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International Journal of Quantum Information

GENERALIZED CONTROLLED DENSE CODING WITH MAXIMALLY ENTANGLED MULTIQUBIT STATES

Atul Kumar, Mangala Sunder Krishnan

Published Sep 1, 2010• 0 citations
Publisher

Abstract

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.

DOI
10.1142/s0219749910006319

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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.
A scheme of realizing controlled dense coding via generalized measurement was presented. In this protocol, the supervisor can control the entanglement between the sender and the receiver and then the average amount of information transmitted from the sender to the receiver by only adjusting measurement angle θ. It is shown that when the quantum channel was a GHZ state, the entanglement and the average amount of information are determined by supervisor's measurement angle θ only; whereas when the quantum channel was a GHZ-class state, those are determined not only by supervisor's measurement angle θ but also the minimal coefficient of the GHZ-class state.
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.
We consider generalizations of the dense coding protocol with an arbitrary number of senders and either one or two receivers, sharing a multiparty quantum state, and using a noiseless channel. For the case of a single receiver, the capacity of such information transfer is found exactly. It is shown that the capacity is not enhanced by allowing the senders to perform joint operations. We provide a nontrivial upper bound on the capacity in the case of two receivers. We also give a classification of the set of all multiparty states in terms of their usefulness for dense coding. We provide examples for each of these classes, and discuss some of their properties.
Using quantum dense coding, a quantum secure direct communication scheme with a six-qubit maximally entangled state is proposed. If the first security test is passed, the sender performs unitary transformations to encode the secret information on her particles and sends to the receiver. The receiver then performs projective measurements to decode the secret information. It enables the sender to transmit six-bit classical secret message by sending three particles to the receiver. The second security test is adopted to guarantee the security of the communication.
Quantum dense coding could be used to transmit two classical bits with one qubit when a maximally entangled state is shared. In realistic channels, entanglement degradation reduces the channel capacity, while bit-flip noise increases decoding errors. To address these issues, we propose a novel probabilistic controlled dense coding protocol that employs the three-qubit repetition code for error correction and an auxiliary qubit for probabilistic decoding. Moreover, this proposed scheme includes a third party to supervise the communication based on a three-qubit entanglement state. The implementation steps of our protocol are presented in detail, and numerical simulations show that it achieves higher average information than dense coding without error correction. The scheme provides a robust solution for quantum communication under noisy conditions and non-maximally entangled state.
In quantum communication, the concept of dense coding traditionally relies on maximally entangled states as quantum channels. Recent advancements have expanded this framework to include non-maximally entangled states within the probabilistic dense coding paradigm. However, such schemes introduce a significant limitation: the receiver cannot always retrieve the complete dense coding information sent by the sender. Consequently, the receiver must inform the sender of the amount of information successfully received. Based on this feedback, the sender determines whether retransmission is necessary, leading to inefficient use of the quantum channel and reduced communication efficiency. To address these shortcomings, we propose an alternative deterministic quantum dense coding scheme that utilizes non-maximally entangled states as the quantum channel. This deterministic approach eliminates the need for retransmissions and significantly enhances communication efficiency while maintaining compatibility with non-maximally entangled states. Our scheme represents a substantial improvement over existing probabilistic methods and paves the way for more efficient quantum communication protocols.