A physical explanation for quantum bounds to nonlocality (Tsirelson's bound) is a fundamental problem in quantum theory, for it is known that no-signaling alone fails to reproduce this limit. Here, information indistinguishability is presented as the indistinguishability of qubits or more general bits, and it suggests an answer to the nonlocality conundrum, ultimately placing it as the origin to quantum limits. Indistinguishability is also connected to exclusivity principle, and it is shown that indistinguishability leads to quantum correlation bounds. This suggests indistinguishability be as fundamental as non-locality and relativistic causality for nonlocal realism.
Local discrimination of quantum states is a fundamental task in distributed quantum information processing and underlies applications such as quantum communication, data hiding, and secret sharing. Here we investigate a weak form of local indistinguishability by asking how easily it can disappear when the candidate set is reduced or an additional copy of the unknown state is supplied. We introduce inclusion-minimal locally indistinguishable sets, namely, locally indistinguishable sets for which every proper subset is perfectly distinguishable by local operations and classical communication (LOCC), and show that every finite locally indistinguishable set contains such a subset. We further find that any inclusion-minimal locally indistinguishable sets becomes perfectly distinguishable by LOCC when two identical copies are available, although a single copy is insufficient. Fininally, We construct explicit inclusion-minimal locally indistinguishable product-state sets in
(Cd)⊗n for every odd
d=2k+1 and
n≥2. These results show that local indistinguishability can be nontrivial at the single-copy level yet fragile under either the removal of candidate states or a modest increase in copy resources, providing a complementary perspective on the structure of quantum nonlocality.