General Photon Subtraction from a Gaussian Perspective

Niklas Budinger; Ulrik L. Andersen; Peter van Loock

Home/Archive/arXiv

arXiv · 2609.34803

General Photon Subtraction from a Gaussian Perspective

Niklas Budinger·Ulrik L. Andersen·Peter van Loock

View original source ↗Read source document ↗Export metadata ↓

Abstract

A near-deterministic source of non-Gaussianity is the missing piece to reach universal and fault-tolerant quantum computing with continuous-variable optics. Due to a lack of strong non-linearities, the probabilistic photon-subtracted Gaussian states remain the most promising contender. In combination with Gaussian measurements and single-mode feed-forward operations, they have been shown to provide sufficient non-Gaussianity at high rates. However, these existing breeding protocols lack the necessary loss tolerance to be experimentally feasible. In this work, we introduce a mathematical formalism based on the application of a Gaussian blur and filter on the measured Fock Wigner function to describe general photon-subtracted Gaussian states. Within our representation, the initial squeezing, Gaussian measurements, and photon loss can all be understood as contributions to the total blurring and interchanged accordingly. We find that this intuitive approach can be used to find improvements to cat, cubic phase, and GKP state generation by compromising between success rates, feed-forward compatibility, and loss tolerance. In the case of multiple photon subtractions, this is achieved by introducing a hybrid setup variant bridging the gap between protocols based on breeding and post-selection. Finally, we establish a general lower bound on the resources needed to generate a given target state near-deterministically by introducing the expected Wigner logarithmic negativity as an additive monotone of non-Gaussianity.

Explore related subjects

quant-ph

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Niklas Budinger, Ulrik L. Andersen, Peter van Loock. 2026-09-28. General Photon Subtraction from a Gaussian Perspective. https://arxiv.org/abs/2609.34803

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Self-duality and Jordan structure of quantum theory follow from homogeneity and pure transitivity

Quantum theory satisfies the mathematically powerful property of self-duality, meaning that its state and effect spaces are made isomorphic by an inner product. This is why both quantum states and effects can be represented by positive Hermitian operators. The seminal Koecher-Vinberg theorem shows that self-duality is a rather special property: any system that is self-dual and also homogeneous, meaning that the group of symmetries of its cone of unnormalised states acts transitively on the strictly positive states, must be isomorphic to a Euclidean Jordan algebra. EJAs have been classified and are known to be just a slight generalisation of quantum systems. This is why the Koecher-Vinberg theorem, and hence self-duality and homogeneity, have been used in several reconstructions of quantum theory from first principles. While homogeneity has an operational derivation from the ability to steer states, self-duality currently lacks such a clear operational motivation. In this paper we prove an alternative to the Koecher-Vinberg theorem, substituting for self-duality the more operational property of pure transitivity: symmetries of the normalised state space act transitively on the pure states. We show that any system that is homogeneous and satisfies pure transitivity must be self-dual, and hence isomorphic to an EJA. Together with various ways of singling out the complex matrix algebras from among EJAs, and known ways of ruling out classicality in these, this yields several new and concise reconstructions of quantum theory. For example, quantum systems, classical systems, and composites of these are the only ones that are homogeneous, satisfy pure transitivity, and allow locally tomographic composites; fully quantum systems are the only ones that are homogeneous, have continuous pure transitivity, and allow a correspondence between observables and generators of reversible transformations.

quant-ph↗

arXiv2026

Quantum algorithm for the gradient of a logarithm-determinant

The logarithm-determinant is a widely-present operation in many areas of physics and computer science. Derivatives of the logarithm-determinant compute physically relevant quantities in statistical physics models, quantum field theories, as well as the inverses of matrices. A multi-variable version of the quantum gradient algorithm is developed here to evaluate the derivative of the logarithm-determinant. From this, the pseudo-inverse of a sparse-rank input operator may be determined efficiently. Measuring an expectation value of the quantum state--instead of all $N^2$ elements of the input operator--can be accomplished in $O(k/\varepsilon^2)$ time in the idealized case for $k$ relevant eigenvectors of the input matrix with precision $\varepsilon$. A practical implementation of the required operator will likely need $\log_2N$ overhead, giving an overall complexity of $O((k\log_2 N)/\varepsilon^2)$. The method applies widely and converges super-linearly in $k$ when the condition number is high. The best classical method we are aware of scales as $N$. Given the same resource assumptions as other algorithms, such that an equal superposition of eigenvectors is available efficiently, the algorithm is evaluated in the practical case as $O(\log_2 N/\varepsilon^2)$. The output is given in $O(1)$ queries of an oracle, which is given explicitly here and only relies on time-evolution operators that can be implemented with arbitrarily small error. The algorithm is envisioned for fully error-corrected quantum computers but may be implementable on near-term machines. We discuss how this algorithm can be used for kernel-based quantum machine-learning.

quant-ph↗

arXiv2026

Spinor Bose-Einstein condensate as an analog simulator of molecular bending vibrations

We demonstrate that spinor Bose-Einstein condensates (BECs) can be operated as an analog simulator of the two-dimensional vibron model. This algebraic model describes bending vibrations of molecules and, in the case of triatomic molecules, exhibits two phases where linear and bent configurations are stabilised. Spinor BECs can be engineered to simulate states that correspond to linear or bent triatomic molecules, with the Wigner function of the BEC encoding information about the molecular configuration. We show how quantum simulations of the bending dynamics of linear molecules can be realised, and how preparing a linear configuration in the bent phase leads to a dynamical instability. In the dynamics triggered by the corresponding instability, a significant amount of entanglement is generated, and we characterise the dynamics with the squeezing parameter and the quantum Fisher information (QFI). The scaling of the non-Gaussian sensitivity, described by the difference between squeezing and QFI, grows with the system size once the spinor system crosses from the linear to the bent phase, thus serving as a dynamical witness for the quantum phase transition.

quant-ph↗