Nonlocality without entanglement: Quantum theory and beyond

arXiv Quantum Physics, 2019

Quantum nonlocality without entanglement (Q-NWE) encapsulates nonlocal behavior of multipartite product states as they may entail global operation for optimal decoding of the classical information encoded within. Here we show that the phenomena of NWE is not specific to quantum theory only, rather a class of generalized probabilistic theories can exhibit such behavior. In fact several manifestations of NWE, e.g., asymmetric local discrimination, suboptimal local discrimination, notion of separable but locally unimplementable measurement arise generically in operational theories other than quantum theory. We propose a framework to compare the strength of NWE in different theories and show that such behavior in quantum theory is limited, suggesting a specific topological feature of quantum theory, namely, the continuity of state space structure. Our work adds profound foundational appeal to the study of NWE phenomena along with its information theoretic relevance.

arXiv: Quantum Physics, 2020

Ensembles containing orthogonal product states are found to be indistinguishable under local operations and classical communication (LOCC), thereby showing irreversibility in the preparation and distinguishing processes, which is commonly known as nonlocality without entanglement. On the other hand, correlations arising from incompatible measurements on entangled states lead to Bell-nonlocality. We unify these two concepts from the change in certain property incurred in the ensemble under a suitable global unitary transformation. Specifically, we prove that under controlled-NOT (CNOT) operation, a full product basis can create entangled states if and only if the full bases or any subspace of it become irreducible in the process of LOCC discrimination. The proposed criteria quantifies the amount of nonlocality associated with the sets of product states which are even incomplete. For a set having entangled states, we modify the quantity accordingly and show that it can provide an expl...

Physical review, 2023

The structure of quantum theory assures the discrimination of any possible orthogonal set of states. However, the scenario becomes highly nontrivial in the limited measurement setting and leads to different classes of impossibility, viz., indistinguishability, unmarkability, irreducibility etc. These phenomena, often referred to as other nonlocal aspects of quantum theory, have utmost importance in the domain of secret sharing etc. It, therefore, becomes a pertinent question to distill/activate such behaviours from a set, apparently devoid of these nonlocal features and free from local redundancy. While the activation of local indisitnguishability in the sets of entangled states has recently been reported, other stronger notion of quantum nonlocality has yet not been inspected in the parlance of activation. Here, we explored all such stronger versions of nonlocality and affirmatively answered to activate each of them. We also find a locally distinguishable set of multipartite entangled states which can be converted with certainty to a nontrivial set of locally irreducible genuinely entangled states.

Physical Review A, 1999

We exhibit an orthogonal set of product states of two three-state particles that nevertheless cannot be reliably distinguished by a pair of separated observers ignorant of which of the states has been presented to them, even if the observers are allowed any sequence of local operations and classical communication between the separate observers. It is proved that there is a finite gap between the mutual information obtainable by a joint measurement on these states and a measurement in which only local actions are permitted. This result implies the existence of separable superoperators that cannot be implemented locally. A set of states are found involving three two-state particles that also appear to be nonmeasurable locally. These and other multipartite states are classified according to the entropy and entanglement costs of preparing and measuring them by local operations. ͓S1050-2947͑99͒00302-9͔

2022

The structure of quantum theory assures the discrimination of any possible orthogonal set of states. However, the scenario becomes highly nontrivial in the limited measurement setting and leads to different classes of impossibility, viz., indistinguishability, unmarkability, irreducibility etc. These phenomena, often referred to as other nonlocal aspects of quantum theory, have utmost importance in the domain of secret sharing etc. It, therefore, becomes a pertinent question to distill/activate such behaviours from a set, apparently devoid of these nonlocal features and free from local redundancy. While the activation of local indisitinguishability in the sets of entangled states has recently been reported, other stronger notion of quantum nonlocality has yet not been inspected in the parlance of activation. Here, we explored all such stronger versions of nonlocality and affirmatively answered to activate each of them. We also find a locally distinguishable set of multipartite entan...

