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Quantum Information Processing

A note on quantum correlations in Werner states under two collective noises

Chuanmei Xie, Yimin Liu, Guofeng Li, Zhanjun Zhang

Published Sep 8, 2014• 8 citations
Publisher
DOI
10.1007/s11128-014-0822-y

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Abstract Disentanglement and loss of quantum correlations due to one global collective noise effect are described for two- qubit Schrödinger cat and Werner states of a four level trapped ion quantum system. Once the Jaynes–Cummings ionic interactions are mapped onto a Dirac spinor structure, the elementary tools for computing quantum correlations of two- qubit ionic states are provided. With two- qubit quantum numbers related to the total angular momentum and to its projection onto the direction of an external magnetic field (which lifts the degeneracy of the ion’s internal levels), a complete analytical profile of entanglement for the Schrödinger cat and Werner states is obtained. Under vacuum noise (during spontaneous emission), the two- qubit entanglement in the Schrödinger cat states is shown to vanish asymptotically. Otherwise, the robustness of Werner states is concomitantly identified, with the entanglement content recovered by their noiseless-like evolution. Most importantly, our results point to a firstly reported sudden transition between classical and quantum decay regimes driven by a classical collective noise on the Schrödinger cat states, which has been quantified by the geometric discord.
We demonstrate a hierarchy of various classes of quantum correlations on experimentally prepared two-qubit Werner-like states with controllable white noise. Werner states, which are white-noise-affected Bell states, are prototypal examples for studying such a hierarchy as a function of the amount of white noise. We experimentally generate Werner states and their generalizations, i.e., partially entangled pure states affected by white noise. These states enable us to study the hierarchy of the following classes of correlations: separability, entanglement, steering in three- and two-measurement scenarios, and Bell nonlocality. We show that the generalized Werner states (GWSs) reveal fundamentally different aspects of the hierarchy compared to the Werner states. In particular, we find five different parameter regimes of the GWSs, including those steerable in a two-measurement scenario but not violating Bell inequalities. This regime cannot be observed for the usual Werner states. Moreover, we find threshold curves separating different regimes of the quantum correlations and find the optimal states which allow for the largest amount of white noise which does not destroy their specific quantum correlations (e.g., unsteerable entanglement). Thus, we could identify the optimal Bell-nondiagonal GWSs which are, for this specific meaning, more robust against the white noise compared to the Bell-diagonal GWSs (i.e., Werner states).
A Werner state, which is the singlet Bell state affected by white noise, is a prototype example of states, which can reveal a hierarchy of quantum entanglement, steering, and Bell nonlocality by controlling the amount of noise. However, experimental demonstrations of this hierarchy in a sufficient and necessary way (i.e., by applying measures or universal witnesses of these quantum correlations) have been mainly based on full quantum state tomography, corresponding to measuring at least 15 real parameters of two-qubit states. Here we report an experimental demonstration of this hierarchy by measuring only six elements of a correlation matrix depending on linear combinations of two-qubit Stokes parameters. We show that our experimental setup can also reveal the hierarchy of these quantum correlations of generalized Werner states, which are any two-qubit pure states affected by white noise.