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arXiv:1511.02272

Spontaneous Quantum Teleportation in a Quenched Spin Lattice

Nickolas Pilgram, T. D. Gutierrez

Published Nov 7, 2015• 0 citations
arXivHTMLPDF

Abstract

An Ising-inspired numerical model is developed to study spontaneous quantum teleportation in a quenched spin lattice. Quantum teleportation is an operation that can, using entangled pairs of particles, transport a quantum state across arbitrary distances with high fidelity. In doing so, it destroys the state in one location and relocates it to another. In this context, teleportation serves as a long range interaction that randomly introduces correlations and disorder into a lattice. In addition, different Bell state projection and entangled pair swapping models are also explored, as are the effects of decoherence. The results are compared to the standard Ising model in one- and two-dimensions across several thermodynamic parameters versus temperature.

DOI
10.48550/arxiv.1511.02272

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An Ising-inspired numerical model is developed to study spontaneous quantum teleportation in a quenched spin lattice. Quantum teleportation is an operation that can, using entangled pairs of particles, transport a quantum state across arbitrary distances with high fidelity. In doing so, it destroys the state in one location and relocates it to another. In this context, teleportation serves as a long range interaction that randomly introduces correlations and disorder into a lattice. In addition, different Bell state projection and entangled pair swapping models are also explored, as are the effects of decoherence. The results are compared to the standard Ising model in one- and two-dimensions across several thermodynamic parameters versus temperature.
We analyse quantum teleportation (QT) and entanglement swapping (ES) for spin systems. If the permitted operations are restricted to the Ising interaction, plus local rotations and spin measurements, high-fidelity teleportation is achievable for quantum states that are close to the maximally weighted spin state. ES is achieved, and is maximized for a combination of entangled states and Bell measurements that is different from the QT case. If more general local unitary transformations are considered, then it is possible to achieve perfect teleportation and ES.
Isotropic XXXXXX models of one-dimensional spin-1/2 chains are investigated with the aim to elucidate the formal structure and the physical properties that allow these systems to act as channels for long-distance, high-fidelity quantum teleportation. We introduce two types of models: (i) open, dimerized XXXXXX chains, and (ii) open XXXXXX chains with small end bonds. For both models we obtain the exact expressions for the end-to-end correlations and the scaling of the energy gap with the length of the chain. We determine the end-to-end concurrence and show that model (i) supports true long-distance entanglement at zero temperature, while model (ii) supports ``quasi-long-distance'' entanglement that slowly falls off with the size of the chain. Due to the different scalings of the gaps, respectively exponential for model (i) and algebraic in model (ii), we demonstrate that the latter allows for efficient qubit teleportation with high fidelity in sufficiently long chains even at moderately low temperatures.
We use numerical linked cluster expansions (NLCEs) to study correlated lattice systems in one and two dimensions.For fermions in the honeycomb lattice, we study its finite-temperature properties and short-range spin correlations using NLCEs and determinantal quantum Monte Carlo (DQMC) simulations.For the homogeneous system, we analyze a number of thermodynamic quantities, including the entropy, the specific heat, uniform and staggered spin susceptibilities, short-range spin correlations, and the double occupancy at and away from half filling.Employing a local density approximation (LDA), we examine the viability of adiabatic cooling by increasing the interaction strength for homogeneous as well as for trapped systems.We also use NLCEs to study thermodynamic properties of the two-dimensional spin-1/2 Ising, XY, and Heisenberg models with bimodal random-bond disorder on the square and honeycomb lattices.In all cases, the nearest-neighbor coupling between the spins takes values ±J with equal probability.We obtain the disorder averaged (over all disorder configurations) energy, entropy, specific heat, and uniform magnetic susceptibility in each case.These results are compared with the corresponding ones in the clean models.Analytic expressions are obtained for low orders in the expansion of these thermodynamic quantities in inverse temperature.For many-body localization in disordered isolated systems, we study quantum quenches in the thermodynamic limit.By a quantum quench it is meant that the initial state is stationary with respect iii to an initial Hamiltonian, which is suddenly changed to a new (time-independent) Hamiltonian.The latter then drives the (unitary) dynamics of the system.We are interested in the time average of observables after relaxation following the quench, which can be computed under the so-called diagonal ensemble.
The spin-1/2 Ising-Heisenberg model on a diamond-decorated square lattice is exactly solved by the decoration-iteration transformation, which establishes an exact mapping correspondence with the spin-1/2 Ising model on a square lattice with an effective temperature-dependent interaction between the nearest-neighbor spins. Exact results for the pair correlation function and spontaneous magnetization of the Heisenberg spins gained from the exact mapping equivalence allow a straightforward implementation of the concurrence, which may serve as a measure of the bipartite entanglement within decorating Heisenberg spin pairs. It is evidenced that the concurrence gradually diminishes upon increase of temperature above a disordered monomer-dimer ground state until it completely vanishes at a threshold temperature, while the concurrence is either always zero above a spontaneously ordered ferrimagnetic ground state or it shows a peculiar thermally assisted reentrance accompanied with a mutual coexistence of the spontaneous ferrimagnetic long-range order and the thermal entanglement.
Quantum teleportation represents a groundbreaking technique in quantum information science that allows for the transfer of quantum states between distant parties without physically transmitting the particle itself. This phenomenon relies heavily on quantum entanglement, where the states of two particles become correlated in such a way that the state of one can be immediately known by measuring the other. This article explores the role of entangled states in quantum teleportation, explaining their fundamental importance, the mechanisms of their creation, and the practical implications for future quantum communication systems. Furthermore, it examines the theoretical models and experimental implementations that demonstrate the viability of quantum teleportation.
We implement the Wormhole-Inspired Teleportation Protocol (WITP) in a pair of coupled Sachdev-Ye-Kitaev (SYK) models prepared in a thermofield-double state, forming a quantum analog of a traversable wormhole. By varying parameters (temperature $\ensuremath{\beta}$, coupling strength ggg, insertion site, and traversal time ttt) we compare the teleportation fidelity against an analogous protocol using a transverse-field Ising model. We find that the chaotic SYK system consistently yields higher teleportation fidelity than the transverse field Ising model, reflecting the SYK Hamiltonian's pronounced many-body chaos. These enhanced fidelities arise from the SYK's effectively random-matrix dynamics, which improve the coherent information transfer through the wormhole channel. Unlike prior single-qubit benchmarks based on $|0\ensuremath{\rangle}$ inputs, the present work defines and evaluates a genuine quantum-state fidelity for a maximally entangled two-qubit Bell input, using a Pauli-stabilizer formalism that captures entanglement-phase coherence. Our central result is achieved by teleporting a maximally entangled two-qubit Bell state through the wormhole. We introduce a Pauli-stabilizer fidelity measure for the two-qubit message and demonstrate that the Bell-state protocol produces a substantial fidelity boost compared to single-qubit teleportation. Furthermore, we examine the time-resolved fidelity for both single-qubit and two-qubit messages, revealing distinct fluctuation patterns that deepen our understanding of dynamical many-body teleportation processes. Finally, we present an argument that our Bell-state WITP simulations provide a concrete numerical testbed for aspects of the ER = EPR conjecture, by mapping entanglement structure and thermal/coupling dependence to traversability diagnostics in an emergent wormhole geometry.