Physical Review A, 2012

We study the nonlocal properties of two-qubit maximally-entangled and N -qubit Greenberger-Horne-Zeilinger states under local decoherence. We show that the (non)resilience of entanglement under local depolarization or dephasing is not necessarily equivalent to the (non)resilience of Bellinequality violations. Apart from entanglement and Bell-inequality violations, we consider also nonlocality as quantified by the nonlocal content of correlations, and provide several examples of anomalous behaviors, both in the bipartite and multipartite cases. In addition, we study the practical implications of these anomalies on the usefulness of noisy Greenberger-Horne-Zeilinger states as resources for nonlocality-based physical protocols given by communication complexity problems. There, we provide examples of quantum gains improving with the number of particles that coexist with exponentially-decaying entanglement and nonlocal contents.

Physical Review A, 2011

Wiseman and co-workers (Phys. Rev. Lett. 98, 140402, 2007) proposed a distinction between the nonlocality classes of Bell nonlocality, steering and entanglement based on whether or not an overseer trusts each party in a bipartite scenario where they are asked to demonstrate entanglement. Here we extend that concept to the multipartite case and derive inequalities that progressively test for those classes of nonlocality, with different thresholds for each level. This framework includes the three classes of nonlocality above in special cases and introduces a family of others.

arXiv (Cornell University), 2023

Discrimination of quantum states under local operations and classical communication (LOCC) is an intriguing question in the context of local retrieval of classical information, encoded in the multipartite quantum systems. All the local quantum state discrimination premises, considered so far, mimic a basic communication setup , where the spatially separated decoding devices are independent of any additional input. Here, exploring a generalized communication scenario we introduce a framework for input-dependent local quantum state discrimination, which we call local random authentication (LRA). Referring to the term nonlocality, often used to indicate the impossibility of local state discrimination, we coin the term conditional nonlocality for the impossibility associated with the task LRA. We report that conditional nonlocality necessitates the presence of entangled states in the ensemble, a feature absent from erstwhile nonlocality arguments based on local state discrimination. Conversely, all the states in a complete basis set being entangled implies conditional nonlocality. However, the impossibility of LRA also exhibits more conditional nonlocality with less entanglement. The relation between the possibility of LRA and local state discrimination for sets of multipartite quantum states, both in the perfect and conclusive cases, has also been established. The results highlight a completely new aspect of the interplay between the security of information in a network and quantum entanglement under the LOCC paradigm.

2012

Quantum nonlocality is presented often as the most remarkable and inexplicable phenomenon known to modern science which was confirmed in the experiments proving the violation of Bell Inequalities (BI). It has been known already for a long time that the probabilistic models used to prove BI for spin polarization correlation experiments (SPCE) are incompatible with the experimental protocols of SPCE. In particular these models use a common probability space together with joint probability distributions for various incompatible coincidence experiments and/or conditional independence (Bell's locality). Strangely enough these results are not known or simply neglected. Therefore so called Bell's or quantum nonlocality has nothing to do with the common notion of the non-locality and it should be rather called quantum non-Kolmogorovness or quantum contextuality. We quickly explain the true meaning of various Bell's locality assumptions and show that if local variables describing...

2011

We show that for two-qubit chained Bell inequalities with an arbitrary number of measurement settings, nonlocality and entanglement are not only different properties but are inversely related. Specifically, we analytically prove that in absence of noise, robustness of nonlocality, defined as the maximum fraction of detection events that can be lost such that the remaining ones still do not admit a local model, and concurrence are inversely related for any chained Bell inequality with an arbitrary number of settings. The closer quantum states are to product states, the harder it is to reproduce quantum correlations with local models. We also show that, in presence of noise, nonlocality and entanglement are simultaneously maximized only when the noise level is equal to the maximum level tolerated by the inequality; in any other case, a more nonlocal state is always obtained by reducing the entanglement. In addition, we observed that robustness of nonlocality and concurrence are also inversely related for the Bell scenarios defined by the tight two-qubit three-setting $I_{3322}$ inequality, and the tight two-qutrit inequality $I_3$.