Experimental Masking of Real Quantum States

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.

Figure 1

Schematic diagram of quantum-information masking (upper plot) and realization of the masker $M$ of the real ququart based on a quantum walk (lower plot). The coin operators featuring in the figure are given by $X=\left(\begin{array}{cc}0& 1\\ 1& 0\end{array}\right)$, $Z=\left(\begin{array}{cc}1& 0\\ 0& -1\end{array}\right)$, $C_1=\frac{1}{\sqrt{2}}\left(\begin{array}{cc}i& 1\\ -i& 1\end{array}\right)$, and $C_2=\frac{1}{\sqrt{2}}\left(\begin{array}{cc}1& i\\ -1& i\end{array}\right)$.

Figure 2

Experimental setup. The heralded single-photon source (labeled by $S$) on top is realized by spontaneous parametric down-conversion in a type-I $\beta$-barium-borate (BBO) crystal. The rest setup consists of three modules: state-preparation module (labeled by $P$), masking module (labeled by Mask), and measurement module (labeled by Meas). The masking module implements the masker defined in Eq. (3) according to the quantum-walk scheme illustrated in Fig. 1. The photon’s spatial modes labeled at the bottom correspond to the walker’s positions defined in Fig. 1. Two combinations of wave plates of the form HWP-QWP-HWP in the masking module realize the coin operators $C_1$ and $C_2$ defined in the caption of Fig. 1. HWP, half-wave plate; QWP, quarter-wave plate; BD, beam displacer; PBS, polarizing beam splitter; SPCM, single-photon counting module; K9, K9 glass plate.

Figure 3

Experimental characterization of the masking module in Fig. 2. Each blue bar represents the fidelity between the actual output state and the ideal output state associated with each probe state as marked at the bottom of the figure. Each red bar represents the average purity of the two reduced states of the output state. The number in the parentheses above the blue (red) bar indicates the 95% confidence interval of each fidelity estimator (the standard deviation of each purity estimator). The methods for quantifying the confidence interval and the standard deviation are detailed in Appendices pp4 and pp5.

Figure 4

Experimental decoding of the masked state from correlation measurements. Here the input state is given by $(|0⟩+|1⟩+|2⟩+|3⟩)/2$. (a) Mean values $⟨{\sigma }_i\otimes {\sigma }_j⟩$ for $i,j\in \{x,y,z\}$. (b) Matrix elements of the reconstructed density matrix (only real part is shown since the imaginary part is zero by reconstruction; see Appendix pp6). Bars without color represent the original input state, while bars with color represent the reconstructed state.

Figure 5

Relation between the concurrence of the output state and the robustness of imaginarity of the input state, which has the form $(|0⟩+e^{i\varphi }|1⟩)/\sqrt{2}$ with $0\le \varphi \le \pi /2$. The error bars represent the standard deviations of the concurrence estimations, which are determined via resampling (see Appendix pp5).

Figure 6

The preparation module of the experimental setup.

Figure 7

The measurement module of the experimental setup.

Figure 8

Experimental results on the reduced density matrices of the path qubit (${\varrho }_{\mathrm{path}}$) and polarization qubit (${\varrho }_{\mathrm{pola}}$), respectively, of the output states of the masker defined in Eq. (3) in the main text. Here “Re” denotes the real part, and “Im” denotes the imaginary part. The bottom line marks the input probe states associated with the output states. The experimental results demonstrate that all the reduced density matrices are nearly maximally mixed.