We introduce a method for performing universal quantum computation on quantum states shared according to general access structures. This generalizes recent attempts for doing quantum computation on $(n,n)$ threshold schemes. In a general access structure certain authorized subsets, depending on their weights, can retrieve a secret shared state, and only by their collaboration universal quantum computation can be performed on the shared state. To achieve this we have used concatenation of seven-qubit codes.We introduce a method for performing universal quantum computation on quantum states shared according to general access structures. This generalizes recent attempts for doing quantum computation on $(n,n)$ threshold schemes. In a general access structure certain authorized subsets, depending on their weights, can retrieve a secret shared state, and only by their collaboration universal quantum computation can be performed on the shared state. To achieve this we have used concatenation of seven-qubit codes.

Jan 8, 20180 citations

Quantum Security Computation on Shared Secrets

Hai-Yan Bai, Zhi-Hui Li, Na Hao

arXiv:1804.03792International Journal of Theoretical PhysicsOct 15, 20181 citation

Computational Quantum Secret Sharing

Alper Çakan, Vipul Goyal, Chen-Da Liu-Zhang +1 more

Quantum secret sharing (QSS) allows a dealer to distribute a secret quantum state among a set of parties in such a way that certain authorized subsets can reconstruct the secret, while unauthorized subsets obtain no information about it. Previous works on QSS for general access structures focused solely on the existence of perfectly secure schemes, and the share size of the known schemes is necessarily exponential even in cases where the access structure is computed by polynomial size monotone circuits. This stands in stark contrast to the classical setting, where polynomial-time computationally-secure secret sharing schemes have been long known for all access structures computed by polynomial-size monotone circuits under standard hardness assumptions, and one can even obtain shares which are much shorter than the secret (which is impossible with perfect security). While QSS was introduced over twenty years ago, previous works only considered information-theoretic privacy. In this work, we initiate the study of computationally-secure QSS and show that computational assumptions help significantly in building QSS schemes, just as in the classical case. We present a simple compiler and use it to obtain a large variety results: We construct polynomial-time computationally-secure QSS schemes under standard hardness assumptions for a rich class of access structures. This includes many access structures for which previous results in QSS necessarily required exponential share size. In fact, we can go even further: We construct QSS schemes for which the size of the quantum shares is significantly smaller than the size of the secret. As in the classical setting, this is impossible with perfect security. We also apply our compiler to obtain results beyond computational QSS. In the information-theoretic setting, we improve the share size of perfect QSS schemes for a large class of n-party access structures to 1.5^{n+o(n)}, improving upon best known schemes and matching the best known result for general access structures in the classical setting. Finally, among other things, we study the class of access structures which can be efficiently implemented when the quantum secret sharing scheme has access to a given number of copies of the secret, including all such functions in 𝖯 and NP.Quantum secret sharing (QSS) allows a dealer to distribute a secret quantum state among a set of parties in such a way that certain authorized subsets can reconstruct the secret, while unauthorized subsets obtain no information about it. Previous works on QSS for general access structures focused solely on the existence of perfectly secure schemes, and the share size of the known schemes is necessarily exponential even in cases where the access structure is computed by polynomial size monotone circuits. This stands in stark contrast to the classical setting, where polynomial-time computationally-secure secret sharing schemes have been long known for all access structures computed by polynomial-size monotone circuits under standard hardness assumptions, and one can even obtain shares which are much shorter than the secret (which is impossible with perfect security). While QSS was introduced over twenty years ago, previous works only considered information-theoretic privacy. In this work, we initiate the study of computationally-secure QSS and show that computational assumptions help significantly in building QSS schemes, just as in the classical case. We present a simple compiler and use it to obtain a large variety results: We construct polynomial-time computationally-secure QSS schemes under standard hardness assumptions for a rich class of access structures. This includes many access structures for which previous results in QSS necessarily required exponential share size. In fact, we can go even further: We construct QSS schemes for which the size of the quantum shares is significantly smaller than the size of the secret. As in the classical setting, this is impossible with perfect security. We also apply our compiler to obtain results beyond computational QSS. In the information-theoretic setting, we improve the share size of perfect QSS schemes for a large class of n-party access structures to 1.5^{n+o(n)}, improving upon best known schemes and matching the best known result for general access structures in the classical setting. Finally, among other things, we study the class of access structures which can be efficiently implemented when the quantum secret sharing scheme has access to a given number of copies of the secret, including all such functions in 𝖯 and NP.

Leibniz international proceedings in informaticsJan 1, 20230 citations

We introduce a method for performing universal quantum computation on quantum states shared according to general access structures. This generalizes recent attempts for doing quantum computation on

(n,n)

threshold schemes. In a general access structure certain authorized subsets, depending on their weights, can retrieve a secret shared state, and only by their collaboration universal quantum computation can be performed on the shared state. To achieve this we have used concatenation of seven-qubit codes.