Witnessing Wigner Negativity

@article{Chabaud2021WitnessingWN,
  title={Witnessing Wigner Negativity},
  author={Ulysse Chabaud and Pierre-Emmanuel Emeriau and Fr{\'e}d{\'e}ric Grosshans},
  journal={Quantum},
  year={2021},
  volume={5},
  pages={471}
}
Negativity of the Wigner function is arguably one of the most striking non-classical features of quantum states. Beyond its fundamental relevance, it is also a necessary resource for quantum speedup with continuous variables. As quantum technologies emerge, the need to identify and characterize the resources which provide an advantage over existing classical technologies becomes more pressing. Here we derive witnesses for Wigner negativity of single mode and multimode quantum states, based on… Expand

Figures and Tables from this paper

Witnessing Bell violations through probabilistic negativity
TLDR
This paper presents a probabilistic simulation of the response of the immune system to quantum entanglement in a non-equilibrium setting and shows clear patterns in response to various immune mechanisms. Expand
Introduction to generation, manipulation and characterization of optical quantum states
In this brief tutorial we provide the theoretical tools needed to describe the generation, manipulation and characterization of optical quantum states and of the main passive (beam splitters) andExpand
Contextuality and Wigner negativity are equivalent for continuous-variable quantum measurements
Quantum computers will provide considerable speedups with respect to their classical counterparts. However, the identification of the innately quantum features that enable these speedups isExpand
Non-Gaussian Quantum States and Where to Find Them
Gaussian states have played on important role in the physics of continuous-variable quantum systems. They are appealing for the experimental ease with which they can be produced, and for theirExpand
Quantum Wigner entropy
We define the Wigner entropy of a quantum state as the differential Shannon entropy of the Wigner function of the state. This quantity is properly defined only for states that possess a positiveExpand

References

SHOWING 1-10 OF 81 REFERENCES
Resource theory of quantum non-Gaussianity and Wigner negativity
We develop a resource theory for continuous-variable systems grounded on operations routinely available within current quantum technologies. In particular, the set of free operations is convex andExpand
Witnessing negativity of Wigner function by estimating fidelities of catlike states from homodyne measurements
We derive sampling functions for estimation of quantum state fidelity with Schr\"odinger cat-like states, which are defined as superpositions of two coherent states with opposite amplitudes. We alsoExpand
Positive Wigner functions render classical simulation of quantum computation efficient.
TLDR
The result generalizes the Gottesman-Knill theorem and provides a way of sampling from the output distribution of a computation or a simulation, including the efficient sampling from an approximate output distribution in the case of sampling imperfections for initial states, gates, or measurements. Expand
Optimization of entanglement witnesses
An entanglement witness (EW) is an operator that allows to detect entangled states. We give necessary and sufficient conditions for such operators to be optimal, i.e. to detect entangled states in anExpand
Hudson's theorem for finite-dimensional quantum systems
We show that, on a Hilbert space of odd dimension, the only pure states to possess a non-negative Wigner function are stabilizer states. The Clifford group is identified as the set of unitaryExpand
Contextuality supplies the ‘magic’ for quantum computation
TLDR
This work proves a remarkable equivalence between the onset of contextuality and the possibility of universal quantum computation via ‘magic state’ distillation, which is the leading model for experimentally realizing a fault-tolerant quantum computer. Expand
Contextuality and Wigner-function negativity in qubit quantum computation
We describe schemes of quantum computation with magic states on qubits for which contextuality and negativity of the Wigner function are necessary resources possessed by the magic states. TheseExpand
A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
We are interested in the problem of characterizing the correlations that arise when performing local measurements on separate quantum systems. In a previous work (Navascues et al 2007 Phys. Rev.Expand
Equivalence between contextuality and negativity of the Wigner function for qudits
Understanding what distinguishes quantum mechanics from classical mechanics is crucial for quantum information processing applications. In this work, we consider two notions of non-classicality forExpand
Extending Hudson’s theorem to mixed quantum states
According to Hudson’s theorem, any pure quantum state with a positive Wigner function is necessarily a Gaussian state. Here, we make a step toward the extension of this theorem to mixed quantumExpand
...
1
2
3
4
5
...