Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1403.3069 · Physical Review A

Multiphoton states related via linear optics

Piotr Migdał, Javier Rodríguez-Laguna, Michał Oszmaniec, Maciej Lewenstein

Published Jun 24, 2014• 19 citations
arXivHTMLPDF

Abstract

The problem of transforming n-photon pure states into each other by linear optics without postselection is investigated by finding functions on the Hilbert space that are invariant under linear optical transformations.
DOI
10.1103/physreva.89.062329

Related papers

Unveiling Hierarchical Invariants in Multiphoton Linear Optics

Yang, Baichuan, Hao Zhan, Minghao Mi +3 more

Linear optical networks driven by quantum states of light are important building blocks of photonic quantum technologies. They access large bosonic Hilbert spaces through multiphoton interference. At the same time, their dynamics are generated by single-particle mode transformations, thereby defining a highly structured subset of multiphoton unitaries and setting boundary on linear optics capability. To elucidate this boundary, we reveal an underlying fine-grained symmetry structure that partitions the multiphoton operator space into invariant subspaces and generates a hierarchy of invariants. We experimentally confirm the conservation of high-order invariants and demonstrate their operational utility in characterizing state reachability and the metrological capability of multiphoton probes. Our framework provides a symmetry-based perspective for understanding and harnessing structured multiphoton dynamics across photonic quantum technologies.

arXiv:2506.12857•Jun 15, 2025•1 citation

Engineering multiphoton states for linear optics computation

Paolo Aniello, Cosmo Lupo, M. Napolitano +1 more

arXiv:quant-ph/0606002•The European Physical Journal D•Dec 6, 2006•3 citations

Generation of Multiphoton Entangled States with Linear Optical Elements

盛宇波, Fu‐Guo Deng, 周宏余

我们建议没有诉诸，产生三光子、四光子的纠缠的状态的一个线性光协议纠缠了来源。在这个协议的安装由三横梁 splitters 和二个一半波浪盘子组成。我们能与 postselection 获得三光子、四光子的纠缠的状态，就象另外的协议。这个协议有高效率的优点并且比其它更可行。[从作者抽象]

Chinese Physics Letters•Jan 1, 2008•0 citations

Optimal mode transformations for linear-optical cluster-state generation

Dmitry B. Uskov, Pavel Lougovski, Paul M. Alsing +3 more

We analyze the generation of linear-optical cluster states (LOCSs) via sequential addition of one and two qubits. Existing approaches employ the stochastic linear-optical two-qubit controlled-Z (cz) gate with success rate of $\frac{1}{9}$ per operation. The question of optimality of the cz gate with respect to LOCS generation has remained open. We report that there are alternative schemes to the cz gate that are exponentially more efficient and show that sequential LOCS growth is indeed globally optimal. We find that the optimal cluster growth operation is a state transformation on a subspace of the full Hilbert space. We show that the maximal success rate of postselected entangling $n$ photonic qubits or $m$ Bell pairs into a cluster is ${(\frac{1}{2})}^{n\ensuremath{-}1}$ and ${(\frac{1}{4})}^{m\ensuremath{-}1}$, respectively, with no ancilla photons, and we give an explicit optical description of the optimal mode transformations.

Physical Review A•Jun 15, 2015•4 citations

Generation of multi-photon entangled states by using linear optical elements and a projective measurement

X.-B. Zou, K. Pahlke, Wolfgang M. Mathis

Physics Letters A•Dec 1, 2002•2 citations

An algebraic approach to linear-optical schemes for deterministic quantum computing

Paolo Aniello, Ruben Coen-Cagli

Linear-optical passive (LOP) devices and photon counters are sufficient to implement universal quantum computation with single photons, and particular schemes have already been proposed. In this paper we discuss the link between the algebraic structure of LOP transformations and quantum computing. We first show how to decompose the Fock space of N optical modes in finite-dimensional subspaces that are suitable for encoding strings of qubits and invariant under LOP transformations (these subspaces are related to the spaces of irreducible unitary representations of U ( N ). Next we show how to design in algorithmic fashion LOP circuits which implement any quantum circuit deterministically. We also present some simple examples, such as the circuits implementing a cNOT gate and a Bell state generator/analyser.

arXiv:quant-ph/0504108•Journal of Optics B Quantum and Semiclassical Optics•Nov 22, 2005•13 citations
Linear optical networks driven by quantum states of light are important building blocks of photonic quantum technologies. They access large bosonic Hilbert spaces through multiphoton interference. At the same time, their dynamics are generated by single-particle mode transformations, thereby defining a highly structured subset of multiphoton unitaries and setting boundary on linear optics capability. To elucidate this boundary, we reveal an underlying fine-grained symmetry structure that partitions the multiphoton operator space into invariant subspaces and generates a hierarchy of invariants. We experimentally confirm the conservation of high-order invariants and demonstrate their operational utility in characterizing state reachability and the metrological capability of multiphoton probes. Our framework provides a symmetry-based perspective for understanding and harnessing structured multiphoton dynamics across photonic quantum technologies.
We analyze the generation of linear-optical cluster states (LOCSs) via sequential addition of one and two qubits. Existing approaches employ the stochastic linear-optical two-qubit controlled-Z (cz) gate with success rate of 19\frac{1}{9}91​ per operation. The question of optimality of the cz gate with respect to LOCS generation has remained open. We report that there are alternative schemes to the cz gate that are exponentially more efficient and show that sequential LOCS growth is indeed globally optimal. We find that the optimal cluster growth operation is a state transformation on a subspace of the full Hilbert space. We show that the maximal success rate of postselected entangling nnn photonic qubits or mmm Bell pairs into a cluster is ${(\frac{1}{2})}^{n\ensuremath{-}1}$ and ${(\frac{1}{4})}^{m\ensuremath{-}1}$, respectively, with no ancilla photons, and we give an explicit optical description of the optimal mode transformations.
Linear-optical passive (LOP) devices and photon counters are sufficient to implement universal quantum computation with single photons, and particular schemes have already been proposed. In this paper we discuss the link between the algebraic structure of LOP transformations and quantum computing. We first show how to decompose the Fock space of N optical modes in finite-dimensional subspaces that are suitable for encoding strings of qubits and invariant under LOP transformations (these subspaces are related to the spaces of irreducible unitary representations of U ( N ). Next we show how to design in algorithmic fashion LOP circuits which implement any quantum circuit deterministically. We also present some simple examples, such as the circuits implementing a cNOT gate and a Bell state generator/analyser.