Conversion of Gaussian states to non-Gaussian states using photon-number-resolving detectors
arXiv:1902.02323 · doi:10.1103/PhysRevA.100.052301
Abstract
Generation of high fidelity photonic non-Gaussian states is a crucial ingredient for universal quantum computation using continous-variable platforms, yet it remains a challenge to do so efficiently. We present a general framework for a probabilistic production of multimode non-Gaussian states by measuring few modes of multimode Gaussian states via photon-number-resolving detectors. We use Gaussian elements consisting of squeezed displaced vacuum states and interferometers, the only non-Gaussian elements consisting of photon-number-resolving detectors. We derive analytic expressions for the output Wigner function, and the probability of generating the states in terms of the mean and the covariance matrix of the Gaussian state and the photon detection pattern. We find that the output states can be written as a Fock basis superposition state followed by a Gaussian gate, and we derive explicit expressions for these parameters. These analytic expressions show exactly what non-Gaussian states can be generated by this probabilistic scheme. Further, it provides a method to search for the Gaussian circuit and measurement pattern that produces a target non-Gaussian state with optimal fidelity and success probability. We present specific examples such as the generation of cat states, ON states, Gottesman-Kitaev-Preskill states, NOON states and bosonic code states. The proposed framework has potential far-reaching implications for the generation of bosonic error-correction codes that require non-Gaussian states, resource states for the implementation of non-Gaussian gates needed for universal quantum computation, among other applications requiring non-Gaussianity. The tools developed here could also prove useful for the quantum resource theory of non-Gaussianity.
37 pages, 15 figures. See also related short paper arXiv:1902.02331 uploaded concurrently. Added references and corrected typos
References in corpus (58)
- Quantum information with continuous variables
- Gaussian Quantum Information
- Encoding a qubit in an oscillator
- Quantum Interferometric Optical Lithography: Exploiting Entanglement to Beat The Diffraction Limit
- Quantum computation over continuous variables
- Detection of 15 dB Squeezed States of Light and their Application for the Absolute Calibration of Photoelectric Quantum Efficiency
- Quantum Optical Metrology -- The Lowdown on High-N00N States
- Quantum state reconstruction of the single-photon Fock state
- Generation of a superposition of odd photon number states for quantum information networks
- Squeezing as an irreducible resource
- Gaussian Boson Sampling
- Schroedinger cat-like states by conditional measurements on a beam-splitter
- New class of quantum error-correcting codes for a bosonic mode
- A No-Go Theorem for Gaussian Quantum Error Correction
- Implementing a Universal Gate Set on a Logical Qubit Encoded in an Oscillator
- Performance and structure of single-mode bosonic codes
- Generation of Optical Coherent State Superpositions by Number-Resolved Photon Subtraction from Squeezed Vacuum
- Generation of large-amplitude coherent-state superposition via ancilla-assisted photon-subtraction
- Resource theory of quantum non-Gaussianity and Wigner negativity
- Remote creation of hybrid entanglement between particle-like and wave-like optical qubits
- Entangling quantum and classical states of light
- Bosonic Quantum Codes for Amplitude Damping
- Conditional Production of Superpositions of Coherent States with Inefficient Photon Detection
- Convex resource theory of non-Gaussianity
- A detailed study of Gaussian Boson Sampling
- Optimal estimation of losses at the ultimate quantum limit with non-Gaussian states
- Generation of arbitrary quantum states of traveling fields
- Quantum state engineering by a coherent superposition of photon subtraction and addition
- Generating superposition of up-to three photons for continuous variable quantum information processing
- The optimal cloning of quantum coherent states is non-Gaussian
- All-optical generation of states for "Encoding a qubit in an oscillator"
- Generating Grid States From Schrödinger Cat States without Post-Selection
- Conditional generation of arbitrary single-mode quantum states of light by repeated photon subtractions
- Photon distribution for one mode mixed light with generic gaussian Wigner function
- Cat codes with optimal decoherence suppression for a lossy bosonic channel
- Multidimensional Hermite polynomials and photon distribution for polymode mixed light
- Quantum-scissors device for optical state truncation: A proposal for practical realization
- Multiphoton Quantum-State Engineering using Conditional Measurements
- Resource theory of non-Gaussian operations
- Quantum error correction against photon loss using NOON states
- Slowing Quantum Decoherence by Squeezing in Phase Space
- Encoding qubits into oscillators with atomic ensembles and squeezed light
- Constructing finite dimensional codes with optical continuous variables
- Production of photonic universal quantum gates enhanced by machine learning
- Robustness of non-Gaussian entanglement against noisy amplifier and attenuator environments
- Tailoring Non-Gaussian Continuous-Variable Graph States
- Non-Gaussian operations on bosonic modes of light: Photon-added Gaussian channels
- On the scalability of parametric down-conversion for generating higher-order Fock states
- ON states as resource units for universal quantum computation with photonic architectures
- Franck-Condon factors by counting perfect matchings of graphs with loops
- Optical-state truncation and teleportation of qudits by conditional eight-port interferometry
- Hardware-Efficient Bosonic Quantum Error-Correcting Codes Based on Symmetry Operators
- Generating continuous variable quantum codewords in the near-field atomic lithography
- Heralded creation of photonic qudits from parametric down conversion using linear optics
- Conditional generation of path-entangled optical NOON states
- All phase-space linear bosonic channels are approximately Gaussian dilatable
- Quantum state engineering by non-deterministic noiseless linear amplification
- Deterministic multi-mode nonlinear coupling for quantum circuits
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