  Noether's theorem is one of the fundamental laws in physics, relating the
symmetry of a physical system to its constant of motion and conservation law.
On the other hand, there exist a variety of non-Hermitian parity-time
(PT)-symmetric systems, which exhibit novel quantum properties and have
attracted increasing interest. In this work, we extend Noether's theorem to a
class of significant PT -symmetric systems for which the eigenvalues of the
PT-symmetric Hamiltonian H change from purely real numbers to purely imaginary
numbers,and introduce a generalized expectation value of an operator based on
biorthogonal quantum mechanics. We find that the generalized expectation value
of a time-independent operator is a constant of motion when the operator
presents a standard symmetry in the PT -symmetry unbroken regime, or a chiral
symmetry in the PT-symmetry broken regime. In addition, we experimentally
investigate the extended Noether's theorem in PT -symmetric single-qubit and
two-qubit systems using an optical setup. Our experiment demonstrates the
existence of the constant of motion and reveals how this constant of motion can
be used to judge whether the PT -symmetry of a system is broken. Furthermore, a
novel phenomenon of masking quantum information is first observed in a PT
-symmetric two-qubit system. This study not only contributes to full
understanding of the relation between symmetry and conservation law in PT
-symmetric physics, but also has potential applications in quantum information
theory and quantum communication protocols.
