The utility of noiseless linear amplification and attenuation in single-rail discrete-variable quantum communications

TL;DR

This paper addresses losses in single-rail discrete-variable quantum communication by optimizing measurements and testing physically realizable loss-mitigation tools. It develops a POVM-based framework and compares it with noiseless attenuation (NA) and noiseless linear amplification (NLA) circuits for SR-DV teleportation and superdense coding, focusing on average fidelity and quantum advantage. Key findings show average teleportation fidelity improvements up to about $78\%$ and quantum-advantage gains exceeding $100\%$ in certain loss regimes, with the surprising result that the optimal POVMs effectively reduce to NA or NLA operations. The results highlight that simple, experimentally accessible NA/NLA circuits can capture the essential performance gains, suggesting robust, near-term approaches for loss-resilient SR-DV quantum communication and informing satellite-based link design where teleportation shows broad applicability.

Abstract

Quantum communication offers many applications, with teleportation and superdense coding being two of the most fundamental. In these protocols, pre-shared entanglement enables either the faithful transfer of quantum states or the transmission of more information than is possible classically. However, channel losses degrade the shared states, reducing teleportation fidelity and the information advantage in superdense coding. Here, we investigate how to mitigate these effects by optimising the measurements applied by the communicating parties. We formulate the problem as an optimisation over general positive operator-valued measurements (POVMs) and compare the results with physically realisable noiseless attenuation (NA) and noiseless linear amplification (NLA) circuits. For teleportation, NLA/NA and optimised POVMs improve the average fidelity by up to 78% while maintaining feasible success probabilities. For superdense coding, they enhance the quantum advantage over the classical channel capacity by more than 100% in some regimes and shift the break-even point, thereby extending the tolerable range of losses. Notably, the optimal POVMs effectively reduce to NA or NLA, showing that simple, experimentally accessible operations already capture the essential performance gains.

Figures (11)

• Figure 1: Schematic of SR-DV teleportation with the POVMs. Charlie prepares a maximally entangled Bell state and distributes one qubit each to Alice and Bob through pure-loss channels with transmittivities $T_A$ and $T_B$, respectively. Both parties apply a POVM to their received qubits. Upon a successful outcome, Alice combines the unknown input state with her qubit and performs a Bell-state measurement, sending the result to Bob, who applies the corresponding correction.
• Figure 2: Circuit used by Alice and Bob to implement NLA or NA. The beam splitter transmittivities $g_A$ and $g_B$ are tuned independently to maximise the mean fidelity of the teleported states. The input $\rho_{\text{in}}$ denotes the qubit (belonging to either Alice or Bob) entering the circuit for amplification or attenuation. For $g_X>0.5$ ($X\in{A,B}$), the corresponding qubit undergoes attenuation, while for $g_X<0.5$ it is amplified. A successful operation is heralded when exactly one detector registers a click, yielding the output state $\rho_{\text{out}}.$
• Figure 3: Schematic of SR-DV teleportation with the NLA/NA circuit. Charlie prepares a maximally entangled Bell state and distributes one qubit each to Alice and Bob through pure-loss channels with transmittivities $T_A$ and $T_B$, respectively. Each party applies an NLA/NA circuit to their received qubit. A successful operation is heralded by a single-photon detection. Alice then combines the unknown input state with her qubit and performs a Bell-state measurement, forwarding the result to Bob, who applies the appropriate correction.
• Figure 4: Fidelities of SR-DV teleportation for $N=300$ input states. Brown boxes show the baseline performance without any additional operation. Blue boxes correspond to teleportation where Alice and Bob apply NLA or NA, with the circuit gains optimised to maximise the average fidelity. Orange boxes correspond to teleportation where Alice and Bob implement a POVM optimised for the best average fidelity. (a) Charlie distributes qubits to Alice and Bob with $T_A = T_B = 0.05$. (b) Charlie distributes qubits to Alice and Bob with $T_A = T_B = 0.9$. (c) Alice receives her qubit without loss ($T_A = 1$), while Bob’s qubit experiences a transmission of $T_B = 0.05$. (d) Bob receives his qubit without loss ($T_B = 1$), while Alice’s qubit experiences a transmission of $T_A = 0.05$.
• Figure 5: Comparison of baseline, NLA/NA, and POVM teleportation across different transmission regimes, shown in terms of average fidelities and optimised gains. (a) Average fidelities for the three cases: baseline teleportation (orange), teleportation with NLA/NA using optimised gains (blue), and teleportation with optimised POVMs (brown). In this panel, Charlie distributes the qubits to Alice and Bob through pure-loss channels with equal transmissions $T_A = T_B$. Panels (b) and (c) present the fidelities under asymmetric transmissions. In panel (b), Alice’s qubit is transmitted without loss ($T_A = 1$), while Bob’s qubit has transmission $T_B$ varying from $0$ to $1$. Conversely, in panel (c), Bob’s qubit is transmitted without loss ($T_B = 1$), while Alice’s qubit has transmission $T_A$. Panels (d), (e), and (f) show the optimised gains for NLA/NA teleportation corresponding to the regimes $T_A = T_B$, $T_A = 1$, and $T_B = 1$, respectively.