Related papers: Discrete phase space and minimum-uncertainty state…
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…
Focusing particularly on one-qubit and two-qubit systems, I explain how the quantum state of a system of n qubits can be expressed as a real function--a generalized Wigner function--on a discrete 2^n x 2^n phase space. The phase space is…
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.…
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…
Discrete coherent states for a system of $n$ qubits are introduced in terms of eigenstates of the finite Fourier transform. The properties of these states are pictured in phase space by resorting to the discrete Wigner function
We further elaborate on a phase-space picture for a system of $N$ qubits and explore the structures compatible with the notion of unbiasedness. These consist of bundles of discrete curves satisfying certain additional properties and…
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 positive Wigner function, which we name…
We show that the behaviour in phase space of the Wigner function associated to the electromagnetic modes carries the information of both, the entanglement properties between matter and field, and the regions in parameter space where quantum…
We study the Wigner function for a quantum system with a discrete, infinite dimensional Hilbert space, such as a spinless particle moving on a one dimensional infinite lattice. We discuss the peculiarities of this scenario and of the…
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,…
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 quantum theory of the shuttle instability in electronic transport through a nanostructure with a mechanical degree of freedom. A phase space formulation in terms of the Wigner function allows us to identify a cross-over from…
Non-classical states are of practical interest in quantum computing and quantum metrology. These states can be detected through their Wigner function negativity in some regions. In this paper, we calculate the ground state of the…
We analyze the quantum walk on a cycle using discrete Wigner functions as a way to represent the states and the evolution of the walker. The method provides some insight on the nature of the interference effects that make quantum and…
The quasiprobability distribution of the discrete Wigner function provides a complete description of a quantum state and is, therefore, a useful alternative to the usual density matrix description. Moreover, the experimental quantum state…
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…
We introduce a quantum phase space representation for the orientation state of extended quantum objects, using the Euler angles and their conjugate momenta as phase space coordinates. It exhibits the same properties as the standard Wigner…
The properties of quantum mechanics with a discrete phase space are studied. The minimum uncertainty states are found, and these states become the Gaussian wave packets in the continuum limit. With a suitably chosen Hamiltonian that gives…
We determine a positive normalised phase space probability distribution $P$ with minimum mean square fractional deviation from the Wigner distribution $W$ .The minimum deviation, an invariant under phase space rotations, is a quantitative…
The state function of a quantum object is undetermined with respect to its phase. This indeterminacy does not matter if it is global, but what if the components of the state have unknown relative phases? Can useful computations be performed…