Photonic Implementation of Quantum Information Masking

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)], 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.

Figure 1

Photonic qubit masking machine. (a) The quantum circuit of the masking machine. ${\mathcal{R}}_{\alpha }^{\theta }$ and H represent an arbitrary SU(2) rotation and the Hadamard gate, respectively. The tilde line in the rounded rectangle denotes the photon fusion gate, with the detailed implementation using the polarizing beam splitter illustrated in the right subpanel. (b) Experimental configuration. See the main text for details.

Figure 2

Masking of a qubit disk. (a) The maskable disk is the intersection of the plane $x+y+z=1$ and the unit ball. Pure states ${\rho }_1\sim {\rho }_4$ and mixed state ${\rho }_5$ fall on the disk. The blue and orange points denote the initial states deduced from quantum state tomography and the reconstructed final states, respectively. The inset shows a projection of these states on the maskable disk, and the axes are defined as ${\widehat{n}}_1=(-\widehat{x}+\widehat{y})/\sqrt{2}$ and ${\widehat{n}}_2=(-\widehat{x}-\widehat{y}+2\widehat{z})/\sqrt{6}$. (b) Experimentally determined marginal states after masking, and the trace distance from their theoretical values. (c) and (d) The density matrix of the bipartite state resulted from masking ${\rho }_1$ and ${\rho }_4$. Solid and dashed bars denote the experimental values and theoretical predictions, respectively.

Figure 3

Zero measure of maskable sets. The maskable disks are encircled by the line of constant latitudes $\varphi$ on the Bloch sphere. Each plot shows the trace distance of Bob’s marginal density matrices from the reference state, when Alice slightly shifts the initial state away from a reference point on different latitudes. The cases of displacement along a parallel or a meridian on the Bloch sphere are plotted, respectively, in green and cyan points (experimental data) and curves (theoretical values). The error bars correspond to the $1\sigma$ standard deviation, deduced from a Poissonian counting statistics.

Figure 4

Application of QIM. (a) Sharing of a secret state among multiple recipients. Alice masks a secret quantum state $\rho$ using three maskers ${\mathcal{U}}_i$, and send one resulting marginal state to ${\mathrm{Bob}}_i$, respectively. From the information of the marginal states and the masker informed by Alice, every Bob independently interprets the possible disk that contains the masked states. The original state is pinned at the intersection of the three disks. (b) Protecting quantum information in a noisy channel. Given only access to the quantum channels with phase errors $\exp (-i{\sigma }_{z}t)$, a qubit can still be correctly transmitted using QIM based on the masker ${\mathcal{U}}_0^0$.