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arXiv:0905.3797

Quantum entanglement and generalized information processing using entangled states with odd number of particles

Kumar, Atul, Mangala Sunder Krishnan

Published May 23, 2009• 0 citations
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Abstract

We discuss and generalize multi-particle entanglement based on statistical correlations using Ursell-Mayer type of cluster coefficients. Cluster coefficients are used to distinguish different, independent entangled systems as well as those which are connected through local unitary transformations. We propose a genuinely and maximally entangled five-particle state for efficient information processing. The physical realization of entangled states and information processing protocols are analyzed using quantum gates and circuit diagrams. We show that the direct as well as controlled communication can be achieved using the state proposed here with certainty in the case of teleportation and with a high degree of optimity in the case of dense coding. In the case of dense coding the amount of information transferred from the sender to the receiver is always a maximum irrespective of the measurement basis used by the controller.

DOI
10.48550/arxiv.0905.3797

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We discuss and generalize multi-particle entanglement based on statistical correlations using Ursell-Mayer type of cluster coefficients. Cluster coefficients are used to distinguish different, independent entangled systems as well as those which are connected through local unitary transformations. We propose a genuinely and maximally entangled five-particle state for efficient information processing. The physical realization of entangled states and information processing protocols are analyzed using quantum gates and circuit diagrams. We show that the direct as well as controlled communication can be achieved using the state proposed here with certainty in the case of teleportation and with a high degree of optimity in the case of dense coding. In the case of dense coding the amount of information transferred from the sender to the receiver is always a maximum irrespective of the measurement basis used by the controller.
Controlled dense coding which uses different five-qubit entangled systems is described in this article. Using a criterion based on quantum-statistical correlations to define the extent of entanglement, five-qubit states are shown to have genuine entanglement. Different schemes which are easily implementable experimentally for a receiver to decode the message from a sender are described. The importance of representation of a quantum channel and distribution of qubits in a communication protocol are emphasized. It is observed that when a controller is involved it is desirable that measurement results are transmitted to the receiver and not to the sender for experimental convenience. In addition, a controlled dense coding protocol for average information transfer is given for arbitrary (2N + 1)-qubit entangled systems, using the above schemes.
Construction of multi-particle entangled states and direct teleportation of N-(spin 1/2) particles are important areas of quantum information processing. A number of different schemes which have been presented already, address the problem through controlled teleportation. In this article, a criterion based on standard quantum statistical correlations employed in the many body virial expansions is used to determine maximum entanglement for a N-particle state. These states remain entangled through proper traces to states for a smaller number of particles and can be generalized for arbitrary number of particles. It is shown that they are quite useful in generalized, N-particle, direct teleportation. The corresponding quantum gates are also indicated for teleportation schemes from simple computational basis states.
Recently, a genuine five-qubit entangled state has been achieved by Brown et al.[ J. Phys. A 38 (2005) 1119 ]. Later it was indicated that this state can be used for quantum teleportation and quantum state sharing. Here we build a quantum secure direct communication protocol with this state, and prove that it is secure in ideal conditions. In the protocol, the sender performs unitary transformations to encode a secret message on his/her particles and sends them to the receiver. The receiver then performs projective determinate measurement to decode the secret message directly. Furthermore, this protocol utilizes superdense coding to achieve a high intrinsic efficiency and source capacity.
Two schemes for teleporting an unknown two-particle entangled state via a four-qubit non-maximally entangled cluster state as quantum channel are proposed.In the first scheme,a special bipartite entangled state was teleported,the receiver Bob can reconstruct the original state with a certain probability according to the sender Alice's measurement results,and the successful probability is determined by the smallest two coefficients' absolute values of the cluster state.In the latter scheme an arbitrary two-particle entangled state was teleported.Contrast to the first scheme, Bob should perform a quantum controlled phase gate operation besides the unitary transformation. The considerable advantage is that it employs a non-maximally entangled cluster state as quantum channel in these two schemes.Thus,the schemes can greatly reduce the amount of entanglement resources and need less classical bits.
A scheme is presented for quantum information splitting of an unknown two-particle entangled state by using five-particle cluster state as the quantum channel.The sender(Alice),the receiver(Bob) and the controller(Charlie) share the quantum channel.The sender Alice sends the quantum information to the receiver Bob,anyone can not obtain the quantum information,unless they cooperate with each other.The receiver can reconstruct two-particle entangled state by performing appropriate unitary transformations on his qubits after the sender and controller perform the appropriate measurements on their qubits.respectively.
Teleportation of an arbitrary two-qubit state with a single partially entangled state, a four-qubit linear cluster-class state, is studied. The case is more practical than previous ones using maximally entangled states as the quantum channel. In order to realize teleportation, we first construct a cluster-basis of 16 orthonormal cluster states. We show that quantum teleportation can be successfully implemented with a certain probability if the receiver can adopt appropriate unitary transformations after receiving the sender's cluster-basis measurement information. In addition, an important conclusion can be obtained that a four-qubit maximally entangled state (cluster state) can be extracted from a single copy of the cluster-class state with the same probability as the teleportation in principle.