Quantum state isomorphism under group actions is BQP-hard for pure states across nontrivial groups and QSZK-complete for mixed states with finite groups; Pauli group version is BQP-complete and Clifford is GI-hard, ruling out efficient quantum algorithms for abelian mixed-state HS unless QSZK=BQP.
hub Canonical reference
Gaussian states in continuous variable quantum information
Canonical reference. 100% of citing Pith papers cite this work as background.
23
Pith papers citing it
Background
100% of classified citations
abstract
These notes originated out of a set of lectures in Quantum Optics and Quantum Information given by one of us (MGAP) at the University of Napoli and the University of Milano. A quite broad set of issues are covered, ranging from elementary concepts to current research topics, and from fundamental concepts to applications. A special emphasis has been given to the phase space analysis of quantum dynamics and to the role of Gaussian states in continuous variable quantum information.
hub tools
citation-role summary
background 7
citation-polarity summary
roles
background 7polarities
background 7representative citing papers
A natural energy condition satisfied by most physical bosonic states, including outputs of universal bosonic circuits, allows the effective dimension for ε-approximations to scale as log(1/ε) instead of 1/ε², enabling improved learning and classical simulation algorithms.
Non-Markovian strong coupling in a bosonic probe produces non-monotonic quantum Fisher information with a finite optimal interrogation time for thermometry, while squeezed states give transient gains and strong coupling softens low-T error scaling from exponential to polynomial.
A variational framework yields closed-form Bayesian estimators for Gaussian quantum states via polynomial quadrature operators and a global optimality condition.
Hawking radiation in a 1+1D analogue black hole induces a UV-finite volume-law term in logarithmic negativity that encodes the density and locations of entangled pairs.
The approximate stellar rank serves as an operational measure of non-Gaussianity that yields bounds and new no-go results for approximate and probabilistic Gaussian state conversion and distillation.
A reverse third-quantization mapping sends Fermi-Hubbard ground states to dissipative Majorana steady states where individual Gaussian trajectories are polynomial but the non-Markovian sign problem restores exponential total cost.
CV-ADAPT-VQE with tailored symmetry-preserving pools achieves significantly shallower circuits than Hamiltonian-based VQE for bosonic lattice models in GPU classical simulations.
In Landau polaritons an exact chiral charge routes dominant anomalous correlations, squeezing, and cavity-matter entanglement to the opposite polarization, producing Gaussian discord between cyclotron resonance and finite-momentum magnetoplasmons but no pairwise matter-matter entanglement.
DeepQuantum is a PyTorch platform that unifies quantum circuits, photonic quantum circuits, and measurement-based quantum computing in one open-source framework for hybrid models and variational algorithms.
Relaxes conditions on two-stage quantum estimators to broaden usable classical post-processing while deriving asymptotics for quantum-enhanced transmittance sensing with nuisance parameters.
Collider scattering processes such as electron-positron annihilation to muon pairs can be represented as quantum circuits with unitary and non-unitary components.
Quantum computers enable exponentially better scaling in the number of modes n for learning n-mode Gaussian optical states, with polynomially improved energy dependence over continuous-variable classical shadows.
Thermal instabilities and noise modify quantum measurement statistics in a sensitive, nontrivial way across the weak-to-strong crossover depending on temperature, probe properties, and state selections.
Photon addition and subtraction enhance QFI for nonlinear parameter estimation on squeezed vacuum states but not on coherent states, where the benefit reduces to extra energy, allowing comparable performance with lower squeezing.
A magnomechanical converter produces optics-microwave entanglement maximized at the same parameters as frequency conversion efficiency, enabling teleportation fidelity of 0.75 in a proposed micrometer-scale YIG implementation.
Separable squeezed inputs in finite-memory structured reservoirs produce detuning-locked entanglement freezing, birth-death-revival cycles, and integer-locked beating oscillations that persist with small deviations at cryogenic and moderate temperatures.
Embedding squeezing in the system Hamiltonian and leveraging environmental memory induces higher-order QFI time dependence and information backflow that can restore or exceed unitary precision in noisy frequency estimation.
Hybrid perovskite quantum dots offer tunable room-temperature single-photon emission that may overcome purity and scalability limits of existing sources, while bright squeezed vacuum provides a path to multiplexable high-purity photons.
Optimal parametric driving in Gaussian quantum systems reduces impulse estimation variance by up to a factor of two relative to steady-state operation.
Noncommutative deformations (θ, η) of phase space induce entanglement in bipartite Gaussian states of a 2D harmonic oscillator, with a gedankenexperiment outlined to detect this via photocurrent measurements as a quantum gravity signature.
A review of quantum uncertainty relations that covers foundational and practical applications of both variance- and entropy-based uncertainties.
Reviews paradigmatic entanglement quantifiers and state-of-the-art detection/certification methods, with emphasis on assumptions about states and measurements.
citing papers explorer
-
Quantum state isomorphism problems for groups
Quantum state isomorphism under group actions is BQP-hard for pure states across nontrivial groups and QSZK-complete for mixed states with finite groups; Pauli group version is BQP-complete and Clifford is GI-hard, ruling out efficient quantum algorithms for abelian mixed-state HS unless QSZK=BQP.
-
Exponentially-improved effective descriptions of physical bosonic systems
A natural energy condition satisfied by most physical bosonic states, including outputs of universal bosonic circuits, allows the effective dimension for ε-approximations to scale as log(1/ε) instead of 1/ε², enabling improved learning and classical simulation algorithms.
