We study the problem of information masking through nonzero linear operators that distribute information encoded in single qubits to the correlations between two qubits. It is shown that a nonzero linear operator cannot mask any nonzero measure set of qubit states. We prove that the maximal maskable set of states on the Bloch sphere with respect to any masker is the ones on a spherical circle. Any states on a spherical circle on the Bloch sphere are maskable, which also proves the conjecture on maskable qubit states given by Modi et al. [Phys. Rev. Lett. 120, 230501 (2018)]. we provide explicitly operational unitary maskers for all maskable sets. As applications, different protocols for secret sharing are introduced.
We study the problem of information masking through nonzero linear operators that distribute information encoded in single qubits to the correlations between two qubits. It is shown that a nonzero linear operator cannot mask any nonzero measure set of qubit states. We prove that the maximal maskable set of states on the Bloch sphere with respect to any masker is the ones on a spherical circle. Any states on a spherical circle on the Bloch sphere are maskable, which also proves the conjecture on maskable qubit states given by Modi et al. [Phys. Rev. Lett. 120, 230501 (2018)]. we provide explicitly operational unitary maskers for all maskable sets. As applications, different protocols for secret sharing are introduced.
We study quantum information masking based on isometric linear operators that distribute the information encoded in pure states to the correlations in bipartite states. It is shown that an isometric linear operator cannot mask any nonzero measure set of pure states. We present a geometric characterization of the maskable sets and show that any maskable set must be on a spherical circle in certain Euclidean spaces. Detailed examples and potential applications such as secret sharing and quantum cryptography are analyzed.
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♯ 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⋄ 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♯ and S⋄, respectively.
Masking of quantum information is a way of hiding information in correlations such that no information is accessible to any local observer. Although the set of all quantum states as a whole cannot be masked into bipartite correlations according to the no-masking theorem, the set of real states is maskable and is a maximal maskable set. In this work, we experimentally realize a masking protocol of the real ququart by virtue of a photonic quantum walk. Our experiment clearly demonstrates that quantum information of the real ququart can be completely hidden in bipartite correlations of two-qubit hybrid entangled states, which are encoded in two different degrees of freedom of a single photon. The hidden information is not accessible from each qubit alone, but can be faithfully retrieved with a fidelity of about 99% from correlation measurements. By contrast, any superset of the set of real density matrices cannot be masked.
Abstract Quantum information masking (QIM) entails the transmission of quantum information from a single qubit to the entanglement within quantum system, demonstrating promise for utilization in quantum communication. However, the absence of a universal masker capable of masking all qubits restricts its utility in quantum communication and poses a threat to information security. Here we successfully implement the improved QIM method by designing a quantum masking machine capable of masking the set of states on arbitrary disks. The analysis of several sets of target-qubit states proves that our study extends the range of maskable sets in QIM. Through this approach, we devise a scheme for quantum secret sharing (QSS) and demonstrate its feasibility using a proof-of principle experiment. This research results not only provides new experimental evidence for QIM, but also lays a solid foundation for its application in quantum communication.1. IntroductionThroughout history, reliable and secure communication has been crucial for the development and even survival of individuals and nations. Classical cryptosystems rely on computational complexity for encryption, while quantum cryptography [1, 2] leverages the principles of quantum information to offer enhanced levels of security [3–5].Various no-go theorems are essential for improving the security and integrity of quantum communication [6–14]. These theorems imply that certain operations that cannot be performed on quantum states used for transmitting information, such as the no-cloning theorem [15–17], the no-broadcasting theorem [18], the no-deleting theorem [19] and the no-hiding theorem [20, 21], etc. A new no-go theorem, known as the no-masking theorem [22], has recently been discovered and proven in relation to the quantum information masking (QIM) [23–30], a technique utilized for transferring information stored in a single qubit to the entanglement of a multi-qubit system. The no-masking theorem demonstrates that there is no universal masker capable of masking all states of a qubit in two-dimensional Hilbert space. For example, the analysis of the maskable sets shows that only quantum information stored strictly in phase can be masked by one masker. This limitation poses a potential security risk in quantum communication, as unmasked information (e.g., latitude of the Bloch sphere) could be exploited by eavesdroppers.In this paper, we proposes an improved QIM method to mask the set of qubit states on any Bloch sphere disk using a single masker and experimentally demonstrates a QSS scheme based on this approach. This approach can extends the range of maskable sets for QIM by utilizing an adapter to aid a single masker in building the improved quantum masking machine. In particular, we ingeniously apply these maskable sets to QSS to prevent hackers from inferring the transmission state solely from the single reduced qubit, while still allowing both parties to extract information from entanglement for secure communication. Our single-photon experiments have clearly demonstrated how QSS can be effectively implemented on an improved quantum information masking machine, enabling the transmission of a set of quantum states across an arbitrary disk. Our research extends the scope of maskable sets in QIM, proposes a QSS scheme based on these sets, and experimentally verifies its feasibility, thereby expanding the potential applications of QIM.
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.
Classical information can be completely hidden in the correlations of bipartite quantum systems. However, it is impossible to hide or mask all quantum information according to the no-hiding and no-masking theorems derived recently. Here we show that any set of informationally complete quantum states is neither hidable nor maskable, thereby strengthening the no-hiding and no-masking theorems known before. Then, by virtue of Hurwitz-Radon matrices (representations of the Clifford algebra), we show that information about real quantum states can be completely hidden in the correlations, although the minimum dimension of the composite Hilbert space required increases exponentially with the dimension of the original Hilbert space. Moreover, the set of real quantum states is a maximal maskable set within quantum theory and has a surprising connection with maximally entangled states. These results offer valuable insight on the potential and limit of hiding and masking quantum information, which are of intrinsic interest to a number of active research areas.