Abstract Quantum information masking (QIM) is a crucial technique for protecting quantum data from being accessed by local subsystems. In this paper, we introduce a novel method for achieving 1-uniform QIM in multipartite systems utilizing a Fourier matrix. We further extend this approach to construct an orthogonal array with the aid of a Hadamard matrix, which is a specific type of Fourier matrix. This allows us to explore the relationship between 2-uniform QIM and orthogonal arrays. Through this framework, we derive two distinct 2-uniform quantum states, enabling the 2-uniform masking of original information within multipartite systems. Furthermore, we prove that the maximum number of quantum bits required for achieving a 2-uniformly masked state is 2 n − 1, and the minimum is 2 n−1 + 3. Moreover, our scheme effectively demonstrates the rich quantum correlations between multipartite systems and has potential application value in quantum secret sharing.
Abstract Quantum information masking (QIM) is a crucial technique for protecting quantum data from being accessed by local subsystems. In this paper, we introduce a novel method for achieving 1-uniform QIM in multipartite systems utilizing a Fourier matrix. We further extend this approach to construct an orthogonal array with the aid of a Hadamard matrix, which is a specific type of Fourier matrix. This allows us to explore the relationship between 2-uniform QIM and orthogonal arrays. Through this framework, we derive two distinct 2-uniform quantum states, enabling the 2-uniform masking of original information within multipartite systems. Furthermore, we prove that the maximum number of quantum bits required for achieving a 2-uniformly masked state is 2 n − 1, and the minimum is 2 n−1 + 3. Moreover, our scheme effectively demonstrates the rich quantum correlations between multipartite systems and has potential application value in quantum secret sharing.
Quantum information masking (QIM) allows encoding quantum information in multipartite systems. Complete QIM is of great significance in quantum foundation and application. However, the realization of complete QIM, even for single-qubit encoded information, is still lacking. Here, we propose to demonstrate complete QIM with 4-qubit entangled states. The proposed QIM can be readily extended to multipartite systems with arbitrary number of subsystems, enabling quantum secret sharing (QSS) and quantum teleportation between multiplayers. In experiment, we build up a 4-qubit hyperentangled state to implement complete QIM. The trace distance of 16 encoded single-qubit states falls within the range of 0.12 ± 0.02 to 0.03 ± 0.02. Furthermore, we implement QSS between six players by expanding the 4-qubit state to a 6-qubit state entangled in hybrid manner, in which we observe an average fidelity 0.85 ± 0.03 of the recovered states. Our results open the door towards QIM-enabled quantum information processing and provide applications in quantum communications. Quantum information masking allows encoding quantum information in multipartite systems, which is hidden from subsystems and can be recovered from the nonlocal correlation. The authors propose and realize the complete quantum information masking and apply it to quantum secret sharing between six players.
Abstract Quantum information masking is a protocol that hides the original quantum information from subsystems and spreads it over quantum correlation, which the original information of input states is completely unknown to local subsystems. In this paper, we explore the possibility of partial masking of quantum information in multipartite systems through using the generator matrices and stabilizer codes, as this approach is more suitable for constructing secret sharing protocols. Furthermore, if the condition for partial masking of quantum information is strengthened, it can be shown that the quantum state α | 0 ⟩ + β | 1 ⟩ can be masked in multipartite systems. Among them, partial masking of quantum information has a wider scope of application because it has fewer restrictions. To some extent, the masking of quantum information can be seen as a special case of partial masking. At last, we provide an example of how masked quantum information can be restored to its original state.
Abstract By studying quantum information masking (QIM) in non-Hermitian quantum systems, we show that mutually orthogonal quantum states can be deterministically masked, while an arbitrary set of quantum states cannot be masked in non-Hermitian quantum systems. We further demonstrate that a set of linearly independent states which are mutually η -orthogonal can be deterministically masked by a pseudo-unitary operator. Moreover, we study robustness of QIM against noisy environments. The robustness of deterministic and probabilistic QIM under different quantum noise channels is analyzed in detail. Accordingly, we propose and discuss the r -uniform probabilistic QIM in multipartite systems.
Abstract Quantum information masking is a protocol that hides the original quantum information from subsystems and spreads it over quantum correlation, which is available to multipartite except bipartite systems. In this work, we explicitly study the quantum information masking in multipartite scenario and prove that there exists an universal quantum masker can mask the information encoding in the unknown states into a multipartite system with lower-dimensional local systems, namely, all the k-level quantum states can be masked into a m-qudit systems (m ≥ 4) whose local dimension d ≤ k . In order to observe the masking process intuitively, explicitly controlled operations are provided. Our scheme well demonstrates the abundance of quantum correlation between multipartite quantum system and has potential application in the security of quantum information processing.
A pure state of N parties with local dimension d is called a k-uniform state if all the reductions to k parties are maximally mixed. Based on the connections among k-uniform states, orthogonal arrays and linear codes, we give general constructions for k-uniform states. We show that when d≥4k−2 (resp. d≥2k−1) is a prime power, there exists a k-uniform state for any N≥2k (resp. 2k≤N≤d+1). Specially, we give the existence of 4,5-uniform states for almost every N-qudits. Further, we generalize the concept of quantum information masking in bipartite systems given by [Modi \emph{et al.} {Phys. Rev. Lett. \textbf{120}, 230501 (2018)}] to k-uniform quantum information masking in multipartite systems, and we show that k-uniform states and quantum error-correcting codes can be used for k-uniform quantum information masking.
It is impossible to mask an arbitrary quantum state into the correlations between two subsystems such that the original information is completely unknown to each local system. This is the no-masking theorem proposed by Modi et al. [K. Modi, A. K. Pati, A. Sen(De), and U. Sen, Phys. Rev. Lett. 120, 230501 (2018)]. In this work, we propose the concept of k-uniform quantum information masking in multipartite systems and indicate the relation between quantum error-correcting codes (QECCs) in heterogeneous systems and quantum information masking. As a consequence, we show that the no-masking theorem is a special case of the quantum Singleton bound for QECCs in heterogeneous systems essentially, and we give a more general no-masking theorem in multipartite systems based on the quantum Singleton bound. We also solve two open questions proposed by Li and Wang [M.-S. Li and Y.-L. Wang, Phys. Rev. A 98, 062306 (2018)]. That is, an arbitrary state of level d cannot be masked in a tripartite system of level d such that the marginal states are not proportional to identity, and an arbitrary state of level d cannot be masked in a tripartite system of level n with n<d. Further, we give some methods for constructing new QECCs from old QECCs in heterogeneous systems.