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Physica Scripta

Entanglement teleportation between distinct decohered qubits mediated via single and double Majorana wire(s)

Ngwa Engelbert Afuoti, Lukong Cornelius Fai, Ateuafack Mathurin, Georges Collince Fouokeng, Jules Carsimir Ngana

Published Oct 16, 2019• 1 citation
Publisher

Abstract

Abstract We investigate the decoherence effects from a spin environment on two detached qubits coupled by a single Majorana wire (SMW) and double Majorana wires (DMWs) respectively when teleporting entanglement between the distinct qubits. The role of the composite system parameters on entanglement and entanglement teleportation are examined. Our results shows that strong coupling between the spin environment and the dots modifies the coupling between the qubits and the Majorana fermions (MFs) thus lifting the degenerate zero energy state for the case of the SMW. The SMW is seen to undergo a topological quantum phase transition as seen from the stable asymptotic increase and decrease in its dynamics as the coupling between the qubits and the MFs are varied. We observed that the DMWs are robust against quantum fluctuations of the spin environment with a characteristic cyclic beating phenomenon. This behavior shows that information is mediated via a channel endowed with the anti-ferromagnetic phase and the topological phase that harbors the Majorana zero-energy state. We probe the extent to which the capacitive and pure coupling that defines the DMWs should be tune for entanglement generation between the two sites and thus enhancement of the teleported state. Our description for the Majorana zero modes is in the spin model for spin based quantum applications.

DOI
10.1088/1402-4896/ab4e30

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Abstract We investigate the decoherence effects from a spin environment on two detached qubits coupled by a single Majorana wire (SMW) and double Majorana wires (DMWs) respectively when teleporting entanglement between the distinct qubits. The role of the composite system parameters on entanglement and entanglement teleportation are examined. Our results shows that strong coupling between the spin environment and the dots modifies the coupling between the qubits and the Majorana fermions (MFs) thus lifting the degenerate zero energy state for the case of the SMW. The SMW is seen to undergo a topological quantum phase transition as seen from the stable asymptotic increase and decrease in its dynamics as the coupling between the qubits and the MFs are varied. We observed that the DMWs are robust against quantum fluctuations of the spin environment with a characteristic cyclic beating phenomenon. This behavior shows that information is mediated via a channel endowed with the anti-ferromagnetic phase and the topological phase that harbors the Majorana zero-energy state. We probe the extent to which the capacitive and pure coupling that defines the DMWs should be tune for entanglement generation between the two sites and thus enhancement of the teleported state. Our description for the Majorana zero modes is in the spin model for spin based quantum applications.
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Abstract Based on the many-particle-number-state treatment for transport through a pair of Majorana zero modes (MZMs) which are coupled to the leads via two quantum dots, we identify that the reason for zero cross correlation of currents at uncoupling limit between the MZMs is from a degeneracy of the teleportation and the Andreev process channels. We then propose a scheme to eliminate the degeneracy by introducing finite charging energy on the Majorana island which allows for coexistence of the two channels. We find nonzero cross correlation established even in the Majorana uncoupling limit (and also in the small charging energy limit), which demonstrates well the teleportation or nonlocal nature of the MZMs. More specifically, the characteristic structure of coherent peaks in the power spectrum of the cross correlation is analyzed to identify the nonlocal and coherent coupling mechanism between the MZMs and the quantum dots. We also display the behaviors of peak shift with variation of the Majorana coupling energy, which can be realized by modulating parameters such as the magnetic field.
We study quantum entanglement in a system comprising two quantum dots interconnected through the short topological superconducting nanowire, which hosts overlapping boundary Majorana modes. Inspecting the fermionic negativity, we analyze the variation of entanglement against the position of the energy levels of quantum dots and their hybridization with the topological superconducting nanowire. In the absence of electron correlations, the optimal entanglement occurs when the energy levels coincide with the zero-energy Majorana modes, whereas upon increasing the hybridizations, the entanglement is gradually suppressed. Such monotonous behavior is no longer valid when the quantum dot levels are detuned from the zero-energy. Under these circumstances, the quantum dots become maximally entangled for a certain optimal hybridization. Moreover, we study the thermal concurrence to explore the entanglement properties at finite temperatures. We also compute the quantum mutual information and propose recipes for robust finite-temperature entanglement transmission via Majorana modes.
Majorana zero modes, quasiparticles with non-Abelian statistics, have gained increasing interest for their fundamental role as building blocks in topological quantum computation. Previous studies have mainly focused on two well-separated Majorana zero modes, which could form two degenerate states serving as one nonlocal qubit for fault-tolerant quantum memory. However, creating and manipulating multiple Majorana zero modes, which could encode more qubits, remain an ongoing research topic. Here we report that multiple Majorana zero modes can exist in atomic Fermi double wires with spin-orbit coupling and perpendicular Zeeman field. This system belongs to the topological BDI class, thus all the topological superfluids are classified by integer numbers. Especially, diverse topological superfluids can be formed in a trap, where the zero energy modes can be found at the interfaces between different topological superfluids. The structure of these zero energy modes in the trap can be engineered by the trapping potential as well as other system parameters. This system would be a significant step towards utilization of Majorana zero modes in quantum computation.
We study quantum entanglement in a system comprising two quantum dots interconnected through the short topological superconducting nanowire, which hosts overlapping boundary Majorana modes. Inspecting the fermionic negativity, we analyze the variation of entanglement against the position of the energy levels of quantum dots and their hybridization with the topological superconducting nanowire. In the absence of electron correlations, the optimal entanglement occurs when the energy levels coincide with the zero-energy Majorana modes, whereas upon increasing the hybridizations, the entanglement is gradually suppressed. Such monotonous behavior is no longer valid when the quantum dot levels are detuned from the zero-energy. Under these circumstances, the quantum dots become maximally entangled for a certain optimal hybridization. Moreover, we study the thermal concurrence to explore the entanglement properties at finite temperatures. We also compute the quantum mutual information and propose recipes for robust finite-temperature entanglement transmission via Majorana modes.
The one-dimensional (1D) J1−J2J_1-J_2J1​−J2​ quantum spin model can be viewed as a strong-coupling analogue of the Schrieffer-Su-Heeger model with two inequivalent alternating Ising couplings along the wire, associated to the physics of resonating valence bonds. Similar to the quantum Ising model, which differently presents a long-range N\' eel ordered phase, this model also maps onto a p-wave superconducting wire which shows a topological phase transition with the emergence of low-energy Majorana fermions. We show how signatures of the topological phase transition for the p-wave superconducting wire, i.e. a half Skyrmion, are revealed through local (short-range) spin observables and their derivatives related to the capacitance of the pairing fermion model. Then, we present an edge correspondence through the edge spin susceptibility in the J1−J2J_1-J_2J1​−J2​ model revealing that the topological phase transition is a metal of Majorana fermions. We justify that the spin magnetization at an edge at very small transverse magnetic field is a good marker of the topological invariant and of Majorana zero modes. We identify a correspondence between the quantum information of resonating valence bonds and the charge fluctuations in a p-wave superconductor through our method "the bipartite fluctuations". Physical properties of this 1D model are in fact robust when including additional interactions, which is optimistic for practical applications e.g. in quantum circuits.