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Laser Physics Letters

The condition of masking quantum qutric states

Qin Wang, Sujuan Zhang, Chen‐Ming Bai, Lu Liu

Published Oct 3, 2022• 2 citations
Publisher

Abstract

Abstract In this paper, we obtain a general condition of quantum information masking by studying the quantum states in C 3 . This condition suggests that quantum information can be masked, if and only if the coefficients of the quantum state satisfy the given system of equations. In this case, we discuss a specific example and give an intuitive representation of the image. For the non-orthogonal case of quantum state in C 3 , we acquire the masking quantum information conclusion about the basis. Finally, under the circumstances that one pair of quantum state is not orthogonal, we classify quantum states based on whether they can be masked.

DOI
10.1088/1612-202x/ac9374

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Abstract In this paper, we obtain a general condition of quantum information masking by studying the quantum states in C 3 . This condition suggests that quantum information can be masked, if and only if the coefficients of the quantum state satisfy the given system of equations. In this case, we discuss a specific example and give an intuitive representation of the image. For the non-orthogonal case of quantum state in C 3 , we acquire the masking quantum information conclusion about the basis. Finally, under the circumstances that one pair of quantum state is not orthogonal, we classify quantum states based on whether they can be masked.
Abstract This paper focuses on quantum information masking for the quantum state in two-dimensional Hilbert space. We present a system of equations as the condition of quantum information masking. It is shown that quantum information contained in a single qubit state can be masked, if and only if the coefficients of the quantum state satisfy the given system of equations. By observing the characteristics of non-orthogonal maskable quantum states, we obtain a related conclusion, namely, if two non-orthogonal two-qubit quantum states can mask a single qubit state, they have the same number of terms and the same basis. Finally, for maskable orthogonal quantum states, we analyze two special examples and give their images for an intuitive description.
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.
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.
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.
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.
We investigate quantum information masking for arbitrary dimensional quantum states. We show that mutually orthogonal quantum states can always be served for deterministic masking of quantum information. We further construct a probabilistic masking machine for linearly independent states. It is shown that a set of d dimensional states, {∣a1⟩A,∣a2⟩A,…,∣an⟩A}\{ \vert a_1 \rangle_A, \vert a_2 \rangle_A, \dots, \vert a_n \rangle_A \}{∣a1​⟩A​,∣a2​⟩A​,…,∣an​⟩A​}, n≤dn \leq dn≤d, can be probabilistically masked by a general unitary-reduction operation if they are linearly independent. The maximal successful probability of probabilistic masking is analyzed and derived for the case of two initial states.