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 this paper we build on the ideas presented in previous works for perfectly transferring a quantum state between opposite ends of a spin chain using a fixed Hamiltonian. While all previous studies have concentrated on nearest-neighbor couplings, we demonstrate how to incorporate additional terms in the Hamiltonian by solving an inverse eigenvalue problem. We also explore issues relating to the choice of the eigenvalue spectrum of the Hamiltonian, such as the tolerance to errors and the rate of information transfer.
Much work has been done in the last two decades on the topic of quantum state transfer in a quantum spin network. One can model such a system of interacting qubits using an undirected graph, and studying vertex-to-vertex dynamics. This setup has recently been relaxed to allow for dynamics between linear combinations of two vertex states, i.e.\ from
u=ea+seb to
μ=eα+reβ, where
r=s is either
−1 (which corresponds to pair state transfer) or
+1 (which corresponds to plus state transfer), or more recently
r=s is taken to be any real number (which corresponds to
s-pair state transfer).
Here, we broaden the investigation of
s-pair state transfer to \textit{perfect
(s,r)-state transfer}, which is perfect state transfer from
u=ea+seb to
μ=eα+reβ (up to some dilation) where
r,s∈C. We identify infinite families of graphs with perfect
(s,r)-state transfer and provide characterizations of cases when
∣r∣=∣s∣ and when
∣r∣=∣s∣, showing situations when the degree of entanglement between vertex states is preserved, and when it is not preserved. The latter is particularly important as it represents perfect state transfer from an entangled pair of qubits to another one where the degree of entanglement need not be the same\mdash in fact, it can be set up so as to ``boost'' (increase) entanglement. We provide an algorithm that finds the vector with two nonzero entries that maximizes the fidelity of transfer for a fixed time
t starting from a given
s-pair state
u. Finally, we provide a sensitivity analysis, with respect to readout time errors, of perfect
(s,r)-state transfer.
We demonstrate that perfect state transfer can be achieved using an engineered spin chain and clean local end-chain operations, without requiring the initialization of the state of the medium nor fine-tuning of control pulses. This considerably relaxes the prerequisites for obtaining reliable transfer of quantum information across interacting-spin systems. Moreover, it allows us to shed light on the interplay among purity, entanglement, and operations on a class of many-body systems potentially useful for quantum information processing tasks.
We present a perfect state transfer protocol via a qubit chain with the evolution governed by the
xx Hamiltonian. In contrast to the recent protocol announced in Phys. Rev. Lett. 101, 230502 (2008), our method does not demand any remote-cooperated initialization and sending classical information about measurement outcomes. We achieve the perfect state transfer only with the assumption of access to two spins at each end of the chain, while the initial state of the whole chain is irrelevant.
When creating a quantum system whose natural dynamics provide useful computational operations, designers have two key tools at their disposal: the (constrained) choice of both the Hamiltonian and the the initial state of the system (an encoding). Typically, we fix the design and utilize encodings to tolerate experimental imperfections. In this paper we describe a vital insight that incorporates encoding into the design process, with radical consequences. This transforms the study of perfect state transfer from the unrealistic scenario of specifying the Hamiltonian of an entire system to the far more realistic situation of being given a Hamiltonian over which we had no choice in the design, and designing time control of just two parameters to still achieve perfect transfer. Published by the American Physical Society 2024