Simple procedure for phase-space measurement and entanglement validation

Abstract

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 values of an observable that has a direct analogy to displaced parity operators. In this work we give a procedure for the measurement of the Wigner function that should be applicable to any quantum system. We have applied our procedure to IBM's Quantum Experience five-qubit quantum processor to demonstrate that we can measure and generate the Wigner functions of two different Bell states as well as the five-qubit Greenberger-Horne-Zeilinger (GHZ) state. As Wigner functions for spin systems are not unique, we define, compare, and contrast two distinct examples. We show how using these Wigner functions leads to an optimal method for quantum state analysis especially in the situation where specific characteristic features are of particular interest (such as for spin Schrödinger cat states). Furthermore we show that this analysis leads to straightforward, and potentially very efficient, entanglement test and state characterisation methods.

Visualization of correlations in hybrid discrete—continuous variable quantum systems

“…where the generalized parity, P â , for a single, two-level, system is s P = + 3 2 a z  (ˆˆ) [23,24,28], for a full derivation of the kernel see [58]. Note that the subscript a here indicates that this is a state for the 'atom', or DV system.…”

“…The methods presented here could be viewed as a form of quantum state spectroscopy.Bloch sphere [20][21][22][23][24][25][26]. For example, there have been various proposals put forward that use a continuous Wigner function to reveal correlations between DV systems [26][27][28]. These methods have further been validated through the direct measurement of phase-space to reveal quantum correlations [28][29][30][31].…”

“…For example, there have been various proposals put forward that use a continuous Wigner function to reveal correlations between DV systems [26][27][28]. These methods have further been validated through the direct measurement of phase-space to reveal quantum correlations [28][29][30][31]. Recently this has been extended to experiments validating atomic Schrödinger cat states of up to 20 superconducting qubits [32].A case that has not been explored in much detail is the phase-space representation of CV-DV hybridization.…”

Quantum phase space with a basis of Wannier functions

“…(ii) As a result, our unitary projection can produce a true probability distribution resembling a classical trajectory as most dramatically seen with the example of harmonic oscillator. The oscillations between positive and negative values in Wigner functions (see figures 3(b), 4(c) and 5(c)) are regarded as an indication of 'quantumness' in the quantum state [6,16]. However, this also makes it dicult to build a connection between quantum dynamics and classical dynamics in phase space.…”

O Computador Quântico da IBM e o IBM Quantum Experience

“…A proposta da IBMé que com essa plataforma qualquer pessoa possa simular e até mesmo executar uma computação em um computador quântico de 5 q-bits.É claro que não se pode fazer muito com apenas 5 q-bits, mas a ideiá e que possamos testar o IBM-QE para determinar se realmente estamos lidando com um computador quântico de fato. Nesse intuito, o IBM-QE tem sido usado recentemente em diversos protocolos de CQ [6][7][8][9]. Essa determinaçãoé o atual problema que cientistas da CQ estão tentando resolver em protótipos como os chips quânticos da IBM, ditos quânticos.…”