Related papers: Selective Wigner phase space tomography and its ap…
To quantify the effect of decoherence in quantum measurements, it is desirable to measure not merely the square modulus of the spatial wavefunction, but the entire density matrix, whose phases carry information about momentum and how pure…
We present a phase space description of the process of quantum teleportation for a system with an $N$ dimensional space of states. For this purpose we define a discrete Wigner function which is a minor variation of previously existing ones.…
By means of a well-grounded mapping scheme linking Schwinger unitary operators and generators of the special unitary group $\mathrm{SU(N)}$, it is possible to establish a self-consistent theoretical framework for finite-dimensional discrete…
It has recently been shown that it is possible to represent the complete quantum state of any system as a phase-space quasi-probability distribution (Wigner function) [Phys Rev Lett 117, 180401]. Such functions take the form of expectation…
Density matrices and Discrete Wigner Functions are equally valid representations of multiqubit quantum states. For density matrices, the partial trace operation is used to obtain the quantum state of subsystems, but an analogous…
The quantum state of a system of qubits can be represented by a Wigner function on a discrete phase space, each axis of the phase space taking values in a finite field. Within this framework, we show that one can make sense of the notion of…
In this paper, we correct a mistake we made in [Phys. Rev. Lett. $\textbf{122}$, 190402 (2019)] and [Phys. Rev. A $\textbf{103}$, 012213 (2021)] regarding the Wigner function of the so-called smoothed Weak-Valued state (SWV state). Here…
We introduce a quasi-probability phase space distribution with two pairs of azimuthal-angular coordinates. This representation is well adapted to describe quantum systems with discrete symmetry. Quantum error correction of states encoded in…
We show how to represent the state and the evolution of a quantum computer (or any system with an $N$--dimensional Hilbert space) in phase space. For this purpose we use a discrete version of the Wigner function which, for arbitrary $N$, is…
We have studied statistical properties of the values of the Wigner function W(x) of 1D quantum maps on compact 2D phase space of finite area V. For this purpose we have defined a Wigner function probability distribution P(w) = (1/V) int…
The original Wigner function provides a way of representing in phase space the quantum states of systems with continuous degrees of freedom. Wigner functions have also been developed for discrete quantum systems, one popular version being…
The quantum state of a light beam can be represented as an infinite dimensional density matrix or equivalently as a density on the plane called the Wigner function. We describe quantum tomography as an inverse statistical problem in which…
We present an experimental scanning-based tomography approach for near-term quantum devices. The underlying method has previously been introduced in an ensemble-based NMR setting. Here we provide a tutorial-style explanation along with…
We propose a method for classical simulation of finite-dimensional quantum systems, based on sampling from a quasiprobability distribution, i.e., a generalized Wigner function. Our construction applies to all finite dimensions, with the…
We apply the Wigner function formalism from quantum optics via two approaches, Wootters' discrete Wigner function and the generalized Wigner function, to detect quantum phase transitions in critical spin-$\tfrac{1}{2}$ systems. We develop a…
We establish the relation of the spin tomogram to the Wigner function on a discrete phase space of qubits. We use the quantizers and dequantizers of the spin tomographic star-product scheme for qubits to derive the expression for the kernel…
We analyse some features of the class of discrete Wigner functions that was recently introduced by Gibbons et al. to represent quantum states of systems with power-of-prime dimensional Hilbert spaces [Phys. Rev. A 70, 062101 (2004)]. We…
We represent both the states and the evolution of a quantum computer in phase space using the discrete Wigner function. We study properties of the phase space representation of quantum algorithms: apart from analyzing important examples,…
Most methods for experimentally reconstructing the quantum state of light involve determining a quasiprobability distribution such as the Wigner function. In this paper we present a scheme for measuring individual density matrix elements in…
We present the experimental reconstruction of the Wigner function of an individual electronic spin qubit associated with a nitrogen-vacancy (NV) center in diamond at room temperature. This spherical Wigner function contains the same…