincide with those of the open-ended line.
“Eqs.(11) and (13), and the nature of Bessel functions, imply that the maxima of E coincide for the line and the ring.”
Quote in the paperSubstantial claim- The authors state this as an assumption: The spin chain is initially cooled to its ground state |0...0>, with each spin in the spin-down state aligned along the -z direction.
- The authors state this as an assumption: The sender and receiver spins are detachable from the chain.
- The authors state this as an assumption: The magnetic fields B_i can be chosen such that γ is a multiple of 2π for any given t0.
- Interpretationreasoning§ Quantum Communication Through an Unmodulated Spin Chain · p. 4
Using a ring, one can communicate as efficiently over distance r-s=N as an open-ended line over distance r-s=N-1.
“This means that by using a ring you can communicate as efficiently over a distance r -s = N as you can with a open ended line over a distance r -s = N -1.”
Quote in the paperSubstantial claim- The authors state this as an assumption: The spin chain is initially cooled to its ground state |0...0>, with each spin in the spin-down state aligned along the -z direction.
- The authors state this as an assumption: The sender and receiver spins are detachable from the chain.
- The authors state this as an assumption: The magnetic fields B_i can be chosen such that γ is a multiple of 2π for any given t0.
- Interpretationreasoning§ Quantum Communication Through an Unmodulated Spin Chain · p. 2
For any non-zero transition amplitude f^N_{r,s}(t0), however small, some entanglement can be shared through the channel.
“Thus, for any non-zero f N r,s ( t 0 ) (however small), some entanglement can be shared through the channel.”
Quote in the paperSubstantial claim- The authors state this as an assumption: The spin chain is initially cooled to its ground state |0...0>, with each spin in the spin-down state aligned along the -z direction.
- The authors state this as an assumption: The sender and receiver spins are detachable from the chain.
- The authors state this as an assumption: The magnetic fields B_i can be chosen such that γ is a multiple of 2π for any given t0.
- Interpretationnone given§ Quantum Communication Through an Unmodulated Spin Chain · p. 4
The protocol allows quantum communication between adjacent quantum computers without interfacing different physical systems.
“It allows quantum communication between adjacent quantum computers without interfacing different physical systems.”
Quote in the paperSubstantial claim - Interpretationreasoning§ Quantum Communication Through an Unmodulated Spin Chain · p. 2
To maximize the average fidelity, the magnetic fields B_i must be chosen such that γ is a multiple of 2π.
“To maximize the above average fidelity, we must choose the magnetic fields B i such that γ is a multiple of 2 π .”
Quote in the paperSubstantial claim- The authors state this as an assumption: The magnetic fields B_i can be chosen such that γ is a multiple of 2π for any given t0.
- May combine two claims. 5
- The quote only partly states this claim. 1
- Classified as probably not a substantial claim. 2
May combine two claims. The quote only partly states this claim.
Findingreasoning§ Quantum Communication Through an Unmodulated Spin Chain · p. 2For an arbitrary Heisenberg ferromagnet, the fidelity of quantum state transfer and the amount of entanglement sharable between any two sites are given by simple expressions in terms of the single transition amplitude f^N_{r,s}(t0).
“Eqs.(6) and (8) are exceptionally simple formulas for the fidelity of quantum communications and the entanglement shared through our spin-graph channel in terms of single transition amplitude f N r,s ( t 0 ).”
Quote in the paperSubstantial claim- The authors state this as an assumption: The spin chain is initially cooled to its ground state |0...0>, with each spin in the spin-down state aligned along the -z direction.
- The authors state this as an assumption: The sender and receiver spins are detachable from the chain.
- The authors state this as an assumption: The magnetic fields B_i can be chosen such that γ is a multiple of 2π for any given t0.
May combine two claims.
Premisecitation§ Quantum Communication Through an Unmodulated Spin Chain · p. 2The entanglement shared through the channel can be distilled into pure singlets and used for teleportation.
“This entanglement, being that of a 2 × 2 system, can also be distilled [7] into pure singlets and used for teleportation.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [7] M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Rev. Lett. 78 , 574-577 (1997). source
Not checked in the free run.
Probably not a substantial claim: may not pass S3 (load-bearing).
Interpretationcitation§ Quantum Communication Through an Unmodulated Spin Chain · p. 4The scheme's principles should be testable in simulated open-ended Heisenberg chains in a 1D optical lattice.
“Principles of the scheme should also be testable in simulated open ended Heisenberg chains in a 1D optical lattice [17].”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [17]
Not checked in the free run.
May combine two claims.
Interpretationcitation§ Quantum Communication Through an Unmodulated Spin Chain · p. 1The spin-chain channel does not require the ability to switch interactions on and off, nor does it require modulation by external fields.
“neither does the spin chain channel require the ability to switch interactions 'on' and 'off' (often a problem in quantum computer implementations [4, 5]), nor does it require any modulation by external fields (essential for quantum computation).”
Quote in the paperSubstantial claim0 of 2 sources checkedMay combine two claims.
Interpretationreasoning§ Quantum Communication Through an Unmodulated Spin Chain · p. 4For large N, the maximum entanglement E scales as N^{-1/3} and is achieved at a time t0 linear in N.
“Thus for any fi nite N , however large, the chain allows us to distribute entanglement of the order N -1 / 3 in a time t 0 linear in N .”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [13] source
Not checked in the free run.
