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Register a new userWitnessing negativity of Wigner function by estimating fidelities of cat-like states from homodyne measurements
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We derive sampling functions for estimation of quantum state fidelity with Schrodinger cat-like states, which are defined as superpositions of two coherent states with opposite amplitudes. We also provide sampling functions for fidelity with squeezed Fock states that can approximate the cat-like states and can be generated from Gaussian squeezed states by conditional photon subtraction. The fidelities can be determined by averaging the sampling functions over quadrature statistics measured by homodyne detection. The sampling functions are designed such that they can compensate for losses and inefficient homodyning provided that the overall efficiency exceeds certain threshold. The fidelity with an odd coherent state and the fidelity with a squeezed odd Fock state provide convenient witnesses of negativity of Wigner function of the measured state. The negativity of Wigner function at the origin of phase space is certified if any of these fidelities exceeds 0.5. Finally, we discuss the possibility of reducing the statistical uncertainty of the fidelity estimates by a suitable choice of the dependence of the number of quadrature samples on the relative phase shift between local oscillator and signal beam.
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A measure of nonclassicality of quantum states based on the volume of the negative part of the Wigner function is proposed. We analyze this quantity for Fock states, squeezed displaced Fock states and cat-like states defined as coherent superposition of two Gaussian wave packets.
We describe a scheme of quantum computation with magic states on qubits for which contextuality is a necessary resource possessed by the magic states. More generally, we establish contextuality as a necessary resource for all schemes of quantum computation with magic states on qubits that satisfy three simple postulates. Furthermore, we identify stringent consistency conditions on such computational schemes, revealing the general structure by which negativity of Wigner functions, hardness of classical simulation of the computation, and contextuality are connected.
Contextuality and negativity of the Wigner function are two notions of non-classicality for quantum systems. Howard, Wallman, Veitch and Emerson proved recently that these two notions coincide for qudits in odd prime dimension. This equivalence is particularly important since it promotes contextuality as a ressource that magic states must possess in order to allow for a quantum speed-up. We propose a simple proof of the equivalence between contextuality and negativity of the Wigner function based on character theory. This simplified approach allows us to generalize this equivalence to multiple qudits and to any qudit system of odd local dimension.
We describe a universal scheme of quantum computation by state injection on rebits (states with real density matrices). For this scheme, we establish contextuality and Wigner function negativity as computational resources, extending results of [M. Howard et al., Nature 510, 351--355 (2014)] to two-level systems. For this purpose, we define a Wigner function suited to systems of $n$ rebits, and prove a corresponding discrete Hudsons theorem. We introduce contextuality witnesses for rebit states, and discuss the compatibility of our result with state-independent contextuality.
We experimentally demonstrate the reconstruction of a photon number conditioned state without using a photon number discriminating detector. By using only phase randomized homodyne measurements, we reconstruct up to the three photon subtracted squeezed vacuum state. The reconstructed Wigner functions of these states show regions of pronounced negativity, signifying the non-classical nature of the reconstructed states. The techniques presented allow for complete characterization of the role of a conditional measurement on an ensemble of states, and might prove useful in systems where photon counting still proves technically challenging.
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