Optimal classical simulation of state-independent quantum contextuality

Simulating quantum contextuality with classical systems requires memory. A fundamental yet open question is what is the minimum memory needed and, therefore, the precise sense in which quantum systems outperform classical ones. Here, we make rigorous the notion of classically simulating quantum state-independent contextuality (QSIC) in the case of a single quantum system submitted to an infinite sequence of measurements randomly chosen from a finite QSIC set. We obtain the minimum memory needed to simulate arbitrary QSIC sets via classical systems under the assumption that the simulation should not contain any oracular information. In particular, we show that, while classically simulating two qubits tested with the Peres-Mermin set requires $\log_2 24 \approx 4.585$ bits, simulating a single qutrit tested with the Yu-Oh set requires, at least, $5.740$ bits.Comment: 7 pages, 4 figure

State-independent contextuality sets for a qutrit

We present a generalized set of complex rays for a qutrit in terms of parameter $q=e^{i2\pi/k}$, a $k$-th root of unity. Remarkably, when $k=2,3$, the set reduces to two well known state-independent contextuality (SIC) sets: the Yu-Oh set and the Bengtsson-Blanchfield-Cabello set. Based on the Ramanathan-Horodecki criterion and the violation of a noncontextuality inequality, we have proven that the sets with $k=3m$ and $k=4$ are SIC, while the set with $k=5$ is not. Our generalized set of rays will theoretically enrich the study of SIC proof, and experimentally stimulate the novel application to quantum information processing.Comment: 4 pages, 2 figures; revised versio

Quantum Nonlocality Enhanced by Homogenization

Homogenization proposed in [Y.-C Wu and M. \.Zukowski, Phys. Rev. A 85, 022119 (2012)] is a procedure to transform a tight Bell inequality with partial correlations into a full-correlation form that is also tight. In this paper, we check the homogenizations of two families of $n$-partite Bell inequalities: the Hardy inequality and the tight Bell inequality without quantum violation. For Hardy's inequalities, their homogenizations bear stronger quantum violation for the maximally entangled state; the tight Bell inequalities without quantum violation give the boundary of quantum and supra-quantum, but their homogenizations do not have the similar properties. We find their homogenization are violated by the maximally entangled state. Numerically computation shows the the domains of quantum violation of homogenized Hardy's inequalities for the generalized GHZ states are smaller than those of Hardy's inequalities.Comment: 4 pages, 2 figure

Demonstration of the double Q^2-rescaling model

In this paper we have demonstrated the double Q^2-rescaling model (DQ^2RM) of parton distribution functions of nucleon bounded in nucleus. With different x-region of l-A deep inelastic scattering process we take different approach: in high x-region (0.1\le x\le 0.7) we use the distorted QCD vacuum model which resulted from topologically multi -connected domain vacuum structure of nucleus; in low x-region (10^{-4}\le x\le10^{-3}) we adopt the Glauber (Mueller) multi- scattering formula for gluon coherently rescattering in nucleus. From these two approach we justified the rescaling parton distribution functions in bound nucleon are in agreement well with those we got from DQ^2RM, thus the validity for this phenomenologically model are demonstrated.Comment: 19 page, RevTex, 5 figures in postscrip

Sharp Contradiction for Local-Hidden-State Model in Quantum Steering

In quantum theory, no-go theorems are important as they rule out the existence of a particular physical model under consideration. For instance, the Greenberger-Horne-Zeilinger (GHZ) theorem serves as a no-go theorem for the nonexistence of local hidden variable models by presenting a full contradiction for the multipartite GHZ states. However, the elegant GHZ argument for Bell's nonlocality does not go through for bipartite Einstein-Podolsky-Rosen (EPR) state. Recent study on quantum nonlocality has shown that the more precise description of EPR's original scenario is "steering", i.e., the nonexistence of local hidden state models. Here, we present a simple GHZ-like contradiction for any bipartite pure entangled state, thus proving a no-go theorem for the nonexistence of local hidden state models in the EPR paradox. This also indicates that the very simple steering paradox presented here is indeed the closest form to the original spirit of the EPR paradox.Comment: 9 pages. Revised version for Scientific Report