Constructing the three-qudit unextendible product bases with strong nonlocality

The unextendible product bases (UPB) are interesting members of the family of orthogonal product bases. In this paper, we investigate the construction of 3-qudit UPB with strong nonlocality. First, a UPB set in ${{C}^{3}}\otimes {{C}^{3}}\otimes {{C}^{3}}$ of size 19 is presented based on the Shifts UPB. By mapping the system to a Rubik's Cube, we provide a general method of constructing UPB in ${{C}^{d}}\otimes {{C}^{d}}\otimes {{C}^{d}}$ of size ${{\left(d-1 \right)}^{3}}+2d+5$, whose corresponding Rubik's Cube is composed of four parts. Second, for the more general case where the dimensions of parties are different, we extend the classical tile structure to the 3-qudit system and propose the Tri-tile structure. By means of this structure, a ${{C}^{4}}\otimes {{C}^{4}}\otimes {{C}^{5}}$ system of size 38 is obtained based on a ${{C}^{3}}\otimes {{C}^{3}}\otimes {{C}^{4}}$ system of size 19. Then, we generalize this approach to ${{C}^{{{d}_{1}}}}\otimes {{C}^{{{d}_{2}}}}\otimes {{C}^{{{d}_{3}}}}$ system which also consists of four parts. Our research provides a positive answer to the open question raised in [Halder, et al., PRL, 122, 040403 (2019)], indicating that there do exist UPB that can exhibit strong quantum nonlocality without entanglement.

Strongly nonlocal unextendible product bases do exist

A set of multipartite orthogonal product states is locally irreducible, if it is not possible to eliminate one or more states from the set by orthogonality-preserving local measurements. An effective way to prove that a set is locally irreducible is to show that only trivial orthogonality-preserving local measurement can be performed to this set. In general, it is difficult to show that such an orthogonality-preserving local measurement must be trivial. In this work, we develop two basic techniques to deal with this problem. Using these techniques, we successfully show the existence of unextendible product bases (UPBs) that are locally irreducible in every bipartition in d⊗d⊗d for any d≥3, and 3⊗3⊗3 achieves the minimum dimension for the existence of such UPBs. These UPBs exhibit the phenomenon of strong quantum nonlocality without entanglement. Our result solves an open question given by Halder et al. [Phys. Rev. Lett. 122, 040403 (2019)] and Yuan et al. [Phys. Rev. A 102, 042228 (2020)]. It also sheds new light on the connections between UPBs and strong quantum nonlocality.

Optimal Unambiguous Discrimination And Quantum Nonlocality Without Entanglement: Locking And Unlocking By Post-Measurement Information

The phenomenon of nonlocality without entanglement(NLWE) arises in discriminating multi-party quantum separable states. Recently, it has been found that the post-measurement information about the prepared subensemble can lock or unlock NLWE in minimum-error discrimination of non-orthogonal separable states. Thus it is natrual to ask whether the availability of the post-measurement information can influence on the occurrence of NLWE even in other state-discrimination stratigies. Here, we show that the post-measurement information can be used to lock as well as unlock the occurence of NLWE in terms of optimal nambiguous discrimination. Our results can provide a useful application for hiding or sharing information based on non-orthogonal separable states.

Strong quantum nonlocality for unextendible product bases in heterogeneous systems

A set of multipartite orthogonal product states is strongly nonlocal if it is locally irreducible in every bipartition, which shows the phenomenon of strong quantum nonlocality without entanglement. It is known that unextendible product bases (UPBs) can show the phenomenon of quantum nonlocality without entanglement. Thus it is interesting to investigate the strong quantum nonlocality for UPBs. Most of the UPBs with the minimum size cannot demonstrate strong quantum nonlocality. In this paper, we construct a series of UPBs with different large sizes in dAXdBxdC and dAxdBxdCxdD for dA, dB, dC, dD ≧3, and we also show that these UPBs have strong quantum nonlocality, which answers an open question given by Halder et al. [Phys. Rev. Lett. 122, 040403 (2019)] and Yuan et al. [Phys. Rev. A 102, 042228 (2020)] for any possible three and four-partite systems. Furthermore, we propose an entanglement-assisted protocol to locally discriminate the UPB in 3x3x4, and it consumes less entanglement resource than the teleportation-based protocol. Our results build the connection between strong quantum nonlocality and UPBs.

Quantum Nonlocality - Possible Cosmophysical Effects

Mutiple experimental results indicate the existence of cosmophysical effects which influence parameters of nuclear decays and chemical reactions in lab. conditions. In particular, variations of nucleus decay parameters are detected which amplitudes are of the order 10−3 and periods of one year, 24 hours or about one month. Similar influence of solar activity on nuclear decays and chemical reactions also was reported. We argue that such deviations from radioactive decay law and other similar effects can be described by novel quantum nonlocality mechanism, different from standard EPR-Bohm nonlocality. Modified Doebner-Goldin model applied for the description of dynamical nonlocal effects concerned with nuclear decays.

Optimal strategy to certify quantum nonlocality

Certification of quantum nonlocality plays a central role in practical applications like device-independent quantum cryptography and random number generation protocols. These applications entail the challenging problem of certifying quantum nonlocality, something that is hard to achieve when the target quantum state is only weakly entangled, or when the source of errors is high, e.g. when photons propagate through the atmosphere or a long optical fiber. Here we introduce a technique to find a Bell inequality with the largest possible gap between the quantum prediction and the classical local hidden variable limit for a given set of measurement frequencies. Our method represents an efficient strategy to certify quantum nonlocal correlations from experimental data without requiring extra measurements, in the sense that there is no Bell inequality with a larger gap than the one provided. Furthermore, we also reduce the photodetector efficiency required to close the detection loophole. We illustrate our technique by improving the detection of quantum nonlocality from experimental data obtained with weakly entangled photons.

Thermal correlations and entropic uncertainty in a two-spin system under DM and KSEA interactions

In this paper, the thermal quantum correlations along with the thermal entropic uncertainty in a two neighboring XYZ Heisenberg spin-1/2 particles subjected to a transverse external magnetic field with the interplay of both antisymmetric Dzyaloshinskii–Moriya and symmetric Kaplan–Shekhtman–Entin–Wohlman–Aharony are investigated. The quantum consonance and uncertainty-induced quantum nonlocality as well as the entropic uncertainty with quantum memory for the considered system are specified and the thermal behaviors of them in terms of the system parameters are examined. The expected decrease of quantum correlations for higher absolute temperatures is confirmed while the inflation of the uncertainty is generated. Moreover, we show that the stronger spin-spin and spin-orbit exchange couplings can enhance the thermal quantum correlations and suppress the uncertainty. Accordingly, our remarks are expected to be beneficent in illustrating the dynamical quantum correlations and entropy-based uncertainty in a general Heisenberg spin-chain model and thus would be useful for practical quantum information processing.