Multi-qubit hierarchical quantum state sharing with authentication

Current hierarchical control quantum communication protocols are mostly limited to linear bidirectional architectures with only two communication agents, lacking cyclic information exchange capabilities and flexible scalability for large-scale scenarios. This limitation impedes the practical deployment of complex quantum communication networks. To address this issue, a novel hierarchical control bidirectional cyclic hybrid quantum information transmission protocol for an arbitrary single-qubit state is proposed. The protocol comprises six participating entities: three communication agents (Alice, Bob, and Charlie) at different levels and three control agents (David, Emma, and Frank) with a clear permission hierarchy. The bidirectional communication tasks of each communication agent require matching control authorization corresponding to their level: high-level communication agents only need David's assistance, mid-level ones require joint control from David and Emma, and low-level ones demand collaborative authorization from all three control agents to complete their quantum teleportation and remote state preparation tasks. Furthermore, the proposed six-party protocol is extended to a 2N-party scenario involving N control agents and N communication agents at different levels, adapting to the needs of large-scale quantum communication networks. This work provides a flexible and scalable theoretical framework for constructing hierarchical quantum communication networks with cyclic information exchange. 

Bidirectional cyclic hybrid quantum information transmission of arbitrary single-qubit state with different levels of control

Hierarchical Quantum Secret Sharing Based On Quantum Fourier Transform

Abstract As a fundamental component of quantum cryptography, quantum secret sharing (SS) faces a critical security challenge: dishonest participants may gain exclusive access to the shared secret through deceptive actions. To address this, recent advances in fair quantum SS have emerged, allowing equitable secret access among all participants. However, our analysis reveals security vulnerabilities in Bai et al ’s fair quantum SS scheme (Physica A, 2022). First, we show that Bai et al ’s scheme is vulnerable to collusion attack by m − 1 dishonest participants when <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>m</mml:mi> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> <mml:mtext>⩾</mml:mtext> <mml:mi>t</mml:mi> </mml:mrow> </mml:math> , where t is the threshold value. Second, we point that Bai et al ’s scheme is insecure under our defined attack model—the latent attack. In this work, a possible improved scheme is proposed to overcome the security flaws and halve the computational cost. 

Cryptanalysis and improvement of fair quantum secret sharing based on symmetric bivariate polynomial

Full threshold change range of threshold changeable secret sharing

For any ( 1 + u 2 ) -constacyclic code C with arbitrary length N over F 2 [ u ] / (cid:2) u 3 (cid:3) , we construct a new map (cid:2) from ( F 2 [ u ] / (cid:2) u 3 (cid:3) ) N to ( F 2 [ v ] / (cid:2) v 2 (cid:3) ) 2 N , and derive (cid:2)( C ) by applying the map to each codeword of C . We ﬁnd that C and its image (cid:2)( C ) have the same homogeneous distance, and the cyclic shift of any codeword of (cid:2)( C ) is still contained in (cid:2)( C ) over F 2 [ v ] / (cid:2) v 2 (cid:3) , but (cid:2)( C ) is not a cyclic code in some cases. These properties help us to determine the lower bound and the upper bound for the homogeneous distance of C by discussing the same problem of (cid:2)( C ) . With these bounds, exact homogeneous distances of some ( 1 + u 2 ) -constacyclic codes are given. On the other hand, we consider the application of homogeneous distances in computing Hamming distances of a class of binary linear quasi-cyclic codes, and derive some optimal binary linear quasi-cyclic codes.

The homogeneous distance of ( 1 + u 2 ) -constacyclic codes over F 2 [ u ] / (cid:2) u 3 (cid:3) and its applications

Standard (k, n)-threshold hierarchical quantum secret sharing

Quantum secret sharing plays a crucial role in quantum cryptography. The two main trends in quantum secret sharing are to address the problem of scheme failure due to participant spoofing and to improve the efficiency of quantum secret sharing. This article focuses on the quantum secret sharing scheme with general access structure due to its flexibility. We design a special entangled state by resorting to monotone span program (MSP). Based on the special 2-D entangled state, an efficient and verifiable general quantum secret sharing (GQSS) scheme is proposed. In the GQSS scheme, the authorized participants only provide the $X$ -basis measurement results of particles to recover and verify the shared secret, which makes that our scheme have lower communication consumption and quantum computational complexity. The analysis shows that the proposed scheme is simpler and more practical compared with related quantum secret sharing schemes.

Efficient and Verifiable General Quantum Secret Sharing Based on Special Entangled State

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Full threshold change range of threshold changeable secret sharing

The homogeneous distance of ( 1 + u 2 ) -constacyclic codes over F 2 [ u ] / (cid:2) u 3 (cid:3) and its applications

Standard (k, n)-threshold hierarchical quantum secret sharing

Efficient and Verifiable General Quantum Secret Sharing Based on Special Entangled State