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Conclusive and arbitrarily perfect quantum state transfer using amplitude delaying spin chain channels

Daniel Klaus Burgarth, Sougato Bose

Published Jun 15, 2004• 0 citations
OpenAlex

Abstract

We suggest a protocol for the transfer of quantum information in spin chain channels with a finite recurrence time. By combining a dual-rail encoding with certain measurements at the receiving end, we can get arbitrarily perfect state transfer, i.e. by performing sufficiently many measurements at the receiving end, we can make the probability of perfect state transfer arbitrary close to unity. As an example of such an amplitude delaying channel, we show how two parallel Heisenberg spin chains can be used as quantum wires in solid state quantum computers. Perfect state transfer with a probability of failure lower than delta in a Heisenberg chain of N spin-1/2 particles can be achieved in a timescale of the order of N^(7/3)*|ln(delta)|. Furthermore, the same scheme can be implemented using a single SU(n) chain which is realizable in quantum dot arrays.

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We suggest a protocol for the transfer of quantum information in spin chain channels with a finite recurrence time. By combining a dual-rail encoding with certain measurements at the receiving end, we can get arbitrarily perfect state transfer, i.e. by performing sufficiently many measurements at the receiving end, we can make the probability of perfect state transfer arbitrary close to unity. As an example of such an amplitude delaying channel, we show how two parallel Heisenberg spin chains can be used as quantum wires in solid state quantum computers. Perfect state transfer with a probability of failure lower than delta in a Heisenberg chain of N spin-1/2 particles can be achieved in a timescale of the order of N^(7/3)*|ln(delta)|. Furthermore, the same scheme can be implemented using a single SU(n) chain which is realizable in quantum dot arrays.
We suggest a protocol for perfect quantum communication through spin-chain channels. By combining a dual-rail encoding with measurements only at the receiving end, we can get conclusively perfect state transfer, whose probability of success can be made arbitrarily close to unity. As an example of such an amplitude-delaying channel, we show how two parallel Heisenberg spin chains can be used as quantum wires. Perfect state transfer with a probability of failure lower than PPP in a Heisenberg chain of NNN spin-12\frac{1}{2}21​ particles can be achieved in a timescale of the order of $(0.33\ensuremath{\hbar}∕J){N}^{1.7}\ensuremath{\mid}\mathrm{ln}\phantom{\rule{0.2em}{0ex}}P\ensuremath{\mid}$. We demonstrate that our scheme is more robust to decoherence and nonoptimal timing than any scheme using single spin chains.
We present a communication protocol for chains of permanently coupled qubits which achieves perfect quantum state transfer and which is efficient with respect to the number of chains employed in the scheme. The system consists of M uncoupled identical quantum chains. Local control (gates, measurements) is only allowed at the sending/receiving end of the chains. Under a quite general hypothesis on the interaction Hamiltonian of the qubits, a theorem can be proved which shows that the receiver is able to asymptotically recover the messages by repetitive monitoring of his qubits. We show how two parallel Heisenberg spin chains can be used as quantum wires. Perfect state transfer with a probability of failure lower than P in a Heisenberg chain of N spin-1/2 particles can be achieved in a time scale of the order of [Formula: see text].
In a one-dimensional Heisenberg chain, we show that there are no sets of coupling strengths such that the evolution perfectly transfers a quantum state between the two ends of the chain without the addition of magnetic fields. In lieu of perfect transfer, we consider a range of options for achieving high quality transfer, whether in finite time, or via "pretty good" transfer where one waits long times in the hope of getting arbitrarily close to perfect transfer. In attempting to engineer arbitrarily accurate transfer, we explore a new paradigm that facilitates time estimates for achieving any target accuracy εεε for the transfer.
We investigate the quantum-state transfer on spin-chian channels with random imperfections.Through combining the advantages of two known schemes, the dual-rail spin-chain channels[9] and the particular ihhomogenous spin-chain channel[10], we propose a protocol that can avoid the quantum noises introduced by many unnecessary measurements and can enhance the anti-decoherence ability. The results show that our protocol is more efficient to transfer an arbitrary quantum state than the original one. In particular, we discuss the effects of couplings fluctuations and imperfect initialization on both of the improved scheme and original one.
We suggest a scheme that allows arbitrarily perfect state transfer even in the presence of random fluctuations in the couplings of a quantum chain. The scheme performs well for both spatially correlated and uncorrelated fluctuations if they are relatively weak (say 5%). Furthermore, we show that given a quite arbitrary pair of quantum chains, one can check whether it is capable of perfect transfer by only local operations at the ends of the chains, and the system in the middle being a 'black box'. We argue that unless some specific symmetries are present in the system, it will be capable of perfect transfer when used with dual-rail encoding. Therefore our scheme puts minimal demand not only on the control of the chains when using them, but also on the design when building them.
We exploit a ferromagnetic chain of interacting ddd-level (d>2d>2d>2) particles for arbitrary perfect transfer of quantum states with $(d\ensuremath{-}1)$ levels. The presence of one extra degree of freedom in the Hilbert space of particles, which is not used in encoding, allows one to achieve perfect transfer even in a uniform chain through a repeated measurement procedure with consecutive single site measurements. Apart from the first iteration, for which the time of evolution grows linearly with the size of the chain, in all other iterations, the evolution times are short and do not scale with the length. The success probability of the mechanism grows with the number of repetitions and practically after a few iterations the transfer is accomplished with a high probability.