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Quantum Information and Computation

Dense quantum communication using single- and two-particle operations on six-particle cluster state

Parminder S. Bhatia

Published Mar 1, 2016• 2 citations
Publisher

Abstract

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.

DOI
10.26421/qic16.3-4-5

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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.
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.
The usefulness of the recent experimentally realized six photon cluster state by C. Y. Lu et al. (2007, Nature {3} {91}), is investigated for quantum communication protocols like teleportation, quantum information splitting (QIS), remote state preparation and dense coding. We show that the present state can be used for the teleportation of an arbitrary two qubit state deterministically. Later we devise two distinct protocols for the QIS of an arbitrary two qubit state among two parties and systematically compare their relative merits in terms of classical communication and security. Sixteen orthogonal measurement basis on the cluster state is constructed, which will lock an arbitrary two qubit state among two parties. The usefulness of the state for dense coding is investigated and it is shown that one can send five classical bits by sending only three qubits using this state as a shared entangled resource. We finally show that this state can also be utilised in the remote state preparation of an arbitrary two qubit state.
Dense coding is a new concept of quantum communication using the nonlocal feature of quantum entangled states. Bob, the information receiver, prepares polarization-entangled photon twins and sends one of them to Alice, the information sender, while retaining the other. She can prepare each of the four Bell states by operating an appropriate manipulation only on the transmitted photon and thus she can encode 2 bits of information. To decode the 2 bits, Bob must execute a joint measurement of the returned and retained photons with a Bell-state analyzer, such as a Hong-Ou-Mandel type of two-photon interferometer. The information capacity of the transmitted photon is limited by the number of usable nonlocal quantum states which can be prepared through the local operation on one photon. A question arises as to whether Alice can enhance the capacity or not, by adopting an additional degree of freedom by use of pulse position modulation or optical frequency modulation for the transmitted photon. At a glance, capacity enhancement appears to be possible by introducing another degree of freedom. The question here is, however, whether or not it is possible by manipulating only one of photon twins. In the paper, however, we show that the information capacity in dense coding can be enhanced from the reported 2 bits to 3 bits provided that photon twins have spectral correlation and a perfect Bell state analyzer is available.
Quantum communication, as a vital area of quantum information science, aims to leverage quantum phenomena—particularly entanglement—to achieve tasks that are impossible or inefficient in classical systems. It plays a key role in the development of secure communication protocols and advanced information processing. This paper focuses on one such protocol, dense coding, which enables the transmission of two classical bits using only one entangled quantum particle.”We introduce the mathematical and physical foundations of quantum communication, such as the entangled state and Kronecker product. Then we propose the quantum communication protocol, namely dense coding using Bell states. It offer unique advantages that are beyond the classical parts. For this purpose, we in detail analyze the quantum measurements using Pauli gates and identity matrix, as well as the transmission of particle from Alice to Bob. They are necessary steps for dense coding. Then we analyze how Bob finishes the protocol using measurement over two qubits.
Abstract Quantum communication is a new emerging inter-discipline in which classical communication theory and quantum mechanics are intertwined. Among them, the utilization of quantum entangled state properties is fundamental to the realization of quantum communication. In this way, we can ensure the security and confidentiality of information during transmission based on a new communication scheme, i.e., a quantum dense coding scheme. It enables the transmission of two bits of classical information by transmitting only one qubit. In the past decades, the scheme has attracted the attention of many researchers because of its promising development. In this paper, on top of quantum mechanics, we first review the two-dimensional dense coding scheme and analyze the process implemented by the above scheme. Then it is successfully extended to higher dimensions (three dimensions), predicting the possibility of implementation in more than two dimensions. Finally, the importance of the maximally entangled state for the transmission of this scheme is briefly explained.