Quantum masking is a special type of secret sharing in which some information gets reversibly distributed into a multipartite system, leaving the original information inaccessible to each subsystem. This paper proposes a dynamical extension of quantum masking to the level of quantum channels. In channel masking, the identity of a channel becomes locally hidden but still globally accessible after its output is sent through a bipartite broadcasting channel. We first characterize all families of d-dimensional unitaries that can be isometrically masked, a condition that holds even in the presence of depolarizing noise. For the case of qubits, we identify which families of Pauli channels can be masked, and we prove that a qubit channel can be masked against the identity if and only if it is unital and has a pure-state fixed point. Masking against the identity describes a scenario in which channel noise becomes completely delocalized through a broadcast map and undetectable through subsystem dynamics alone.
Quantum masking is a special type of secret sharing in which some information gets reversibly distributed into a multipartite system, leaving the original information inaccessible to each subsystem. This paper proposes a dynamical extension of quantum masking to the level of quantum channels. In channel masking, the identity of a channel becomes locally hidden but still globally accessible after its output is sent through a bipartite broadcasting channel. We first characterize all families of d-dimensional unitaries that can be isometrically masked, a condition that holds even in the presence of depolarizing noise. For the case of qubits, we identify which families of Pauli channels can be masked, and we prove that a qubit channel can be masked against the identity if and only if it is unital and has a pure-state fixed point. Masking against the identity describes a scenario in which channel noise becomes completely delocalized through a broadcast map and undetectable through subsystem dynamics alone.
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 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.
Since masking of quantum information was introduced by Modi et al. in [PRL 120, 230501 (2018)], many discussions on this topic have been published. In this paper, we consider relationship between quantum multipartite maskers (QMMs) and quantum error-correcting codes (QECCs). We say that a subset Q of pure states of a system K can be masked by an operator S into a multipartite system $\H^{(n)}$ if all of the image states S∣ψ of states ∣ψ in Q have the same marginal states on each subsystem. We call such an S a QMM of Q. By establishing an expression of a QMM, we obtain a relationship between QMMs and QECCs, which reads that an isometry is a QMM of all pure states of a system if and only if its range is a QECC of any one-erasure channel. As an application, we prove that there is no an isometric universal masker from $\C^2$ into $\C^2\otimes\C^2\otimes\C^2$ and then the states of $\C^3$ can not be masked isometrically into $\C^2\otimes\C^2\otimes\C^2$. This gives a consummation to a main result and leads to a negative answer to an open question in [PRA 98, 062306 (2018)]. Another application is that arbitrary quantum states of $\C^d$ can be completely hidden in correlations between any two subsystems of the tripartite system $\C^{d+1}\otimes\C^{d+1}\otimes\C^{d+1}$, while arbitrary quantum states cannot be completely hidden in the correlations between subsystems of a bipartite system [PRL 98, 080502 (2007)].
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.
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.
Since masking of quantum information was introduced by Modi et al. in [PRL 120, 230501 (2018)], many discussions on this topic have been published. In this paper, we consider relationship between quantum multipartite maskers (QMMs) and quantum error-correcting codes (QECCs). We say that a subset Q of pure states of a system K can be masked by an operator S into a multipartite system $\H^{(n)}$ if all of the image states S∣ψ of states ∣ψ in Q have the same marginal states on each subsystem. We call such an S a QMM of Q. By establishing an expression of a QMM, we obtain a relationship between QMMs and QECCs, which reads that an isometry is a QMM of all pure states of a system if and only if its range is a QECC of any one-erasure channel. As an application, we prove that there is no an isometric universal masker from $\C^2$ into $\C^2\otimes\C^2\otimes\C^2$ and then the states of $\C^3$ can not be masked isometrically into $\C^2\otimes\C^2\otimes\C^2$. This gives a consummation to a main result and leads to a negative answer to an open question in [PRA 98, 062306 (2018)]. Another application is that arbitrary quantum states of $\C^d$ can be completely hidden in correlations between any two subsystems of the tripartite system $\C^{d+1}\otimes\C^{d+1}\otimes\C^{d+1}$, while arbitrary quantum states cannot be completely hidden in the correlations between subsystems of a bipartite system [PRL 98, 080502 (2007)].