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arXiv:cond-mat/0407152

Diffusive teleportation on a quantum dot chain

FERDINANDO DE PASQUALE, Gian Luca Giorgi, Simone Paganelli

Published Jul 7, 2004• 0 citations
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Abstract

We introduce a model of quantum teleportation on a channel built on a quantum dot chain. Quantum dots are coupled through hopping and each dot can accept zero, one or two electrons. Vacuum and double occupation states have the same potential energy, while single occupation states are characterized by a lower potential energy. A single dot initially decoupled from the others is weakly coupled with an external element (Bob), where a pair of electrons has been previously localized. Because of hopping after a suitable time the two dots charge states become maximally entangled. Another chain dot (Alice) is put in an unknown superposition of vacuum and double occupation states, and the other dots are initially empty. The time evolution of the system involves an electron diffusive process. A post selection procedure represented by the detection of charge pairs in a region of the chain equidistant from Alice and Bob, allows, if successful, the reconstruction on the Bob site of the unknown state initially encoded by Alice. The peculiar feature of the model is that the introduction of a trapped magnetic field strongly improves the process efficiency.

DOI
10.48550/arxiv.cond-mat/0407152

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We introduce a model of quantum teleportation on a channel built on a quantum dot chain. Quantum dots are coupled through hopping and each dot can accept zero, one or two electrons. Vacuum and double occupation states have the same potential energy, while single occupation states are characterized by a lower potential energy. A single dot initially decoupled from the others is weakly coupled with an external element (Bob), where a pair of electrons has been previously localized. Because of hopping after a suitable time the two dots charge states become maximally entangled. Another chain dot (Alice) is put in an unknown superposition of vacuum and double occupation states, and the other dots are initially empty. The time evolution of the system involves an electron diffusive process. A post selection procedure represented by the detection of charge pairs in a region of the chain equidistant from Alice and Bob, allows, if successful, the reconstruction on the Bob site of the unknown state initially encoded by Alice. The peculiar feature of the model is that the introduction of a trapped magnetic field strongly improves the process efficiency.
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.
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).
We propose a feasible scheme for implementing probabilistic teleportation of an unknown atomic state. In this scheme, atom 1 is initially in an arbitrary state, atoms 2 and 3 are prepared in a partially entangled pure state. After receiving the result of Bell-state measurement performed by Alice on atoms 1 ant 2, Bob lets atoms 2 and auxiliary atom A simultaneously interact with a single-mode vacuum cavity. Only controlling the interact time, we can reconstruct the initial state of atom 1 on the atom 3, i.e. double of square of mode of smaller coefficient of superposition state serving as quantum channel. Moreover, our scheme is insensitive to cavity decay, because atoms are interacting with a large detuning vacuum cavity field.
Quantum teleportation circumvents the uncertainty principle using dual channels: a quantum one consisting of previously-shared entanglement, and a classical one, together allowing the disembodied transport of an unknown quantum state over distance. It has recently been shown that a classical bit can be counterfactually communicated between two parties in empty space, “Alice” and “Bob”. Here, by using our “dual” version of the chained quantum Zeno effect to achieve a counterfactual CNOT gate, we propose a protocol for transporting an unknown qubit counterfactually, that is without any physical particles travelling between Alice and Bob—no classical channel and no previously-shared entanglement.