Measuring Entanglement Through the Wigner Function

Jie Li, Gang Li, Junmin Wang +2 more

Two measures of nonclassicality, the entanglement potential and the negativity of the Wigner distribution function defined by the volume of its negative domains, are compared based on an investigation of the nonclassicality for Fock states and Schrödinger cat states in a decoherence process. Both the entanglement potential and the total negative probability are reduced in the linear loss process and the partial negative distribution of the Wigner function is wiped out for large losses while the entanglement potential is always positive. We give a bound condition and find that, though not yet mathematically proven in general, the upper bound of 50% is the maximum allowed loss for the survival of the negative distribution of the Wigner function.

Leah Henderson

Zhi‐Ming Zhang

We propose a scheme for measuring the Wigner function of a two-mode cavity field. The scheme bases on the interaction between the two-mode cavity field and three-level atoms. We find a simple relation between the Wigner function and the atomic population. One can obtain the Wigner function by measuring the atomic population with a micromaser-like experiment and doing a numerical integral. By using the two-mode Wigner function one can obtain the Clauser–Horne combination and test the Bell's inequalities. We test our equations with a two-mode entanglement state and the results are rather good.

P. K. Aravind

Prashanna Simkhada, Jean-François S. Van Huele

R. P. Rundle, P. W. Mills, Todd Tilma +2 more

It has recently been shown that it is possible to represent the complete quantum state of any system as a phase-space quasiprobability distribution (Wigner function) [Phys. Rev. Lett. 117, 180401 (2016)]. 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 state. Because Wigner functions for spin systems are not unique, we define, compare, and contrast two distinct examples. We show how the use of 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 Schr\"odinger cat states). Furthermore we show that this analysis leads to straightforward, and potentially very efficient, entanglement test and state characterization methods.