Quantum teleportation in one-dimensional quantum dots system

We present a model of quantum teleportation protocol based on one-dimensional quantum dots system. Three quantum dots with three electrons are used to perform teleportation, the unknown qubit is encoded using one electron spin on quantum dot A, the other two dots B and C are coupled to form a mixed space-spin entangled state. By choosing the Hamiltonian for the mixed space-spin entangled system, we can filter the space (spin) entanglement to obtain pure spin (space) entanglement and after a Bell measurement, the unknown qubit is transferred to quantum dot B. Selecting an appropriate Hamiltonian for the quantum gate allows the spin-based information to be transformed into a charge-based information. The possibility of generalizing this model to N-electrons is discussed. 2006 Elsevier B.V. All rights reserved. Quantum teleportation is a technique for transferring quantum states from one place to another. A concise description of the protocol for teleporting a qubit can be described as follows [1]: The sender Alice has a source qubit which she wants to send to Bob and share with Bob an entangled pair, an Einstein–Podolsky–Rosen (EPR) pair [2]. Alice does a Bell measurement on the source qubit and her half of the EPR pair, projecting the target qubit hold by Bob into a state being the same as the original state of the source qubit up to a unitary transformation. Then Bob rotate the target qubit into the original state of the source qubit based on the two bits of classical information from Alice. The details of the protocol are shown in Fig. 1: Alice performs a controlled-NOT (C-NOT) operation on her two qubits, using the source qubit as the control line. Then perform a Hadamard transformation on the source qubit. Alice then performs a measurement on her two qubits. After the measurement, Alice sends Bob two bits of classical information about the result of her measurement, which is used by Bob to rotate the target qubit into the correct state. Quantum teleportation 0009-2614/$ see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2006.01.093 * Corresponding author. Fax: +1 765 494 0239. E-mail addresses: [email protected], [email protected] (S. Kais). using pairs of entangled photons [3–8] and atoms [9,10] have been demonstrated experimentally. There are also schemes suggesting using electrons to perform quantum teleportation [11–13]. In this Letter, we study the quantum entanglement in an array of quantum dots and propose a scheme to perform quantum teleportation in this system. We show that the space entanglement and spin entanglement contained in the quantum dots system modeled by the one-dimensional Hubbard Hamiltonian can be applied selectively to perform quantum teleportation. Quantum entanglement is one of the most important concepts in quantum information theory and quantum computation. It is key to the implementation of quantum information processing technology. It has been realized that quantum entanglement can be used as a controllable physical resource [14]. Theoretically, finding a measure for the quantum entanglement is an important issue. For the fermion system, we choose Zanardi’s measure [15], which is given in Fock space as the von Neumann entropy. Quantum dots system is one of the proposals for building a quantum computer [17,18]. To describe the quantum dots, a simple approximation is to regard each dot as having one valence orbital, the electron occupation could be j0æ, j›æ, jflæ and j›flæ, with other electrons treated as core