Classical state masking over a quantum channel

Transmission of classical information over a quantum state-dependent channel is considered, when the encoder can measure channel side information (CSI) and is required to mask information on the quantum channel state from the decoder. In this quantum setting, it is essential to conceal the CSI measurement as well. A regularized formula is derived for the masking equivocation region, and a full characterization is established for a class of measurement channels.

Figure 1

Coding for a quantum state-dependent channel ${\mathcal{N}}_{EA\to B}$ given side information at the encoder and masking from the decoder. The quantum systems of Alice and Bob are marked in red and blue, respectively. The channel state systems $E^n$ and $C^n$ are marked in brown. Alice wishes to send a classical message $m$ to Bob. She has access to side-information systems $E_0^n$, which are entangled with the channel state systems $E^n$. Alice performs a measurement $\mathcal{T}$, and obtains a measurement outcome $V$. Then, she applies an encoding map $\mathcal{F}:(m,V)\to {\rho }_{A^n}$, and transmits the system $A^n$ over the channel. Bob receives the channel output system $B^n$, and applies the decoding measurement $\mathcal{D}:{\rho }_{B^n}\to \widehat{m}$ to obtain an estimate $\widehat{m}$ for Alice's message, as a measurement outcome. A leakage rate $L$ is achieved if $\frac{1}{n}I{(B^n;C^{n}V)}_{\rho }\le L$.