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arXiv:1701.00647

Quantum state transfer on distance regular spin networks with intrinsic decoherence

Rahime Sufiani, Pedram, A.

Published Jan 3, 2017• 0 citations
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Abstract

By considering distance-regular graphs as spin networks, we investigate the state transfer fidelity in this class of networks. The effect of environment on the dynamics of state transfer is modeled using Milburn's intrinsic decoherence [G. J. Milburn, Phys. Rev. A 44, 5401 (1991)]. We consider a particular type of spin Hamiltonians which are extended version of those of Christandl et al [Phys. Rev. A 71, 032312 (2005)]. It is shown that decoherence destroys perfect communication channels. Using optimal coupling strengths derived by Jafarizadeh and Sufiani [Phys. Rev. A 77, 022315 (2008)], we show that destructive effect of environment on the communication channel increases by increasing the decoherence rate, however the state transfer fidelity reaches a steady value as time approaches infinity which is independent of the decoherence rate. Moreover, it is shown that for a given decoherence rate, the fidelity of transfer decreases by increasing the distance between the sender and the receiver.

DOI
10.48550/arxiv.1701.00647

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By considering distance-regular graphs as spin networks, we investigate the state transfer fidelity in this class of networks. The effect of environment on the dynamics of state transfer is modeled using Milburn's intrinsic decoherence [G. J. Milburn, Phys. Rev. A 44, 5401 (1991)]. We consider a particular type of spin Hamiltonians which are extended version of those of Christandl et al [Phys. Rev. A 71, 032312 (2005)]. It is shown that decoherence destroys perfect communication channels. Using optimal coupling strengths derived by Jafarizadeh and Sufiani [Phys. Rev. A 77, 022315 (2008)], we show that destructive effect of environment on the communication channel increases by increasing the decoherence rate, however the state transfer fidelity reaches a steady value as time approaches infinity which is independent of the decoherence rate. Moreover, it is shown that for a given decoherence rate, the fidelity of transfer decreases by increasing the distance between the sender and the receiver.
We consider an unmodulated linear spin chain composed of two qubits at the ends, which undergo nearest-neighbor interactions, with an arbitrary spin between them. The state of the qubit on one end is to be transmitted through the arbitrary spin and is received by the qubit on the other end with some fidelity. We look at the behavior of the average f idelity of state transfer through time as affected by the spin quantum number of the arbitrary spin in between the qubits. We f ind that the higher the spin quantum number becomes, the earlier it takes to achieve perfect or nearly perfect state transfer. Moreover, when the channel with arbitrary spin is subjected to environment interaction, results from the calculation of average fidelity suggest that increasing the spin quantum number of the channel provides a countermeasure to the effects of decoherence induced by the environment.
An open ended spin chain can serve as a quantum data bus for the coherent transfer of quantum state information. In this paper, we investigate the efficiency of such quantum spin channels which work in a decoherence environment. Our results show that the decoherence will significantly reduce the fidelity of quantum communication through the spin channels. Generally speaking, as the distance increases, the decoherence effects become more serious, which will put some constraints on the spin chains for long distance quantum state transfer.
Christandl et al. have noted that the ddd-dimensional hypercube can be projected to a linear chain with d+1d+1d+1 sites so that, by considering fixed but different couplings between the qubits assigned to the sites, the perfect state transfer (PST) can be achieved over arbitrarily long distances in the chain [Phys. Rev. Lett. 92, 187902 (2004); Phys. Rev. A 71, 032312 (2005)]. In this work we consider distance-regular graphs as spin networks and note that any such network (not just the hypercube) can be projected to a linear chain and so can allow PST over long distances. We consider some particular spin Hamiltonians which are the extended version of those of Christandl et al. Then, by using techniques such as stratification of distance-regular graphs and spectral analysis methods, we give a procedure for finding a set of coupling constants in the Hamiltonians so that a particular state initially encoded on one site will evolve freely to the opposite site without any dynamical control, i.e., we show how to derive the parameters of the system so that PST can be achieved. It is seen that PST is only allowed in distance-regular spin networks for which, starting from an arbitrary vertex as reference vertex (prepared in the initial state which we wish to transfer), the last stratum of the networks with respect to the reference state contains only one vertex; i.e., stratification of these networks plays an important role which determines in which kinds of networks and between which vertices of them, PST can be allowed. As examples, the cycle network with even number of vertices and ddd-dimensional hypercube are considered in details and the method is applied for some important distance-regular networks.
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 NNN-qubit spin networks of identical qubit couplings, we show that 2log3N2\phantom{\rule{0.2em}{0ex}}{\mathrm{log}}_{3}N2log3​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).
Following the prescription of Ref. \cite{PST} in which perfect state transference (PST) of a qubit over distance regular spin networks was discussed, in this paper PST of an arbitrary ddd-level quantum state (qudit) over antipodes of more general networks called pseudo distance-regular networks, is investigated. In fact, the spectral analysis techniques used in the previous work \cite{PST}, and algebraic structures of pseudo distance-regular graphs are employed to give an explicit formula for suitable coupling constants in the Hamiltonians so that the state of a particular qudit initially encoded on one site will evolve freely to the opposite site without any dynamical control, i.e., we show that how to derive the parameters of the system so that PST can be achieved. Keywords:Perfect state transfer, ddd-level quantum state, Stratification, Pseudo-distance-regular network PACs Index: 01.55.+b, 02.10.Yn