Deterministic Gaussian conversion protocols for non-Gaussian single-mode resources

Abstract

In the context of quantum technologies over continuous variables, Gaussian states and operations are typically regarded as freely available, as they are relatively easily accessible experimentally. In contrast, the generation of non-Gaussian states, as well as the implementation of non-Gaussian operations, pose significant challenges. This divide has motivated the introduction of resource theories of non-Gaussianity. As for any resource theory, it is of practical relevance to identify free conversion protocols between resources, namely Gaussian conversion protocols between non-Gaussian states. Via systematic numerical investigations, we address the approximate conversion between experimentally relevant single-mode non-Gaussian states via arbitrary deterministic one-to-one mode Gaussian maps. First, we show that cat and binomial states are approximately equivalent for finite energy, while this equivalence was previously known only in the infinite-energy limit. Then we consider the generation of cat states from photon-added and photon-subtracted squeezed states, improving over known schemes by introducing additional squeezing operations. The numerical tools that we develop also allow to devise conversions of trisqueezed into cubic-phase states beyond previously reported performances. Finally, we identify various other conversions which instead are not viable.

References in corpus (67)

• Gaussian Quantum Information
• QuTiP 2: A Python framework for the dynamics of open quantum systems
• QuTiP: An open-source Python framework for the dynamics of open quantum systems
• Encoding a qubit in an oscillator
• Quantum computation over continuous variables
• Generation of a superposition of odd photon number states for quantum information networks
• Positive Wigner functions render classical simulation of quantum computation efficient
• Schroedinger cat-like states by conditional measurements on a beam-splitter
• Quantum error correction of a qubit encoded in grid states of an oscillator
• New class of quantum error-correcting codes for a bosonic mode
• Encoding a qubit in a trapped-ion mechanical oscillator
• Negative Quasi-Probability as a Resource for Quantum Computation
• Quantum Computing with Continuous-Variable Clusters
• Quantum Nonlocality in Phase Space
• Negativity and contextuality are equivalent notions of nonclassicality
• Performance and structure of single-mode bosonic codes
• Controllable generation of highly nonclassical states from nearly pure squeezed vacua
• Fault-tolerant linear optical quantum computing with small-amplitude coherent states
• Demonstration of quantum error correction and universal gate set on a binomial bosonic logical qubit
• Resource theory of quantum non-Gaussianity and Wigner negativity
• Bosonic quantum error correction codes in superconducting quantum circuits
• Quantifying non-Gaussianity for quantum information
• Convex resource theory of non-Gaussianity
• A measure of the non-Gaussian character of a quantum state
• Fault-tolerant detection of a quantum error
• Quantum computing with rotation-symmetric bosonic codes
• Optomechanical circuits for nanomechanical continuous variable quantum state processing
• Observation of Three-Photon Spontaneous Parametric Downconversion in a Superconducting Parametric Cavity
• Towards Scalable Bosonic Quantum Error Correction
• Quantum Error Correction with the Gottesman-Kitaev-Preskill Code
• Continuous-variable quantum computing in the quantum optical frequency comb
• Implementation of a quantum cubic gate by adaptive non-Gaussian measurement
• Conditional generation of arbitrary single-mode quantum states of light by repeated photon subtractions
• Quantum control of bosonic modes with superconducting circuits
• Stellar representation of non-Gaussian quantum states
• Generation of optical Schrödinger's cat states by generalized photon subtraction
• Methods for Producing Optical Coherent State Superpositions
• Deterministic implementation of weak quantum cubic nonlinearity
• Non-classicality criteria from phase-space representations and information-theoretical constraints are maximally inequivalent
• Squeezing and quantum state engineering with Josephson traveling wave amplifiers
• Repeat-until-success cubic phase gate for universal continuous-variable quantum computation
• Universal Gate Set for Continuous-Variable Quantum Computation with Microwave Circuits
• Quantum Interference in Three Photon Down Conversion
• Generation and characterization of resource state for nonlinear cubic phase gate
• Encoding qubits into oscillators with atomic ensembles and squeezed light
• Relative entropy is an exact measure of non-Gaussianity
• Production of photonic universal quantum gates enhanced by machine learning
• Engineering a Kerr-based Deterministic Cubic Phase Gate via Gaussian Operations
• General implementation of arbitrary nonlinear quadrature phase gates
• Generation of cluster states in optomechanical quantum systems
• Polynomial approximation of non-Gaussian unitaries by counting one photon at a time
• Drawbacks of the use of fidelity to assess quantum resources
• Unconditional preparation of nonclassical states via linear-and-quadratic optomechanics
• Manipulating the quantum information of the radial modes of trapped ions: Linear phononics, entanglement generation, quantum state transmission and non-locality tests
• Assessing the significance of fidelity as a figure of merit in quantum state reconstruction of discrete and continuous variable systems
• Gapped Two-Body Hamiltonian for continuous-variable quantum computation
• Gaussian conversion protocols for cubic phase state generation
• Efficient simulatability of continuous-variable circuits with large Wigner negativity
• Deterministic generation of Gaussian pure state in quasi-local dissipative system
• Normal form decomposition for Gaussian-to-Gaussian superoperators
• Linear-and-quadratic reservoir engineering of non-Gaussian states
• Probabilistic Fault-Tolerant Universal Quantum Computation and Sampling Problems in Continuous Variables
• Stroboscopic high-order nonlinearity for quantum optomechanics
• Composite Cluster States and Alternative Architectures for One- Way Quantum Computation
• Upper bounds on the relative energy difference of pure and mixed Gaussian states with a fixed fidelity
• Manipulating mesoscopic multipartite entanglement with atom-light interfaces
• Conversion of Gaussian states under incoherent Gaussian operations