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arXiv:1604.00780 · Europhysics Letters (EPL)

Quantum state transfer by time reversal in the continuum

Stefano Longhi

Published Mar 1, 2016• 7 citations
arXivHTMLPDF

Abstract

A method for high-fidelity quantum state transfer in a quantum network coupled to a continuum, based on time reversal in the continuum after decay, is theoretically suggested. Provided that the energy spectrum of the network is symmetric around a reference energy and symmetric energy states are coupled the same way to the common continuum, ideal perfect state transfer can be obtained after time reversal. In particular, it is shown that in a linear tight-binding chain a quantum state can be transformed into its mirror image with respect to the center of the chain after a controllable time. As compared to a quantum mirror image based on coherent transport in a static chain with properly tailored inhomogeneous hopping rates, our method does not require hopping rate engineering and is less sensitive to disorder for long transfer times.

DOI
10.1209/0295-5075/113/60006

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A method for high-fidelity quantum state transfer in a quantum network coupled to a continuum, based on time reversal in the continuum after decay, is theoretically suggested. Provided that the energy spectrum of the network is symmetric around a reference energy and symmetric energy states are coupled the same way to the common continuum, ideal perfect state transfer can be obtained after time reversal. In particular, it is shown that in a linear tight-binding chain a quantum state can be transformed into its mirror image with respect to the center of the chain after a controllable time. As compared to a quantum mirror image based on coherent transport in a static chain with properly tailored inhomogeneous hopping rates, our method does not require hopping rate engineering and is less sensitive to disorder for long transfer times.
Quantum information transfer is an important part of quantum information processing. Several proposals for quantum information transfer along linear arrays of nearest-neighbor coupled qubits or spins were made recently. Perfect transfer was shown to exist in two models with specifically designed strongly inhomogeneous couplings. We show that perfect transfer occurs in an entire class of chains, including systems whose nearest-neighbor couplings vary only weakly along the chain. The key to these observations is the Jordan-Wigner mapping of spins to noninteracting lattice fermions that display perfectly periodic dynamics if the single-particle energy spectrum is appropriate. After a half-period of that dynamics, any state is transformed into its mirror image with respect to the center of the chain. The absence of fermion interactions preserves these features at an arbitrary temperature and allows for the transfer of nontrivially entangled states of several spins or qubits.
Hybrid integrated quantum photonic circuits have the potential to scale up the number of quantum nodes and to build a network with distributed quantum-information-processing units at affordable resources. A central need of such systems is to have near-unity success-rate state transfer between the quantum nodes. This turns out to be a grand challenge since stringent conditions of spatial mode matching and time-reversal symmetry between the sending and receiving nodes have to be simultaneously satisfied. Here we devise a type of hybrid quantum node consisting of a single solid-state quantum system and a coupled-cavity structure toward achieving perfect state transfer between two distant nodes connected via waveguides. The hybrid node possesses flexibility in tailoring the temporal profile of the emitted single-photon wave packet without any dynamic modulation. In particular, we show it could emit time-reversal symmetric single-photon wave packets and fully couple the emission to the waveguide, fulfilling the conditions for perfect quantum state transfer. We develop a complete theoretical framework and provide a clear physical picture of the protocol for transferring a superposition state. We show ideally the simple node structures with one, two, and three chain-coupled microring resonators could lead to total success rates of 90.5%, 97.5%, and 99.3%, respectively. We then further discuss the influence of imperfections and experimental realizations of our scheme with integrated quantum photonics.
Achieving quantum state transfer in passive ways can become a powerful asset for scalable quantum networks. Here, we demonstrate how giant atoms coupled to 1D waveguides provide a platform for such a passive, deterministic transfer. Specifically, we show that when the giant atom's extent is comparable to the width of the emitted wavepacket, this wavepacket can be designed to be time-reversal-symmetric by engineering the positions and strengths of atom-waveguide coupling points. We first derive general analytical conditions under which arbitrary qubit decays can be mapped to wavevector-dependent couplings that guarantee perfect state transfer in the continuum limit of infinitely many coupling points. Then, for experimentally relevant configurations with a finite number of coupling points, we optimize the coupling positions and values. We demonstrate that the transfer fidelity can be boosted well beyond the value for a single coupling point (54%), reaching 87% with only two coupling points and exceeding 99% with ten or more. We further analyze the robustness of the protocol against disorder in the coupling points as well as frequency variations of the qubits and extend the formalism to environments with nonlinear dispersion, showing that dispersion-induced distortions can be fully compensated by judiciously chosen setups. Our results establish giant atoms as a powerful platform for realizing high-fidelity quantum state transfer and demonstrate how time-dependent control can be instead encoded into the device design.
Abstract Quantum state transfer (QST) is a fundamental requirement for scalable quantum computation, where fast and reliable communication between distant subsystems is essential. In this work, we present a protocol for QST in linear Ising chains. Starting from a perfect state transfer scheme via a Heisenberg Hamiltonian with inhomogeneous couplings, we adapt it for architectures implementing the transverse-field Ising model by encoding the information in domain walls. The resulting linear Ising chain makes quantum transport experiments accessible to many platforms for analog quantum simulation. We test the protocol for 1-, 2-, and 3- spin states, obtaining high transfer fidelities of up to 0.99 and study the accuracy dependence on the domain wall approximation. These results are the first step in paving the way for an experimental implementation of the protocol.
High-fidelity state transfer is fundamentally limited by time-reversal symmetry: one qubit emits a photon with a certain temporal pulse shape, whereas a second qubit requires the time-reversed pulse shape to efficiently absorb this photon. This limit is often overcome by introducing active elements. Here, we propose an alternative solution: by tailoring the dispersion relation of a waveguide, the photon pulse emitted by one qubit is passively reshaped into its time-reversed counterpart, thus enabling perfect absorption. We analytically derive the optimal dispersion relations in the limit of small and large qubit-qubit separations, and numerically extend our results to arbitrary separations via multiparameter optimization. We further propose a spatially inhomogeneous waveguide that renders the state transfer robust to variations in qubit separations. In all cases, we obtain near-unity transfer fidelity (>= 98%) that is robust against imperfections in parameter values and propagation loss. Our dispersion-engineered waveguide provides a compact and passive route toward on-chip quantum networks, highlighting dispersion as a powerful resource in waveguide quantum electrodynamics.
We study the quantum-state transfer (QST) of a class of tight-bonding Bloch electron systems with mirror symmetry by considering the mode entanglement. Some rigorous results are obtained to reveal the intrinsic relationship between the fidelity of QST and the mirror mode concurrence (MMC), which is defined to measure the mode entanglement with a certain spatial symmetry and is just the overlap of a proper wave function with its mirror image. A complementarity is discovered as the maximum fidelity is accompanied by a minimum of the MMC. At the instant that is just half of the characteristic time required to accomplish a perfect QST, the MMC can reach its maximum value of 1. A large class of perfect QST models with a certain spectral structure is discovered to support our analytical results.