A unitary operator construction solution based on Pauli group for maximal dense coding with a class of symmetric states
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A unitary operator construction solution based on Pauli group for maximal dense coding with a class of symmetric states Wenjie Liu1
· Junxiu Chen2 · Wenbin Yu2 · Zhihao Liu3 · Hanwu Chen3
Received: 26 November 2019 / Accepted: 14 June 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Quantum dense coding plays an important role in quantum cryptography communication, and how to select a set of appropriate unitary operators to encode message is the primary work in the design of quantum communication protocols. Shukla et al. proposed a preliminary method for unitary operator construction based on Pauli group under multiplication, which is used for dense coding in quantum dialogue. However, this method lacks feasible steps or conditions and cannot construct all the possible unitary operator sets. In this study, a feasible solution of constructing unitary operator sets for quantum maximal dense coding is proposed, which aims to use minimum qubits to maximally encode a class of t-qubit symmetric states. These states have an even number of superposition items, and there is at least one set of 2t qubits whose superposition items are orthogonal to each other. Firstly, we propose the procedure and the corresponding algorithm for constructing 2t -order multiplicative modified generalized Pauli subgroups (multiplicative MGP subgroups). Then, two conditions for t-qubit symmetric states are given to select appropriate unitary operator sets from the above subgroups. Finally, we take 3-qubit GHZ, 4-qubit W, 4-qubit cluster and 5-qubit cluster states as examples and demonstrate how to find all unitary operator sets for maximal dense coding through our construction solution, which shows that our solution is feasible and convenient. Keywords Quantum cryptography communication · Maximal dense coding · Unitary operator construction · Unitary operator set · Modified generalized Pauli group
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Wenjie Liu [email protected]
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Engineering Research Center of Digital Forensics, Ministry of Education, School of Computer and Software, Nanjing University of Information Science and Technology, Nanjing 210044, China
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School of Computer and Software, Nanjing University of Information Science and Technology, Nanjing 210044, China
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School of Computer Science and Engineering, Southeast University, Nanjing 211189, China 0123456789().: V,-vol
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1 Introduction With the development of quantum technology, quantum cryptography has become a hot topic, which has attracted more and more attention in the field of cryptography and physics. Many kinds of quantum cryptography protocols have been proposed, including quantum key distribution (QKD) [1–3], quantum secret sharing (QSS) [4– 7], quantum secure direct communication (QSDC) [8–11], quantum key agreement (QKA) [12,13,13,14], quantum signature [15,16], quantum sealed-bid auction [17,18] and quantum machine learning [19–22] that has recently become a research hot spot. Quantum dense coding [23–25] is a frequently used method i
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