  Entanglement is a physical phenomenon, which has fueled recent successes of
quantum algorithms. Although quantum neural networks (QNNs) have shown
promising results in solving simple machine learning tasks recently, for the
time being, the effect of entanglement in QNNs and the behavior of QNNs in
binary pattern classification are still underexplored. In this work, we provide
some theoretical insight into the properties of QNNs by presenting and
analyzing a new form of invariance embedded in QNNs for both quantum binary
classification and quantum representation learning, which we term negational
symmetry. Given a quantum binary signal and its negational counterpart where a
bitwise NOT operation is applied to each quantum bit of the binary signal, a
QNN outputs the same logits. That is to say, QNNs cannot differentiate a
quantum binary signal and its negational counterpart in a binary classification
task. We further empirically evaluate the negational symmetry of QNNs in binary
pattern classification tasks using Google's quantum computing framework. The
theoretical and experimental results suggest that negational symmetry is a
fundamental property of QNNs, which is not shared by classical models. Our
findings also imply that negational symmetry is a double-edged sword in
practical quantum applications.
