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Journal of quantum computing

The Development and Application of Quantum Masking

Tao Chen, Zhiguo Qu, Yi Chen

Published Jan 1, 2020• 0 citations
Publisher

Abstract

To solve the problem of hiding quantum information in simplified subsystems, Modi et al. [1] introduced the concept of quantum masking. Quantum masking is the encoding of quantum information by composite quantum states in such a way that the quantum information is hidden to the subsystem and spreads to the correlation of the composite systems. The concept of quantum masking was developed along with a new quantum impossibility theorem, the quantum no-masking theorem. The question of whether a quantum state can be masked has been studied by many people from the perspective of the types of quantum states, the number of masking participants, and error correction codes. Others have studied the relationships between maskable quantum states, the deterministic and probabilistic masking of quantum states, and the problem of probabilistic masking. Quantum masking techniques have been shown to outperform previous strategies in quantum bit commitment, quantum multi-party secret sharing, and so on.

DOI
10.32604/jqc.2020.015855

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•Jan 1, 2019•6 citations
To solve the problem of hiding quantum information in simplified subsystems, Modi et al. [1] introduced the concept of quantum masking. Quantum masking is the encoding of quantum information by composite quantum states in such a way that the quantum information is hidden to the subsystem and spreads to the correlation of the composite systems. The concept of quantum masking was developed along with a new quantum impossibility theorem, the quantum no-masking theorem. The question of whether a quantum state can be masked has been studied by many people from the perspective of the types of quantum states, the number of masking participants, and error correction codes. Others have studied the relationships between maskable quantum states, the deterministic and probabilistic masking of quantum states, and the problem of probabilistic masking. Quantum masking techniques have been shown to outperform previous strategies in quantum bit commitment, quantum multi-party secret sharing, and so on.
Classical information encoded in composite quantum states can be completely hidden from the reduced subsystems and may be found only in the correlations. Can the same be true for quantum information? If quantum information is hidden from subsystems and spread over quantum correlation, we call it masking of quantum information. We show that while this may still be true for some restricted sets of nonorthogonal quantum states, it is not possible for arbitrary quantum states. This result suggests that quantum qubit commitment-a stronger version of the quantum bit commitment-is not possible in general. Our findings may have potential applications in secret sharing and future quantum communication protocols.
Masking of quantum information spreads it over nonlocal correlations and hides it from the subsystems. It is known that no operation can simultaneously mask all pure states [Phys. Rev. Lett. 120, 230501 (2018)PRLTAO0031-900710.1103/PhysRevLett.120.230501], so in what sense is quantum information masking useful? Here, we extend the definition of quantum information masking to general mixed states, and show that the resource of maskable quantum states is far more abundant than the no-go theorem seemingly suggests. Geometrically, the simultaneously maskable states lays on hyperdisks in the state hypersphere, and strictly contains the broadcastable states. We devise a photonic quantum information masking machine using time-correlated photons to experimentally investigate the properties of qubit masking, and demonstrate the transfer of quantum information into bipartite correlations and its faithful retrieval. The versatile masking machine has decent extensibility, and may be applicable to quantum secret sharing and fault-tolerant quantum communication. Our results provide some insights on the comprehension and potential application of quantum information masking.
Masking of quantum information means that information is hidden from a subsystem and spread over a composite system. Modi et al. proved in [Phys. Rev. Lett. 120, 230501 (2018)] that this is true for some restricted sets of nonorthogonal quantum states and it is not possible for arbitrary quantum states. In this paper, we discuss the problem of masking quantum information encoded in pure and mixed states, respectively. Based on an established necessary and sufficient condition for a set of pure states to be masked by an operator, we find that there exists a set of four states that can not be masked, which implies that to mask unknown pure states is impossible. We construct a masker S♯S^\sharpS♯ and obtain its maximal maskable set, leading to an affirmative answer to a conjecture proposed in Modi's paper mentioned above. We also prove that an orthogonal (resp. linearly independent) subset of pure states can be masked by an isometry (resp. injection). Generalizing the case of pure states, we introduce the maskability of a set of mixed states and prove that a commuting subset of mixed states can be masked by an isometry S⋄S^{\diamond}S⋄ while it is impossible to mask all of mixed states by any operator. We also find the maximal maskable sets of mixed states of the isometries S♯{S^{\sharp}}S♯ and S⋄{S^{\diamond}}S⋄, respectively.
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.
Masking of data is a method to protect information by shielding it from a third party, however keeping it usable for further usages like application development, building program extensions to name a few. Whereas it is possible for classical information encoded in composite quantum states to be completely masked from reduced sub-systems, it has to be checked if quantum information can also be masked when the future possibilities of a quantum computer are increasing day by day. Newly proposed no-masking theorem [Phys. Rev. Lett. 120, 230501 (2018)], one of the no-go theorems, demands that except for some restricted sets of non-orthogonal states, it's impossible to mask arbitrary quantum states. Here, we explore the possibility of masking in the IBM quantum experience platform by designing the quantum circuits and running them on the 5-qubit quantum computer. We choose two particular states considering both the orthogonal and non-orthogonal basis states and illustrate their masking through both the theoretical calculation as well as verification in the quantum computer. By quantum state tomography, it is concluded that the experimental results are collected with high fidelity and hence the possibility of masking is realized.