Bosonic pure-loss channel, which represents the process of photons decaying into a vacuum environment, has zero quantum capacity when the channel’s transmissivity is less than 50%. Modeled as a beam splitter interaction between the system and its environment, the performance of bosonic pure-loss channel can be enhanced by controlling the environment state. We show that by choosing the ideal Gottesman-Kitaev-Preskill (GKP) states for the system and its environment, perfect transmission of quantum information through a beam splitter is achievable at arbitrarily low transmissivities. Our explicit constructions allow for experimental demonstration of the improved performance of a quantum channel through passive environment assistance, which is potentially useful for quantum transduction where the environment state can be naturally controlled. In practice, it is crucial to consider finite-energy constraints, and high-fidelity quantum communication through a beam splitter remains achievable with GKP states at the few-photon level.
Bosonic pure-loss channel, which represents the process of photons decaying into a vacuum environment, has zero quantum capacity when the channel’s transmissivity is less than 50%. Modeled as a beam splitter interaction between the system and its environment, the performance of bosonic pure-loss channel can be enhanced by controlling the environment state. We show that by choosing the ideal Gottesman-Kitaev-Preskill (GKP) states for the system and its environment, perfect transmission of quantum information through a beam splitter is achievable at arbitrarily low transmissivities. Our explicit constructions allow for experimental demonstration of the improved performance of a quantum channel through passive environment assistance, which is potentially useful for quantum transduction where the environment state can be naturally controlled. In practice, it is crucial to consider finite-energy constraints, and high-fidelity quantum communication through a beam splitter remains achievable with GKP states at the few-photon level.
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.
The Gottesman-Kitaev-Preskill (GKP) code is a promising bosonic quantum error-correcting code, encoding logical qubits into a bosonic mode in such a way that many physically relevant noise types can be corrected effectively. A particularly relevant noise channel is the pure loss channel, which the GKP code is known to protect against. In particular, it is commonly pointed out that losses can be corrected by the GKP code by transforming the losses into random Gaussian displacements through a quantum-limited amplification channel. However, implementing such amplification in practice is not ideal and could easily introduce an additional overhead of noise from associated experimental imperfections. Here, we analyze the performance of teleportation-based GKP error correction against loss in the absence of an amplification channel. We show that amplification is not required to perform GKP error correction and that performing amplification actually worsens the performance for practically relevant parameter regimes.
Quantum error-correction codes protect information from realistic noisy channels and lie at the heart of quantum computation and communication tasks. Understanding the optimal performance and other information-theoretic properties, such as the achievable rates, of a given code is crucial, as these factors determine the fundamental limits imposed by the encoding in conjunction with the noise channel. Here, we use the transpose channel to analytically obtain the near-optimal performance of any Gottesman-Kitaev-Preskill (GKP) code under pure loss and pure amplification. We present rigorous connections between GKP code’s near-optimal performance and its dual lattice geometry and average input energy. With no energy constraint, we show that when | τ / ( 1 − τ ) | is an integer, specific families of GKP codes simultaneously achieve the loss and amplification capacity. τ is the transmissivity (gain) for loss (amplification). Our results establish GKP code as the first structured bosonic code family that achieves the capacity of loss and amplification.
Quantum repeaters constitute a promising platform for enabling long-distance quantum communication and may ultimately serve as the backbone of a secure quantum internet, a scalable quantum network, or a distributed quantum computer. An efficient approach to encoding qubits within an error correcting code is provided by bosonic codes, in which even a single oscillator mode can function as a sufficiently large physical system. In this work, we initially investigate the bosonic Gottesman Kitaev Preskill (GKP) code as a promising platform for loss correcting quantum repeaters, compatible with room temperature implementation, and analyse how loss and other noise sources propagate through the circuit using Heisenberg evolution. We analyse three quantum repeater protocols in which transmission loss is suppressed at the cost of logical errors, identifying a relay-like teleamplifier as the optimal scheme. This enables long distance quantum communication via densely packed nodes without higher-level encoding, and we evaluate the resulting secure key rates exploiting analog syndrome information. Furthermore, we propose a concatenated Bell-state measurement (CBSM) scheme with a modified parity encoding based on GKP qubits, CV measurement with teleamplifier and a clipping method that corrects transmission loss without introducing logical errors. This significantly enhances the possible secure key distance. We find that GKP based repeaters can achieve performance comparable to approaches relying on photonic qubits, while requiring orders of magnitude fewer qubits. Our parity encoded GKP repeater protocol achieves a substantially higher secret key rate than existing GKP based repeater schemes while maintaining a comparable resource overhead.
A general attenuator ${\mathrm{\ensuremath{\Phi}}}_{\ensuremath{\lambda},\ensuremath{\sigma}}$ is a bosonic quantum channel that acts by combining the input with a fixed environment state $\ensuremath{\sigma}$ in a beam splitter of transmissivity $\ensuremath{\lambda}$. If $\ensuremath{\sigma}$ is a thermal state, the resulting channel is a thermal attenuator, whose quantum capacity vanishes for $\ensuremath{\lambda}\ensuremath{\le}1/2$. We study the quantum capacity of these objects for generic $\ensuremath{\sigma}$, proving a number of unexpected results. Most notably, we show that for any arbitrary value of $\ensuremath{\lambda}>0$ there exists a suitable single-mode state $\ensuremath{\sigma}(\ensuremath{\lambda})$ such that the quantum capacity of ${\mathrm{\ensuremath{\Phi}}}_{\ensuremath{\lambda},\ensuremath{\sigma}(\ensuremath{\lambda})}$ is larger than a universal constant c>0. Our result holds even when we fix an energy constraint at the input of the channel, and implies that quantum communication at a constant rate is possible even in the limit of arbitrarily low transmissivity, provided that the environment state is appropriately controlled. We also find examples of states $\ensuremath{\sigma}$ such that the quantum capacity of ${\mathrm{\ensuremath{\Phi}}}_{\ensuremath{\lambda},\ensuremath{\sigma}}$ is not monotonic in $\ensuremath{\lambda}$. These findings may have implications for the study of communication lines running across integrated optical circuits, of which general attenuators provide natural models.
Bosonic quantum computation harnesses the infinite-dimensional Hilbert space of harmonic oscillators, offering scalable architectures with inherent error correction advantages over qubit-based systems. Despite their potential, bosonic modes encounter significant challenges from prevalent noise sources, particularly photon loss and dephasing, which degrade quantum coherence. Among bosonic error-correcting codes, the Gottesman-Kitaev-Preskill (GKP) code stands out for its ability to correct small phase-space displacements, enabling applications in quantum communication, sensing, and computation. While ideal GKP states require infinite squeezing and are unphysical, the finite squeezing approximate GKP states have been experimentally realized, though their performance depend critically on the squeezing level and measurement strategies. This work addresses a central challenge: how to optimize the squeezing parameter of approximate GKP states and the local oscillator (LO) phase in homodyne detection to maximize precision in estimating bosonic loss-dephasing channel parameters. To address this question, we introduce an adaptive optimization framework guided by classical Fisher information (CFI) and quantum Fisher information (QFI). Numerical simulations demonstrate that this adaptive protocol consistently converges to optimal parameter configurations, determining optimized squeezing levels and LO phases. By offering a practical approach to highprecision quantum channel parameter estimation, this framework has broad implications, from quantum metrology to enabling robust quantum communication systems.