In quantum secret sharing, a quantum secret state is mapped to multiple shares such that shares from qualified sets can recover the secret state and shares from other forbidden sets reveal nothing about the secret state; we study the setting where there are both classical shares and quantum shares. We show that the quantum secret sharing problem with both classical and quantum shares is feasible if and only if any two qualified sets have some quantum share in common. Next, for threshold quantum secret sharing where there are $N_1$ classical shares, $N_2$ quantum shares and qualified sets consist of any $K_1$ (or more) classical shares and any $K_2 > N_2/2$ (or more) quantum shares, we show that to share $1$ qubit secret, each classical share needs to be at least $2$ bits and each quantum share needs to be at least $1$ qubit. Finally, we characterize the minimum share sizes for quantum secret sharing with at most $2$ classical shares and at most $2$ quantum shares. The converse proofs rely on quantum information inequalities and the achievable schemes use classical secret sharing, (encrypted) quantum secret sharing with only quantum shares, superdense coding, treating quantum digits as classical digits, and their various combinations.In quantum secret sharing, a quantum secret state is mapped to multiple shares such that shares from qualified sets can recover the secret state and shares from other forbidden sets reveal nothing about the secret state; we study the setting where there are both classical shares and quantum shares. We show that the quantum secret sharing problem with both classical and quantum shares is feasible if and only if any two qualified sets have some quantum share in common. Next, for threshold quantum secret sharing where there are $N_1$ classical shares, $N_2$ quantum shares and qualified sets consist of any $K_1$ (or more) classical shares and any $K_2 > N_2/2$ (or more) quantum shares, we show that to share $1$ qubit secret, each classical share needs to be at least $2$ bits and each quantum share needs to be at least $1$ qubit. Finally, we characterize the minimum share sizes for quantum secret sharing with at most $2$ classical shares and at most $2$ quantum shares. The converse proofs rely on quantum information inequalities and the achievable schemes use classical secret sharing, (encrypted) quantum secret sharing with only quantum shares, superdense coding, treating quantum digits as classical digits, and their various combinations.

arXiv:2507.17364Jul 23, 20250 citations

Theory of quantum secret sharing

Daniel Gottesman

I present a variety of results on the theory of quantum secret sharing. I show that any mixed state quantum secret sharing scheme can be derived by discarding a share from a pure state scheme, and that the size of each share in a quantum secret sharing scheme must be at least as large as the size of the secret. I show that the only constraints on the existence of quantum secret sharing schemes with general access structures are monotonicity (if a set is authorized, so are larger sets) and the no-cloning theorem. I also discuss some aspects of sharing classical secrets using quantum states. In this situation, the size of each share can sometimes be half the size of the classical secret.I present a variety of results on the theory of quantum secret sharing. I show that any mixed state quantum secret sharing scheme can be derived by discarding a share from a pure state scheme, and that the size of each share in a quantum secret sharing scheme must be at least as large as the size of the secret. I show that the only constraints on the existence of quantum secret sharing schemes with general access structures are monotonicity (if a set is authorized, so are larger sets) and the no-cloning theorem. I also discuss some aspects of sharing classical secrets using quantum states. In this situation, the size of each share can sometimes be half the size of the classical secret.

arXiv:quant-ph/9910067Physical Review AMar 16, 2000618 citations

Splitting Quantum States

ScienceFeb 4, 20100 citations

Entangled Quantum States

Willi-Hans Steeb, Yorick Hardy

International Journal of Theoretical PhysicsDec 1, 20002 citations

Quantum state sharing of arbitrary known multi-qubit and multi-qudit states

Ming‐Ming Wang, Xiu‐Bo Chen, Jinguang Chen +1 more

In this paper, we propose a new version of quantum state sharing (QSTS) scheme of an arbitrary multi-qubit state. Then we extend the scheme to a general form of sharing an arbitrary multi-qudit state in the high-dimensional system. The schemes consider the most general case where an arbitrary quantum state can be shared among an arbitrary number of agents in a symmetric way that any agent can recover the state with the help of the others. Compared with a traditional QSTS scheme sharing an unknown state, our schemes are more efficient since the dealer only needs to perform a simpler measurement and consume less classical communication costs.In this paper, we propose a new version of quantum state sharing (QSTS) scheme of an arbitrary multi-qubit state. Then we extend the scheme to a general form of sharing an arbitrary multi-qudit state in the high-dimensional system. The schemes consider the most general case where an arbitrary quantum state can be shared among an arbitrary number of agents in a symmetric way that any agent can recover the state with the help of the others. Compared with a traditional QSTS scheme sharing an unknown state, our schemes are more efficient since the dealer only needs to perform a simpler measurement and consume less classical communication costs.

International Journal of Quantum InformationApr 1, 20149 citations

N_1

classical shares,

N_2

quantum shares and qualified sets consist of any

K_1

(or more) classical shares and any

K_2 > N_2/2

(or more) quantum shares, we show that to share

1

qubit secret, each classical share needs to be at least

2

bits and each quantum share needs to be at least

1

qubit. Finally, we characterize the minimum share sizes for quantum secret sharing with at most

2

classical shares and at most

2

quantum shares. The converse proofs rely on quantum information inequalities and the achievable schemes use classical secret sharing, (encrypted) quantum secret sharing with only quantum shares, superdense coding, treating quantum digits as classical digits, and their various combinations.