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Journal of the Optical Society of America B

Experimental tripartite quantum state sharing and perfect teleportation of the two-qubit photonic state using genuinely entangled multipartite states

Parminder S. Bhatia

Published Dec 19, 2013• 5 citations
Publisher

Abstract

An experimental scheme, its hardware implementation, and procedure for experimental verification of tripartite quantum state sharing and perfect teleportation of the two-qubit photonic state using four different multipartite quantum channels is presented. The four multipartite channels considered are (1) a pair of Greenberger–Horne–Zeilinger triplets, (2) a six-particle cluster state, (3) a highly entangled five-particle Brown state, and (4) a highly entangled six-particle Borras state. In this experiment, optical pulses are delivered by a high repetition rate mode-locked pulsed laser and arbitrary photonic states, in the two-qubit Bloch sphere, are created by the spontaneous parametric down-conversion of optical pulses in a nonlinear crystal. The experimental implementation of the scheme is based on both single-particle and two-particle complete Bell-state measurements, and the unitary transformation required for reconstruction of the qubit is performed using single- and two-qubit operations. Two-qubit operations are implemented using the quantum controlled phase and C-NOT gates. Relative comparison among different multipartite channels along with experimental difficulties and their solutions are also discussed.

DOI
10.1364/josab.31.000154

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An experimental scheme, its hardware implementation, and procedure for experimental verification of tripartite quantum state sharing and perfect teleportation of the two-qubit photonic state using four different multipartite quantum channels is presented. The four multipartite channels considered are (1) a pair of Greenberger–Horne–Zeilinger triplets, (2) a six-particle cluster state, (3) a highly entangled five-particle Brown state, and (4) a highly entangled six-particle Borras state. In this experiment, optical pulses are delivered by a high repetition rate mode-locked pulsed laser and arbitrary photonic states, in the two-qubit Bloch sphere, are created by the spontaneous parametric down-conversion of optical pulses in a nonlinear crystal. The experimental implementation of the scheme is based on both single-particle and two-particle complete Bell-state measurements, and the unitary transformation required for reconstruction of the qubit is performed using single- and two-qubit operations. Two-qubit operations are implemented using the quantum controlled phase and C-NOT gates. Relative comparison among different multipartite channels along with experimental difficulties and their solutions are also discussed.
Full detail of a proposed experiment required for implementing and verifying a theoretical scheme for four-partite splitting and open-destination teleportation of an arbitrary two-qubit photonic state is discussed. In this proposed experiment the quantum channel is provided by a pair of decomposable generalized (G) Bell states, which offer the experimental advantage that they can be very easily generated in photonic experiments. Our experiment is based on generating a two-qubit photonic state by ultrafast spontaneous parametric downconversion in nonlinear crystal and relies on Bell-state measurements, which in this experiment are performed by an optical Bell-state analyzer that can unambiguously determine all four Bell states. In this proposed experiment unitary transformation required at the destination station is implemented using a quantum control NOT gate. We finally show that in our four-partite optical system the two-qubit photonic state originally prepared at a sending station can be experimentally split and subsequently regenerated at any one of the three distinct receiving stations.
Abstract An elementary tripartite quantum communication network for discrete variables is proposed. In this network three nodes are quantum wired with quantum channel created by a pair of Greenberger–Horne–Zeilinger (GHZ) triplet. We show that in this network by local operations and classical communication an arbitrary two-qubit state can be deterministically teleported from any node to any other node. In this network tripartite teleportation of two-qubit state is achieved by first splitting the qubit into fragments and then at the destination, qubit is re-constructed from the fragments. A high flux source for generation of fully inseparable GHZ photonic quantum channel required for developing an ideal tripartite quantum network is presented. This GHZ source employ a group velocity matched periodically poled potassium titanyl phosphate crystal in pulsed polarization Sagnac interferometer configuration and is based on selecting a three-photon entangled state from the product state of an entangled photon pair and a weak coherent