Abstract
The XX model with uniform couplings represents the most natural choice for quantum state transfer through spin chains. Given that it has long been established that single-qubit states cannot be transferred with perfect fidelity in this model, the notion of pretty good state transfer has been recently introduced as a relaxation of the constraints on fidelity. In this paper, we study the transfer of multi-qubit entangled and unentangled states through unmodulated spin chains, and we prove that it is possible to have pretty good state transfer of any multi-particle state. This significantly generalizes the previous results on single-qubit state transfer and opens the way to using uniformly coupled spin chains as short-distance quantum channels for the transfer of arbitrary states of any dimension. Our results could be tested with current technology.
Highlights
The transfer of quantum states from one site to another is a key task in quantum information processing
We focus on the notion of pretty good state transfer (PGST), which has recently been introduced as a significant alternative to perfect state transfer (PST) [21, 22]
We have proved that any multi-qubit state can be transferred with arbitrarily large fidelity through the uniform XX quantum spin chain if and only if the length of the chain is n = p − 1, n = 2p − 1, or n = 2k − 1
Summary
The transfer of quantum states from one site to another is a key task in quantum information processing. Experimental realization of the uniformly coupled XX chain as a quantum channel clearly depends on whether or not many-particle qubit states and, in particular, entangled states, can be transferred with arbitrarily high fidelity through a single chain This topic has already been addressed for PST protocols [13, 26], and it has been established that, in the XX model, PST of arbitrary single-qubit states is a sufficient condition for PST of multi-qubit states. This highlights that the link between quantum dynamics and primality goes beyond the established applications in the field of quantum algorithms
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