Abstract In this paper, by utilizing d -dimensional single-particle states, three semiquantum cryptography protocols, i.e., the multi-party semiquantum private comparison (MSQPC) protocol, the multi-party semiquantum multiplication (MSQM) protocol and the multi-party semiquantum summation (MSQS) protocol, can be achieved simultaneously under the assistance of two semi-honest quantum third parties (TPs). Here, the proposed MSQPC scheme is the only protocol which is devoted to judging the size relationship of secret integers from more than two semiquantum participants without a pre-shared key. And the proposed MSQM protocol absorbs the innovative concept of semiquantumness into quantum multiplication for the first time, which can calculate the modulo d multiplication of private inputs from more than two semiquantum users. As for the proposed MSQS protocol, it is the only semiquantum summation protocol which aims to accomplish the modulo d addition of more than three semiquantum users’ private integers. Neither quantum entanglement swapping nor unitary operations are necessary in the three proposed protocols. The security analysis verifies in detail that both the external attacks and the internal attacks can be resisted in the three proposed protocols. 

pdf/hybrid-protocols-for-multi-party-semiquantum-private-2hgxwrx1j1.pdf

Hybrid protocols for multi-party semiquantum private comparison, multiplication and summation without a pre-shared key based on d-dimensional single-particle states

Efficient multiparty quantum private comparison protocol based on single photons and rotation encryption

Abstract Quantum secret sharing (QSS) is a multi-party quantum communication mode, which allows the dealer to split a key into several parts and send each part of a key to a participant. The participants can obtain the key only by cooperation. Entanglement swapping is a promising method to construct the entanglement channel. In the paper, we propose a multiple-participant measurement-device-independent QSS protocol based on entanglement swapping. All the measurement tasks are handed over to an untrusted measurement party, so that our protocol can resist all possible attacks from imperfect measurement devices. Our protocol requires the linear-optical Bell state analysis, which is easy to operate. Our protocol has application potential in the future quantum communication field. 

Multiple-participant measurement-device-independent quantum secret sharing protocol based on entanglement swapping

With entanglement-assisted (EA) formalism, arbitrary classical linear codes are allowed to transform into EAQECCs by using pre-shared entanglement between the sender and the receiver. In this paper, based on classical cyclic MDS codes by exploiting pre-shared maximally entangled states, we construct two families of q-ary entanglement-assisted quantum MDS codes $$ \left[\left[\frac{q^2+1}{a},\frac{q^2+1}{a}-2\left(d-1\right)+c,d;c\right]\right] $$
 , where q is a prime power in the form of am + l, and a = (l2 + 1) or $$ a=\frac{\left({l}^2+1\right)}{5} $$
 . We show that all of q-ary EAQMDS have minimum distance upper limit much larger than the known quantum MDS (QMDS) codes of the same length. Most of these q-ary EAQMDS codes are new in the sense that their parameters are not covered by the codes available in the literature.

Two Families of Entanglement-Assisted Quantum MDS Codes from Cyclic Codes

By utilizing the non-maximally entangled four-qubit cluster states as the quantum channel, we first propose a hierarchical quantum information splitting scheme of arbitrary three-qubit states among three agents with a certain probability. Then we generalize the scheme to arbitrary multi-qubit states. Hierarchy is reflected on the different abilities of agents to restore the target state. The high-grade agent only needs the help of one low-grade agent, while the low-grade agent requires all the other agents’ assistance. The designated receiver performs positive operator-valued measurement (POVM) which is elaborately constructed with the aid of Hadamard matrix. It is worth mentioning that a general expression of recovery operation is derived to disclose the relationship with measurement outcomes. Moreover, the scheme is extended to multiple agents by means of the symmetry of cluster states.

/pdf/probabilistic-hierarchical-quantum-information-splitting-of-3beuiz79.pdf

Probabilistic Hierarchical Quantum Information Splitting of Arbitrary Multi-Qubit States

A verifiable (k, n)-threshold dynamic quantum secret sharing scheme

In this paper, we construct some new entanglement-assisted quantum maximum distance separable (EAQMDS) codes with lengths $$n=q^2+1$$ and $$n=(q^2+1)/2$$ from negacyclic MDS codes and constacyclic MDS codes, respectively. All of them have flexible parameters. These EAQMDS codes we constructed have larger minimum distance and contain the known EAQMDS codes with same length in previous papers.

New entanglement-assisted quantum MDS codes with larger minimum distance

Dynamic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e341" altimg="si356.svg"><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> threshold quantum secret sharing based on <mml:math xmlns:mml="h

A new (w, t, n)-weighted threshold quantum secret sharing scheme based on two-qubit system

A (t, n) Threshold Quantum Secret Sharing Scheme with Fairness

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