We prove Gaussian optimality for the energy-constrained one-shot Holevo capacity of single-mode bosonic Gaussian channels, including phase-sensitive channels with arbitrarily squeezed thermal noise. The unresolved regime is the low energy branch, where the Gaussian optimizer modulates only one quadrature and minimum-output-entropy arguments cannot decouple the average state from the letters. For pure one-mode dilations we retain a stronger pointwise result: moment-matched Gaussianization improves the fixed average Holevo function for every input. For mixed environments, whose purification produces a 1:2 entanglement-of-formation problem, we avoid any generic 1:2 Gaussian extremality conjecture. The optimal Gaussian letter selects an effective environmental Schmidt mode and an affine two-mode EPR witness. Its null direction is exactly the modulated quadrature, while its slope equals the negative derivative of the Gaussian letter-output entropy. This produces a supporting lower bound on the dilated entanglement of formation; Gaussian maximum entropy and concavity then give a global upper bound tangent at the Gaussian optimizer. Consequently the known Gaussian formulas for attenuating, amplifying, phase-conjugating, and additive-noise fiducial channels are exact over unrestricted ensembles at every input energy. Via the passive-input fiducial decomposition and energy-constrained continuity, the result extends to every single-mode Gaussian channel, including lower-rank canonical limits. No additivity across channel uses is assumed.
The quantum capacity of the bosonic thermal attenuator, which is given by the regularization of its coherent information, is unknown. The seminal work of Holevo and Werner established in 1999 the standard one-use lower bound obtained from input thermal states. We first prove that this long-standing lower bound is the exact supremum over all single-mode Gaussian states and then show that, crucially, a non-Gaussian state can do better. As a consequence, we prove positivity of the quantum capacity in a parameter region where the channel is not antidegradable, yet its coherent information optimized over single-mode Gaussian states vanishes. For example, with one thermal photon in the environment and at transmissivity $\eta=0.8$, the coherent information is non-positive for every single-mode Gaussian input. We give an explicit rank-two non-Gaussian state, supported on only six Fock levels, whose coherent information is certified to be at least $4.7\times10^{-4}$ qubits per channel use. This short witness is far from numerically optimal: a numerical optimization over fixed non-Gaussian families reaches at least $8.4\times 10^{-3}$ qubits per channel use at the same point. More generally, at $\nu=1$, using non-Gaussian inputs we certify positivity of the coherent information, and therefore of the quantum capacity, down to $\eta=0.7841$; by contrast, the channel is antidegradable, and hence has zero quantum capacity, for $\eta\leq0.75$. Overall, our work identifies new high-noise regimes in which bosonic quantum communication is possible.
Francesco Anna Mele, Giuseppe Catalano, Marco Fanizza et al.· 0 citations
The results identify that complexity of learning arises from irreducible mixing of non-Gaussianity and entanglement, rather than either resource alone.
Quantum convolution provides a discrete-variable analogue of classical convolution, with the mean state capturing the stabilizer structure preserved under repeated convolution. We establish a finite-step entropy hierarchy generated by compatible stabilizer dephasings. Along every compatible isotropic flag, the entropy increases toward the mean-state entropy ceiling, while the relative-entropy distance to the mean state decomposes exactly into successive coherence losses and a terminal classical nonuniformity. Optimizing over compatible subspaces yields an intrinsic entropy profile of the state. For quantum convolutional channels, Weyl covariance reduces the one-shot classical communication problem to minimal output entropy. A spectral-transfer argument shows that suitable stabilizer inputs reproduce stabilizer-measurement distributions of the environment as channel-output spectra. This gives a computable Holevo lower bound over all complete stabilizer measurements; its compatible restriction is characterized by the entropy hierarchy and refines the previous mean-state bound of Bu, Gu, and Jaffe. The bound is exact for stabilizer-diagonal environments, for which the Holevo capacity is strongly additive, and yields a single-letter formula for a nonstabilizer qutrit family. The same family also exhibits a coexistence region with simultaneously positive classical and quantum communication rates
Chunhe Xiong, Sunho Kim, Qing-Hua Zhang et al.· 1 citation
Gaussian states are fundamental in continuous-variable quantum information, yet characterizing non-Gaussianity remains challenging due to the non-convexity of the Gaussian set. Existing witnesses typically rely on Wigner negativity or other information-theoretic quantities. In this work, we develop a group-theoretic, multi-copy approach to detect non-Gaussianity in bosonic systems. We study passive linear optical transformations that mix copies of a quantum state and analyze their commutation with identical Gaussian unitaries applied to each copy. Orthogonal copy-mixing transformations commute with the symplectic part of the Gaussian action, while the displacement part restricts the symmetry to the stabilizer of the collective mode. This structure yields a family of witnesses satisfied by all single-mode Gaussian states. Fixing the thermal reference parameter via the purity, violation of these identities certifies non-Gaussianity. We illustrate the method with several single-mode examples and present an experimental protocol based on passive interferometry and photon-number-resolved detection, showing that the relevant multi-copy expectation values can be estimated from bounded phase observables. Finally, we extend the construction to multi-mode systems and discuss how the same symmetry framework may lead to quantitative measures of non-Gaussianity.
We develop a quantum-decision-theoretic framework for detecting phase-space displacements with finite-energy, $d$-level Gottesman-Kitaev-Preskill (GKP) probes. For single-mode and entanglement-assisted architectures, we derive the Bayesian minimum-error probability, the optimal Neyman-Pearson receiver-operating characteristic, and the corresponding minimum detectable displacement. Finite-energy effects are treated through exact theta-series displacement kernels, while pure loss followed by quantum-limited amplification is mapped to an effective Gaussian random-displacement channel. Entanglement removes preparation-dependent blind directions and preserves both logical displacement labels, although it does not surpass the pointwise optimized single-mode strategy in the noiseless pure-state setting. We benchmark the resulting protocols against coherent-state, direction-matched squeezed-vacuum, and twin-beam schemes at equal nominal squeezing. Numerical results identify finite-squeezing and lossy regimes in which GKP probes achieve both a lower Bayesian error and a smaller minimum detectable perturbation than the selected Gaussian receivers.
Spin-squeezed states enable entanglement-enhanced frequency estimation; however, the achievable performance is limited in practice by decoherence. We study the problem of parameter estimation under \emph{classical collective noise} that acts along a \emph{fixed} direction during signal encoding. While we restrict our analysis to Gaussian noise statistics, no assumption is made on the nature of the noise temporal correlations. Our approach captures both parallel (dephasing) and single-axis transverse noise as special cases, and covers both Markovian and non-Markovian metrological regimes. In the properly squeezed limit, where a Holstein-Primakoff description is accurate, we identify a geometric noise-immunity mechanism: for \emph{known} non-parallel signal and noise axes, an appropriate one-axis-twisted input encodes the signal in a quadrature that is metric-orthogonal to the direction of noise-induced diffusion. Irrespective of the noise temporal correlations, the resulting estimation precision exhibits Heisenberg scaling in the probe number. Optimal performance is achievable by measuring a single collective spin component. Imperfect knowledge of the noise axis produces a crossover from Heisenberg scaling at moderate probe number back to the known collective-dephasing bounds asymptotically.
Francisco Riberi, L. Viola, M. Marvian· 0 citations