Steerability detection of an arbitrary two-qubit state via machine learning

Quantum steering is an important nonclassical resource for quantum information processing. However, even though lots of steering criteria exist, it is still very difficult to efficiently determine whether an arbitrary two-qubit state shared by Alice and Bob is steerable or not, because the optimal measurement directions of Alice are unknown. In this work, we provide an efficient quantum steering detection scheme for an arbitrary two-qubit state with the help of machine learning, where Alice and Bob only need to measure in a few fixed measurement directions. In order to prove the validity of this method, we first realize a high-performance quantum steering classifier with the whole information. Furthermore, a high-performance quantum steering classifier with partial information is realized, where Alice and Bob only need to measure in three fixed measurement directions. Our method outperforms the existing methods in generic cases in terms of both speed and accuracy, opening up the avenues to explore quantum steering via the machine learning approach.

Figure 1

Classification accuracy of machine learning with the whole information ($F_1$ features). The first column (diagonal-filled blue) depicts the accuracy of cross validation, the second column (grid-filled orange) depicts the classification accuracy on random states, and the third column (pure green) depicts the classification accuracy on the Werner state.

Figure 2

The predictions of steerability for generalized Werner states by learned classifiers and SDP. The blue-circle line is the result predicted by learning classifiers with $F_1$ features. Similarly, the red-star line is the result predicted by SDP. And the yellow line is the steerability bound from Alice to Bob.

Figure 3

Classification accuracy of machine learning with partial information ($F_2$ features). The first column (diagonal-filled blue) depicts the accuracy of cross validation, the second column (grid-filled orange) depicts the classification accuracy on random states, and the third column (pure green) depicts the classification accuracy on the Werner state.

Figure 4

The predictions of steerability for generalized Werner states by learning classifiers and SDP. The blue-circle line is the results predicted by learning classifiers with $F_2$ features. Similarly, the red-star line is the results predicted by SDP. And the yellow line is the steerability bound from Alice to Bob.

Figure 5

Classification accuracy of machine learning with partial information ($F_3$ features). The first column (diagonal-filled blue) depicts the accuracy of cross validation, the second column (grid-filled orange) depicts the classification accuracy on random states, and the third column (pure green) depicts the classification accuracy on the Werner states.

Figure 6

The predictions of steerability for generalized Werner states by machine learning classifiers and SDP. The blue-circle line is the results predicted by learned classifiers with $F_3$ features. Similarly, the red-star line is the results predicted by SDP. And the yellow line is the steerability bound from Alice to Bob.

Figure 7

Classification accuracy of machine learning with partial information ($F_4$ features). The first column (diagonal-filled blue) depicts the accuracy of cross validation, the second column (grid-filled orange) depicts the classification accuracy on random states, and the third column (pure green) depicts the classification accuracy on the Werner states.

Figure 8

The predictions of steerability for generalized Werner states by learning classifiers and SDP. The blue-circle line is the result predicted by learning classifiers with $F_4$ features. Similarly, the red-star line is the result predicted by SDP. And the yellow line is the steerability bound from Alice to Bob.

Figure 9

Error of classification on random test data of $m=8$ by each machine learning classifier with the different features: $F_1, F_2, F_3$, and $F_4$, respectively.

Figure 10

Classification error for generalized Werner states with different classifiers.