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arXiv:2210.03978 · Physica Scripta

Quantum information masking of an arbitrary unknown state can be realized in the multipartite lower-dimensional systems

Wei-Min Shang, Xing-Yan Fan, Fulin Zhang, Jing‐Ling Chen

Published Jan 31, 2023• 7 citations
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Abstract

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.

DOI
10.1088/1402-4896/acb7ad

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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.
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.
The no-masking theories show that it is impossible to mask the set of all qubit states into the quantum correlation of bipartite qubit system or tripartite qubit system. In this paper, we give a new proof of the no-masking situation of the tripartite qubit system. Recent work has shown that there exists a universal masker which can mask an arbitrary set of qubit states in four-qubit systems perfectly by means of the maximum entangled states. Here we show that there exist more than one masking scheme even for the same multipartite qubit system. Basing on the maximum entangled states we give the deterministic masking scenario for N-qubit system. In practice, decoherence hinders us from obtaining the maximum entangled states. From this viewpoint, the masking scenario based on non-maximum entangled states becomes more universal. Furthermore, we provide an approximate quantum masking scenario and investigate the relation between approximate masking and quantum entanglement.
The no-masking theorem says that masking quantum information is impossible in a bipartite scenario. However, there exist schemes to mask quantum states in multipartite systems. In this work, we show that, the joint measurement in the teleportation is really a masking process, when the apparatus is regarded as a quantum participant in the whole system. Based on the view, we present two four-partite maskers and a tripartite masker. One of the former provides a generalization in arbitrary dimension of the four-qubit scheme given by Li and Wang [Phys. Rev. A 98, 062306 (2018)], and the latter is precisely their tripartite scheme. The occupation probabilities and coherence of quantum states are masked in two steps of our schemes. And the information can be extracted naturally in their reverse processes.
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 kkk-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 ddd cannot be masked in a tripartite system of level ddd such that the marginal states are not proportional to identity, and an arbitrary state of level ddd cannot be masked in a tripartite system of level nnn with n<dn<dn<d. Further, we give some methods for constructing new QECCs from old QECCs in heterogeneous systems.
The no-masking theorem for quantum information proves that it is impossible to encode an arbitrary input state into a larger bipartite entangled state such that the full information is stored in the correlation but the individual subsystems have no information about the input state. Here, we ask the question: Is it possible to mask an observable such that the information about the observable is available in the joint system, but individual subsystems reveal nothing about the imprints of the observable? This generalizes the notion of masking to observables. We show that a universal unitary that can mask an arbitrary observable in any dimension does not exist. For a qubit system, we show that the masking operation for a given observable is locally unitarily connected to the swap operation. This suggests a conservation law for information content of observables that goes beyond the conservation laws under symmetry operations. Furthermore, we prove that the unconditional no-bit commitment result follows from the no-masking theorem for observables. Our results can have important applications in quantum information and quantum communication where we encode information not in states but in observables.
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.