Quantum secret sharing between m-party and n-party with six states

Abstract

We propose a quantum secret sharing scheme between m-party and n-party using three conjugate bases, i.e. six states. A sequence of single photons, each of which is prepared in one of the six states, is used directly to encode classical information in the quantum secret sharing process. In this scheme, each of all m members in group 1 choose randomly their own secret key individually and independently, and then directly encode their respective secret information on the states of single photons via unitary operations, then the last one (the mth member of group 1) sends 1/n of the resulting qubits to each of group 2. By measuring their respective qubits, all members in group 2 share the secret information shared by all members in group 1. The secret message shared by group 1 and group 2 in such a way that neither subset of each group nor the union of a subset of group 1 and a subset of group 2 can extract the secret message, but each whole group (all the members of each group) can. The scheme is asymptotically 100% in efficiency. It makes the Trojan horse attack with a multi-photon signal, the fake-signal attack with EPR pairs, the attack with single photons, and the attack with invisible photons to be nullification. We show that it is secure and has an advantage over the one based on two conjugate bases. We also give the upper bounds of the average success probabilities for dishonest agent eavesdropping encryption using the fake-signal attack with any two-particle entangled states. This protocol is feasible with present-day technique.

An efficient scheme for multi-party quantum state sharing via non-maximally entangled states

“…In previous schemes [11][12][13][14][15][16][17][18][19][20][21][22][23][24]30,31], the shared quantum state via different maximally entangled states can, in principle, be recovered if all participants agree to collaborate. Similar to most existing QSTS schemes, our scheme also presents a control and probabilistic teleportation protocol.…”

“…So far, various entangled states have been extensively used in QSTS protocols, such as Bell states [7][8][9][10][11], GHZ states [12][13][14][15], W states [16,17], cluster states [18][19][20], and Brown states [21][22][23]. Recently, Gao et al [24] presented a scheme for quantum state sharing between a multi-party and a multi-party with three conjugate bases. In recent techniques, Einstein-PodolskyRosen (EPR) pairs are ideally entangled resources for quantum state sharing [13,14].…”

Quantum key distribution using four-level particles

“…In other words, the quantum key distribution between Bob and Charlie is controlled by Alice. In fact, this controlled quantum key distribution protocol is just a secret sharing protocol [22][23][24][25].…”

Quantum secret sharing between multiparty and multiparty with Bell states and Bell measurements

“…One only deals with the QSS of classical information [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28], in which a classical secret is shared among all participants based on quantum mechanics, and the other with the QSS of quantum information [29][30][31][32][33][34][35][36][37][38][39], in which the secret is an arbitrary unknown quantum state. This paper mainly focuses on the former.…”

“…Unfortunately, Li et al [25] and Han et al [26] pointed out that this protocol is insecure. Later, Yan et al [27] and Gao et al [28] respectively presented two improved schemes for QSS between multiparty and multiparty. However, these improved schemes still make it necessary to use quantum memory and to publish much information about the measurement basis, so the total efficiency is low.…”