state. This GHZ source generates tripartite entangled photons at telecom wavelength (1584 nm). Genuine entanglement in the generated GHZ state is detected with a witness ( W ) operator. Complete detail of the experimental apparatus required for developing an ideal tripartite quantum communication photonic network, which employ fully inseparable quantum channel, is presented. This quantum network fully operates at wavelength 1584 nm, which occurs in the L-band of the technologically important third telecom window. Success probability for teleportation of two-qubit photonic state within the tripartite quantum network is determined. We show that such quantum network is experimentally feasible. Experimental procedure to unambiguously verify the teleportation of an arbitrary two-qubit photonic state within the network is discussed. It is shown that our scheme can be implemented in a programmed teleportation system and it paves the way towards a large-scale quantum network.
We provide two schemes for tripartite Controlled Teleportation (CT) of an arbitrary two-qubit state by using five- and six-qubit cluster states as the quantum channel. It is found that the five-partite cluster state can be used for CT of an arbitrary two-qubit state with three agents and the six-partite cluster state can be used for symmetric CT scheme. In comparison with the similar scheme using the same quantum channels by Muralidharan and Panigrahi [Phys. Rev. A 78 (2008) 062333] and by Menona et al. [arXiv:/0906.3874v1], not multipartite entanglement measurements, which makes our schemes simpler than the existing schemes.
We present a scheme for symmetric multiparty quantum state sharing of an arbitrary m -qubit state with m Greenberger–Horne–Zeilinger states following some ideas from the controlled teleportation (2005 Phys. Rev. A 72 02338). The sender Alice performs m Bell-state measurements on her 2 m particles and the controllers need only take some single-photon product measurements on their photons independently, not multipartite entanglement measurements, which makes this scheme more convenient than the latter. Also it does not require the parties to perform a controlled-NOT gate on the photons for reconstructing the unknown m -qubit state and it is an optimal one as its efficiency for qubits approaches 100% in principle.
Theory of controlled tripartite quantum dense coding for the transmission of four-binary bits between two distinct locations is presented. The entanglement resource for this transmission is provided by a six-qubit cluster state. Theoretical detail of an encoder that can encode sixteen different operations and a four-bit binary decoder required for this transmission is discussed. We show that in the absence of availability of any four-state analyzer decoding can be reduced to single-particle and two-particle Bell-state measurements ( BSM ). In our scheme, Bell-state measurements ( BSM ) performed during decoding, result in Bell-pairs, which along with single-particle projections are used to unambiguously discriminate all sixteen encoding operations. Proposed experiment to verify theory of tripartite quantum dense coding scheme, using photonic entanglement, is also briefly discussed. Success probability of the scheme is determined. In addition, long-distance implementation of this tripartite quantum dense coding scheme is discussed. Fault-tolerant quantum repeaters used in this long-distance scheme are based on quantum errorcorrection, which is achieved with the aid of Calderbank-Shor-Steane ( CSS ) encoding.
In recent years, there has been heightened interest in quantum teleportation, which allows for the transfer of unknown quantum states over arbitrary distances. Quantum teleportation not only serves as an essential ingredient in long-distance quantum communication, but also provides enabling technologies for practical quantum computation. Of particular interest is the scheme proposed by D. Gottesman and I. L. Chuang [(1999) Nature 402:390-393], showing that quantum gates can be implemented by teleporting qubits with the help of some special entangled states. Therefore, the construction of a quantum computer can be simply based on some multiparticle entangled states, Bell-state measurements, and single-qubit operations. The feasibility of this scheme relaxes experimental constraints on realizing universal quantum computation. Using two different methods, we demonstrate the smallest nontrivial module in such a scheme--a teleportation-based quantum entangling gate for two different photonic qubits. One uses a high-fidelity six-photon interferometer to realize controlled-NOT gates, and the other uses four-photon hyperentanglement to realize controlled-Phase gates. The results clearly demonstrate the working principles and the entangling capability of the gates. Our experiment represents an important step toward the realization of practical quantum computers and could lead to many further applications in linear optics quantum information processing.