Quantum nonlocality is usually associated with entangled states by their violations of Bell-type inequalities. However, even unentangled systems, whose parts may have been prepared separately, can show nonlocal properties. In particular, a set of product states is said to exhibit “quantum nonlocality without entanglement” if the states are locally indistinguishable; i.e., it is not possible to optimally distinguish the states by any sequence of local operations and classical communication. Here, we present a stronger manifestation of this kind of nonlocality in multiparty systems through the notion of local irreducibility. A set of multiparty orthogonal quantum states is defined to be locally irreducible if it is not possible to locally eliminate one or more states from the set while preserving orthogonality of the postmeasurement states. Such a set, by definition, is locally indistinguishable, but we show that the converse does not always hold. We provide the first examples of orthogonal product bases on ${\mathbb{C}}^d\otimes {\mathbb{C}}^d\otimes {\mathbb{C}}^d$ for $d=3$, 4 that are locally irreducible in all bipartitions, where the construction for $d=3$ achieves the minimum dimension necessary for such product states to exist. The existence of such product bases implies that local implementation of a multiparty separable measurement may require entangled resources across all bipartitions.

Quantum mechanics is compatible with scenarios where the relative order between two events can be indefinite. Here we show that two independent instances of a noisy process can behave as a perfect quantum communication channel when used in a coherent superposition of two alternative orders. This phenomenon occurs even if the original process has zero capacity to transmit quantum information. In contrast, perfect quantum communication does not occur when the message is sent directly from the sender to the receiver through a superposition of alternative paths, with an independent noise process acting on each path. The possibility of perfect quantum communication through independent noisy channels highlights a fundamental difference between the superposition of orders in time and the superposition of paths in space.

Bohr's complementarity principle is one of the central concepts in quantum mechanics which restricts joint measurement for certain observables. Of course, later development shows that joint measurement could be possible for such observables with the introduction of a certain degree of unsharpness or fuzziness in the measurement. In this paper, we show that the optimal degree of unsharpness, which guarantees the joint measurement of all possible pairs of dichotomic observables, determines the degree of nonlocality in quantum mechanics as well as in more general no-signaling theories.

The quantum ontological feature of contextuality apart from being central to foundations of quantum theory forms the basis of quantum advantage in a multitude of information processing tasks. In particular, the contextuality of preparation procedures was shown to power a particular two-party information processing task “parity oblivious multiplexing” (Spekkens et al. Phys Rev Lett 102:010401 (2009 ). Specifically, it was shown that there exists a limit to how well any preparation noncontextual theory can perform in this task. This limit constitutes a noncontextuality inequality. Moreover, the authors demonstrated quantum violation of this inequality along with preparation contextuality associated with the ontic description underlying two-level completely mixed quantum state. In this work, we extend these arguments to apply to arbitrary dimensions by introducing a class of two-party information processing tasks, namely d-level parity oblivious random access codes. We analytically obtain classical (or equivalently preparation noncontextual) bounds on the success probability for these tasks for arbitrary d. For each value of d, this bound constitutes a unique noncontextuality inequality. Remarkably, these bounds are independent of the amount of communication. Furthermore, we find a classical protocol utilizing a \(d_\mathrm{c}=d\)-dimensional classical message which saturates this bound. In order to establish nontriviality of these inequalities, we provide evidence of significant quantum violations. Specifically, by numerical techniques, we show that for \(d=3,\ldots ,10\), the noncontextuality bound is violated by quantum theory. (1) We provide explicit quantum protocols which violate the associated noncontextuality inequality for \(d=3,4,5\) employing \(d_\mathrm{q}=d\)-leveled quantum systems. (2) Using see-saw semi-definite programming (SDP) technique, we find evidence (lower bounds) of significant quantum violation of these inequalities for \(d=3,\ldots ,10\). (3) With the help of state-of-the-art (NPA-hierarchy like) SDP technique, we provide upper bounds (independent of the dimension of the involved quantum systems) on quantum violation for \(d=3,\ldots ,10\). The introduced class of information tasks, thus, provides for operational depiction of preparation contextuality of the ontic description underlying mixed higher dimensional quantum systems.

An orthogonal product basis of a composite Hilbert space is genuinely nonlocal if the basis states are locally indistinguishable across every bipartition. From an operational point of view, such a basis corresponds to a separable measurement that cannot be implemented by local operations and classical communication unless all the parties come together in a single location. In this work we classify genuinely nonlocal product bases into different categories. Our classification is based on the state elimination property of the set via orthogonality-preserving measurements when all the parties are spatially separated or different subsets of the parties come together. We then study local state discrimination protocols for several such bases with additional entangled resources shared among the parties. Apart from consuming less entanglement than teleportation-based schemes, our protocols indicate operational significance of the proposed classification and exhibit nontrivial use of genuine entanglement in the local state discrimination problem.

In a multipartite scenario quantum entanglement manifests its most dramatic form when the state is genuinely entangled. Such a state is more beneficial for information theoretic applications if it contains distillable entanglement in every bipartition. It is, therefore, of significant operational interest to identify subspaces of multipartite quantum systems that contain such properties a priori. In this article we introduce the notion of unextendible biseparable bases (UBB) that provides an adequate method to construct genuinely entangled subspaces (GES). We provide explicit construction of two types of UBBs—party symmetric and party asymmetric—for every 3-qudit quantum system, with local dimension $d\ge 3$. Furthermore, we show that the GES resulting from the symmetric construction is indeed a bidistillable subspace, i.e., all the states supported on it contain distillable entanglement across every bipartition.