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arXiv:1510.08425 · Laser Physics

Teleportation with two-dimensional electron gas formed at the interface of a GaAs heterostructure

Adenike Grace Adepoju, B. J. Falaye, Guo-Hua Sun, Oscar Camacho-Nieto, Shi‐Hai Dong

Published Jan 13, 2017• 6 citations
arXivHTMLPDF

Abstract

Abstract Inspired by the scenario proposed by Bennett et al , a teleportation protocol of qubits formed in a two-dimensional electron gas formed at the interface of a GaAs heterostructure is presented. The teleportation is carried out using three GaAs quantum dots (say P P ′ , Q Q ′ , R R ′ ) and three electrons. The electron spin on GaAs quantum dots P P ′ is used to encode the unknown qubit. The GaAs quantum dot Q Q ′ and R R ′ combine to form an entangled state. Alice (the sender) performs a Bell measurement on pairs ( P , Q ) and ( P ′ , Q ′ ). Depending on the outcome of the measurement, a suitable Hamiltonian for the quantum gate can be used by Bob (the receiver) to transform the information based on spin to charge-based information. This work offers relevant corrections to the misconception in Weng and Kais (2006 Chem. Phys. Lett . 421 338).

DOI
10.1088/1555-6611/aa5492

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Abstract Inspired by the scenario proposed by Bennett et al , a teleportation protocol of qubits formed in a two-dimensional electron gas formed at the interface of a GaAs heterostructure is presented. The teleportation is carried out using three GaAs quantum dots (say P P ′ , Q Q ′ , R R ′ ) and three electrons. The electron spin on GaAs quantum dots P P ′ is used to encode the unknown qubit. The GaAs quantum dot Q Q ′ and R R ′ combine to form an entangled state. Alice (the sender) performs a Bell measurement on pairs ( P , Q ) and ( P ′ , Q ′ ). Depending on the outcome of the measurement, a suitable Hamiltonian for the quantum gate can be used by Bob (the receiver) to transform the information based on spin to charge-based information. This work offers relevant corrections to the misconception in Weng and Kais (2006 Chem. Phys. Lett . 421 338).
An electron teleportation protocol, inspired by the scenario by Bennett et al., is proposed in a mesoscopic set-up. A superconducting circuit allows to both inject and measure entangled singlet electron pairs in an array of three normal quantum dots. The selection of the teleportation process is achieved in the steady state with the help of two superconducting dots and appropriate gating. Teleportation of the electron spin is detected by measuring the spin-polarized current through the normal dot array. This current is perfectly correlated to the pair current flowing inside the superconducting circuit. The classical channel required by Bennett's protocol, which signals the completion of a teleportation cycle, is identified with the detection of an electron charge in the superconducting circuit.
We present a model of quantum teleportation protocol based on a double quantum dot array. The unknown qubit is encoded using a pair of quantum dots, with one excess electron, coupled by tunneling. It is shown how to create a maximally entangled state using an adiabatically increasing Coulomb repulsion between different dot pairs. This entangled state is exploited to perform teleportation again using an adiabatic coupling between itself and the incoming unknown state. Finally, a sudden separation of Bob’s qubit allows a time evolution of Alice’s which amounts to a modified version of standard Bell measurement. A transmission over a long distance could be obtained by considering the entangled state of a chain of N coupled double quantum dots. The system is shown to be increasingly robust with N against decoherence due to phonons.
We present a model of quantum teleportation protocol based on a double quantum dot array. The unknown qubit is encoded using a pair of quantum dots, with one excess electron, coupled by tunneling. It is shown how to create a maximally entangled state using an adiabatically increasing Coulomb repulsion between different dot pairs. This entangled state is exploited to perform teleportation again using an adiabatic coupling between itself and the incoming unknown state. Finally, a sudden separation of Bob's qubit allows a time evolution of Alice's, which amounts to a modified version of standard Bell measurement. A transmission over a long distance could be obtained by considering the entangled state of a chain of N coupled double quantum dots. The system is shown to be increasingly robust with N against decoherence due to phonons.
An electron-spin state teleportation scheme is described in detail. It is based on the protocol by Bennett et al. [Phys. Rev. Lett. 70, 1895 (1993)], and involves the production and detection by superconductors of entangled pairs of electrons. Quantum dots filter individual electron transitions, and the whole teleportation sequence is selected in a five-dot cell by electrostatic gating in the stationary regime (no time-dependent gate voltages): (i) a normal dot carries the electron-spin state to be teleported, two others carry the ancillary entangled pair; (ii) two superconducting dots, coupled by a superconducting circuit, control the injection of the source electron and the detection of the teleported electron. This teleportation cell is coupled to emitter and receiver reservoirs. In a steady state, a spin-conserving current flows between the reservoirs, most exclusively carried by the teleportation channel. This current is perfectly correlated to a Cooper pair current flowing in the superconducting circuit, and which triggers detection of the teleported electron. This latter current indeed carries the classical information, which is necessary to achieve teleportation. The average teleportation current is calculated using the Bloch equations, for weakly coupled spin reservoirs. A diagnosis of teleportation is proposed using noise correlations.
Summary form only given. Characterizing the entanglement of a general bipartite quantum system is a difficult problem. Most measures involve difficult extremizations and their physical motivation is not always clear. In this paper we propose an experimental measure of entanglement based on a modified version of the familiar teleportation protocol of Bennett et al. (1993). Briefly, teleportation traditionally involves two parties, Alice and Bob. Initially, Alice has a qubit in an unknown quantum state which she would like to communicate to Bob and Bob has two qubits in an entangled Einstein-Podolsky-Rosen (EPR) pair. To accomplish this transfer, Bob shares one qubit of his EPR pair with Alice. She then performs a joint measurement or Bell measurement on her two qubits and relays this information back to Bob over a classical channel. Bob then uses the outcome of Alice's Bell measurement to transform his qubit, with a local unitary transformation, into the original quantum state, always with a fidelity of one.
In the past decades, various schemes of teleportation of quantum states through different types of quantum channels (a prior shared entangled state between the sender and the receiver), e.g. EPR pairs, generalized Bell states, qubit GHZ states, standard W states and its variations, genuine multiqubit entanglement states, etc., have been developed. Recently, three-qutrit quantum states and two-qudit quantum states have also been considered as quantum channels for teleportation. In this paper, we investigate the teleportation of an unknown qudit using a d level GHZ state, i.e. a three-qudit maximally entangled state, as quantum channel. We design a general scheme of faithful teleportation of an unknown qudit using a d-level GHZ state shared between the sender and the receiver, or among the sender, the receiver and the controller; an unknown two-qudit of Schmidt form using a d level GHZ state shared between the sender and the receiver; as well as an unknown arbitrary two-qudit using two shared d level GHZ states between the sender, the receiver and the controller, or using one shared d level GHZ state and one shared generalized Bell state. We obtain the general formulas of Alice's measurement basis, Charlie's measurement basis and Bob's unitary operations to recover the input state of Alice. It is intuitionistic to generalize the protocols of teleporting an arbitrary two-qudit state to teleporting an arbitrary n-qudit state.