Communication through the combination of quantum switch and coherent superposition of channels

TL;DR

This work investigates how higher-order quantum maps—specifically quantum switches and coherent superpositions of channels—influence the transmission of classical and quantum information through noisy channels. Using a CPTP/Kraus framework and vacuum-extension construction, it derives Kraus representations for a range of configurations, including nested and hybrid supermaps. The authors compute one-shot classical capacity $C(\mathcal{E})$ and quantum capacity $Q(\mathcal{E})$, defined as $C(\mathcal{E})=\max_{\{p_i,\rho_i\}} \chi(\{\mathcal{E}(\rho_i),p_i\})$ and $Q(\mathcal{E})=\max_{\rho} I_c(\rho,\mathcal{E})$, across Bit-Flip, Phase-Flip, and Depolarizing channels, revealing that coherent superposition of two channels often yields the largest capacities, while some nested configurations provide limited or no advantage. The results guide practical design choices for robust quantum communication, showing when indefinite causal order or path superposition offers meaningful gains. In particular, coherent superposition of two identical channels frequently outperforms more complex hybrids, while for mixed-channel scenarios, specific configurations (e.g., certain switch-based schemes) can be optimal depending on the channel types and noise levels.

Abstract

The quantization of particle trajectories gives rise to remarkable features such as the coherent superposition of quantum channels and the quantum switch, which offer significant advantages in the communication of both classical and quantum information. In this study, we investigate the classical and quantum capacities of various supermaps, including individual quantum switches, coherent superpositions of channels, their combinations, and hybrid superpositions. A comparative analysis of these configurations reveals the scenarios in which specific combinations yield enhanced communication advantages.

Figures (9)

• Figure 1: This is a diagram of a quantum switch. (a) In the case where the control is in the $\dyad{0}{0}$ state, the information passes $\boldsymbol{\mathcal{E}}^{(1)}$ before proceeding to $\boldsymbol{\mathcal{E}}^{(2)}$. (b) In this case, the control is in $\dyad{1}{1}$ state, the order is $\boldsymbol{\mathcal{E}}^{(2)}$ then $\boldsymbol{\mathcal{E}}^{(1)}$. (c) For control qubits in the superposition $\ketbra{+}{+}$, the information passes concurrently through a superposition of the two pathways at the same time. $\boldsymbol{\mathcal{E}}^{(1)}$$\&$$\boldsymbol{\mathcal{E}}^{(2)}$ are two quantum channels.
• Figure 2: A diagram of coherent Superposition of two individual quantum channels defined as $\boldsymbol{\mathcal{E}^{(1)}}$ and $\boldsymbol{\mathcal{E}^{(2)}}$. $\rho_c$ is the control qubit, which is initiated in the state $\dyad{+}{+}$, and $\rho_t$ is the target qubit, on which the information that needs to be transferred is encoded.
• Figure 3: Diagram of a quantum switch $\mathcal{S}^{\prime}$ Consist of quantum switch $\mathcal{S}_1$ (above) and, $\mathcal{S}_2$ (below). $\rho_c$ is the control which is equal to $\dyad{++}{++}$ . $\rho_t$ is the target qubit. $\mathcal{S}_1$ has $\boldsymbol{\mathcal{E}^{(1)}}$, $\boldsymbol{\mathcal{E}^{(2)}}$$\&$$\mathcal{S}_2$ has $\boldsymbol{\mathcal{E}^{(3)}}$, $\boldsymbol{\mathcal{E}^{(4)}}$.
• Figure 4: A diagram of coherent superposition of coherent superposition
• Figure 5: A diagram of a quantum switch of coherent superposition