Passive Environment-Assisted Quantum Communication

Abstract

As quantum information systems mature, efficient and coherent transfer of quantum information through noisy channels becomes increasingly important. We examine how passive environment-assisted quantum communication enhances direct quantum information transfer efficiency. A bosonic pure-loss channel, modeled as transmission through a beam splitter with a vacuum input state at the dark port, has zero quantum capacity when transmissivity is below 50%. Quantum communication through the channel can be enhanced by passive environment assistance, achieved via the selection of an appropriate input state for the ancilla port. Although ideal Gottesman-Kitaev-Preskill (GKP) states enable perfect quantum information transmission at arbitrarily small transmissivity, they are challenging to realize experimentally. We therefore explore more experimentally accessible non-Gaussian ancilla states, such as Fock, cat, and squeezed cat states, and numerically determine the optimal encoding and decoding strategies. We also construct analytical schemes that yield high-fidelity transmission and good information rates.

Figures (11)

• Figure 1: (a) Beam splitter with efficiency $\eta$. (b) Beam splitter unitary $\hat{U}_\theta$ with quantum channels $\mathcal{E}_1$ and $\mathcal{E}_2$ that convert the input states $\hat{\rho}_1$ and $\hat{\rho}_2$ to output states $\hat{\rho}_3$ and $\hat{\rho}_4$, respectively. (c) Schematic of a two-mode transducer.
• Figure 2: (a) Encoding/decoding scheme: the encoded input state $\mathcal{C}(\hat{\rho})$ and environment state $\hat{\sigma}$ are acted upon by the unitary $\hat{U}_\theta$, after which the system state is decoded by $\mathcal{D}$. (b) Illustration of the entanglement fidelity calculation.
• Figure 3: (a) Wigner functions of optimal encodings for a Fock $|1\rangle$ environment, cat state $\ket{\texttt{cat}_{2,\alpha}}$ with $\alpha=2.0$, and squeezed cat state $\hat{S}(r)\ket{\texttt{cat}_{2,\alpha}}$ with amplitude $\alpha = 1.5$ and squeezing parameter $r = 1.4$. (b) Entanglement fidelity and coherent information rates for the channel (without decoding) with the Fock, cat, and squeezed cat environment states paired with their optimal encodings.
• Figure 4: Panel (a) displays the 2D wavefunctions over real space $x_1$-$x_2$ for the global states $\ket{0_L}\otimes \ket{\mathtt{cat}_{2,\beta}}$ (purple) and $\ket{1_L}\otimes \ket{\mathtt{cat}_{2,\beta}}$ (yellow). The shading represents the amplitude of each wavefunction. The purified action of the loss channel is realized by the unitary $\hat{U}_{\theta}$, which rotates the space clockwise by an angle $\theta = \arccos\sqrt{\eta} \in[0,\pi/2]$. Panels (b) and (c) show the single-letter quantum capacity $\mathcal{Q}^{(1)}$ of $\Lambda\equiv\Lambda_{\texttt{cat},\eta}$ for different values of $\alpha$, $\beta$, and $\eta$. The vertical axis is rescaled as $(1+|\beta/\alpha|^2)^{-1}$. Panels (d) and (e) provide detailed views along the orange dotted line cuts in panels (b,c), showing the channel fidelities and single-letter quantum capacities for different decoders.
• Figure 5: The markers (crosses, circles) represent the coordinates of the transformed infinitely squeezed Gaussian functions in Eq. \ref{['eq:inf_sq_cat']}. The rotation angle due to the beam splitter is $\theta = \pi/2 - \delta$. The environment state is denoted $\ket{\delta;2}$. Each Kraus operator $\hat{L}_k$ corresponds to markers sharing the same $x_2$ coordinate.

Theorems & Definitions (1)

• proof