-
Non-equilibrium quantum thermometry with bosonic samples
Non-Markovian strong coupling in a bosonic probe produces non-monotonic quantum Fisher information with a finite optimal interrogation time for thermometry, while squeezed states give transient gains and strong coupling softens low-T error scaling from exponential to polynomial.
-
Closed-form Bayesian quantum estimation of Gaussian states
A variational framework yields closed-form Bayesian estimators for Gaussian quantum states via polynomial quadrature operators and a global optimality condition.
-
Emergence of volume-law scaling for entanglement negativity from the Hawking radiation of analogue black holes
Hawking radiation in a 1+1D analogue black hole induces a UV-finite volume-law term in logarithmic negativity that encodes the density and locations of entangled pairs.
-
Assessing non-Gaussian quantum state conversion with the stellar rank
The approximate stellar rank serves as an operational measure of non-Gaussianity that yields bounds and new no-go results for approximate and probabilistic Gaussian state conversion and distillation.
-
Calculating strongly correlated ground states from the non-Markovian dissipative dynamics of Gaussian fermions
A reverse third-quantization mapping sends Fermi-Hubbard ground states to dissipative Majorana steady states where individual Gaussian trajectories are polynomial but the non-Markovian sign problem restores exponential total cost.
-
Continuous-variable ADAPT-VQE for bosonic lattice models
CV-ADAPT-VQE with tailored symmetry-preserving pools achieves significantly shallower circuits than Hamiltonian-based VQE for bosonic lattice models in GPU classical simulations.
-
Chirality routing non-polaritonic vacuum correlations in Landau polaritons
In Landau polaritons an exact chiral charge routes dominant anomalous correlations, squeezing, and cavity-matter entanglement to the opposite polarization, producing Gaussian discord between cyclotron resonance and finite-momentum magnetoplasmons but no pairwise matter-matter entanglement.
-
DeepQuantum: A PyTorch-based Software Platform for Quantum Machine Learning and Photonic Quantum Computing
DeepQuantum is a PyTorch platform that unifies quantum circuits, photonic quantum circuits, and measurement-based quantum computing in one open-source framework for hybrid models and variational algorithms.
-
Two-stage Quantum Estimation and the Asymptotics of Quantum-enhanced Transmittance Sensing
Relaxes conditions on two-stage quantum estimators to broaden usable classical post-processing while deriving asymptotics for quantum-enhanced transmittance sensing with nuisance parameters.
-
A collider as a quantum computer
Collider scattering processes such as electron-positron annihilation to muon pairs can be represented as quantum circuits with unitary and non-unitary components.
-
Learning Gaussian optical states with quantum computers
Quantum computers enable exponentially better scaling in the number of modes n for learning n-mode Gaussian optical states, with polynomially improved energy dependence over continuous-variable classical shadows.
-
Weak-to-Strong Measurement Transition with Thermal Instabilities
Thermal instabilities and noise modify quantum measurement statistics in a sensitive, nontrivial way across the weak-to-strong crossover depending on temperature, probe properties, and state selections.
-
Squeezing as a catalyst for non-Gaussian advantage in characterization of nonlinear media
Photon addition and subtraction enhance QFI for nonlinear parameter estimation on squeezed vacuum states but not on coherent states, where the benefit reduces to extra energy, allowing comparable performance with lower squeezing.
-
Optics-microwave entanglement and state teleportation mediated by a cavity magnomechanical system
A magnomechanical converter produces optics-microwave entanglement maximized at the same parameters as frequency conversion efficiency, enabling teleportation fidelity of 0.75 in a proposed micrometer-scale YIG implementation.
-
Entanglement Dynamics of Separable Squeezed States in Finite Memory Structured Reservoir
Separable squeezed inputs in finite-memory structured reservoirs produce detuning-locked entanglement freezing, birth-death-revival cycles, and integer-locked beating oscillations that persist with small deviations at cryogenic and moderate temperatures.
-
Beating noise in frequency estimation with squeezing and memory in continuous-variable systems
Embedding squeezing in the system Hamiltonian and leveraging environmental memory induces higher-order QFI time dependence and information backflow that can restore or exceed unitary precision in noisy frequency estimation.
-
Mechanisms and Opportunities for Tunable High-Purity Single Photon Emitters: A Review of Hybrid Perovskites and Prospects for Bright Squeezed Vacuum
Hybrid perovskite quantum dots offer tunable room-temperature single-photon emission that may overcome purity and scalability limits of existing sources, while bright squeezed vacuum provides a path to multiplexable high-purity photons.
-
Optimal State Preparation for Impulse Estimation in Gaussian Quantum Systems
Optimal parametric driving in Gaussian quantum systems reduces impulse estimation variance by up to a factor of two relative to steady-state operation.
-
On the entanglement induced by the deformation of phase-space
Noncommutative deformations (θ, η) of phase space induce entanglement in bipartite Gaussian states of a 2D harmonic oscillator, with a gedankenexperiment outlined to detect this via photocurrent measurements as a quantum gravity signature.
-
Quantum Uncertainty and Entropy
A review of quantum uncertainty relations that covers foundational and practical applications of both variance- and entropy-based uncertainties.
-
Entanglement Certification $-$ From Theory to Experiment
Reviews paradigmatic entanglement quantifiers and state-of-the-art detection/certification methods, with emphasis on assumptions about states and measurements.