- The authors state this as an assumption: The spin chain is initially cooled to its ground state |0...0>, with each spin in the spin-down state aligned along the -z direction.
- The authors state this as an assumption: The sender and receiver spins are detachable from the chain.
- The authors state this as an assumption: The magnetic fields B_i can be chosen such that γ is a multiple of 2π for any given t0.
Classified as probably not a substantial claim. May combine two claims.
Interpretationnone given§ Quantum Communication Through an Unmodulated Spin Chain · p. 4The scheme can be implemented in Josephson junction arrays, excitons in quantum dots, and real 1D magnets without the elaborate control required for quantum computation.
“Our scheme can be implemented in such systems without the elaborate control required for quantum computation.”
Quote in the paperSubstantial claim
The authors state this as an assumption.
The spin chain is initially cooled to its ground state |0...0>, with each spin in the spin-down state aligned along the -z direction.
“We assume that initially the system is initially cooled to its ground state | 0 〉 = | 000 ... 0 〉 where | 0 〉 denotes the spin down state (i.e., spin aligned along -z direction) of a spin.”
The authors state this as an assumption.
The sender and receiver spins are detachable from the chain.
“It is also assumed that the sender and receiver spins are detachable from the chain.”
The authors state this as an assumption.
The magnetic fields B_i can be chosen such that γ is a multiple of 2π for any given t0.
“Assuming this special choice of magnetic field value (which can always be made for any given t 0 ) to be a part of our protocol”
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
By tailoring hopping rates between waveguides of an array to match the matrix elements of the J_x angular momentum operator, perfect quantum state transfer becomes possible.
“Inspired by spin chains [100-102] (see figure 12(a)), by tailoring the hopping rates between the waveguides of an array to match the matrix elements of the J x angular momentum operator, such a task becomes possible.”
From Integrated photonic quantum walks (2020) · cites this paper as [100]
The paper reports perfect state transfer for certain short spin chains (p. 3), so it supports that limited outcome. But its open-chain model uses equal-strength nearest-neighbor interactions (p. 2); it does not describe waveguide hopping rates tailored to Jₓ matrix elements as the means of achieving transfer. (LLM, conf=0.83)
Experimental — accuracy not yet measuredImperfect QST over a uniform spin chain is impossible for long chains.
“Imperfect QST [8, 9] over a uniform spin chain was studied numerically, showing that perfect state transfer is impossible for long chains.”
From Quantum speed limit for perfect state transfer in one dimension (2006) · cites this paper as [9]
The speed limit for 1D QST could be overcome by increasing either network complexity or Hamiltonian complexity if not confined to nearest-neighbor interactions in one dimension.
“We lastly comment that such speed limit, if not confined with nearest-neighbor interactions in one dimension, could be overcome by increasing either the network complexity [9] or the Hamiltonian complexity [26].”
From Quantum speed limit for perfect state transfer in one dimension (2006) · cites this paper as [9]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
Each contradiction between two passages listed here was confirmed by an independent check.
General-site transition amplitude replaced by an end-to-end amplitude
MinorThe paper says its fidelity formula applies to transfer between arbitrary sender and receiver sites s and r, but then says to replace that transition amplitude with the amplitude specifically from site 1 to site N. Choosing the magnetic field to remove a phase does not make those different site-to-site amplitudes equal.
“we can simply replace f N r,s ( t 0 ) by | f N N, 1 ( t 0 ) | in Eq.(5).”
“We first obtain simple expressions for the fidelity of quantum state transfer and the amount of entanglement sharable between any two sites of an arbitrary Heisenberg ferromagnet using our scheme.”
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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
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Li, Y., Caruso, F., Gauger, E., & Benjamin, S. C. (2015) · New Journal of Physics · doi:10.1088/1367-2630/17/1/013057 · Cited by 19 · see citing works
Quantum Turbo Decoding for Quantum Channels Exhibiting Memory
Mohd Izhar, M. A., Babar, Z., Nguyen, H. V., Botsinis, P., Alanis, D., Chandra, D., Ng, S. X., & Hanzo, L. (2018) · IEEE Access · doi:10.1109/access.2018.2808373 · Cited by 9 · see citing works
- Authors
- Bose, S.
- Affiliations
- California Institute of Technology (US)
- Corresponding author
- Bose, Sougato
- ORCID
- Bose, Sougato
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2003-11-10
- Volume
- 91
- Issue
- 20
- Pages
- 207901-207901
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W1983655155
- Semantic Scholar
- 83fc7012e35663eaa3e0293a5cf815fa1afea072
- Cited by
- 1,407
- References
- 7
- Citations by year
- 2026: 42 · 2025: 78 · 2024: 54 · 2023: 70 · 2022: 71 · 2021: 59 · 2020: 64 · 2019: 68 · 2018: 52 · 2017: 67 · 2016: 74 · 2015: 72 · 2014: 64 · 2013: 73 · 2012: 69
- FWCI
- 35.81
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- UCL Discovery (University College London) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Keywords
- quantum state transfer, Heisenberg ferromagnet, quantum channels, entanglement distribution, distillable entanglement, fidelity, discrete cosine transform, Bessel function series, nearest-neighbor interactions
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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.
Claims read by deepseek-v4.1-flash under definition version 3 (extract-v3) on 2026-10-06.
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