See also arxiv
Jie Zhou, Hui-Xian Meng, Shu-Han Jiang, Zhen-Peng Xu, Changliang Ren, Hong-Yi Su and Jing-Ling Chen
Deriving Einstein-Podolsky-Rosen steering inequalities from the few-body Abner Shimony inequalities
For the Abner Shimony (AS) inequalities, the simplest unified forms of directions attaining the maximum quantum violation are investigated. Based on these directions, a family of Einstein-Podolsky-Rosen (EPR) steering inequalities is derived from the AS inequalities in a systematic manner. For these inequalities, the local hidden state (LHS) bounds are strictly less than the local hidden variable (LHV) bounds. This means that the EPR steering is a form of quantum nonlocality strictly weaker than Bell-nonlocality.
Mu Yang, Hui-Xian Meng, Jie Zhou, Zhen-Peng Xu, Ya Xiao, Kai Sun, Jing-Ling Chen, Jin-Shi Xu, Chuan-Feng Li and Guang-Can Guo
General Hardy-Type Paradox Based on Bell inequality and its Experimental Test
Phys. Rev. A 99, 032103 (2019), arXiv:1809.04289
Local realistic models cannot completely describe all predictions of quantum mechanics. This is known as Bell's theorem that can be revealed either by violations of Bell inequality, or all-versus-nothing proof of nonlocality. Hardy's paradox is an important all-versus-nothing proof and is considered as "the simplest form of Bell's theorem". In this work, we theoretically build the general framework of Hardy-type paradox based on Bell inequality. Previous Hardy's paradoxes have been found to be special cases within the framework. Stronger Hardy-type paradox has been found even for the two-qubit two-setting case, and the corresponding successful probability is about four times larger than the original one, thus providing a more friendly test for experiment. We also find that GHZ paradox can be viewed as a perfect Hardy-type paradox. Meanwhile, we experimentally test the stronger Hardy-type paradoxes in a two-qubit system. Within the experimental errors, the experimental results coincide with the theoretical predictions.
Measurement incompatibility is the most basic resource that distinguishes quantum from classical physics. Contextuality is the critical resource behind the power of some models of quantum computation and is also a necessary ingredient for many applications in quantum information. A fundamental problem is thus identifying when incompatibility produces contextuality. Here, we show that, given a structure of incompatibility characterized by a graph in which nonadjacent vertices represent incompatible ideal measurements, the necessary and sufficient condition for the existence of a quantum realization producing contextuality is that this graph contains induced cycles of size larger than three.
Xiao, Ya; Xu, Zhen-Peng; Li, Qiang; Xu, Jin-Shi; Sun, Kai; Cui, Jin-Ming; Zhou, Zong-Quan; Su, Hong-Yi; Cabello, Adán; Chen, Jing-Ling; Li, Chuan-Feng; Guo, Guang-Can
Experimental observation of quantum state-independent contextuality under no-signaling conditions
Opt. Express 26, 32-50 (2018)
Contextuality, the impossibility of assigning context-independent measurement outcomes, is a critical resource for quantum computation and communication. No-signaling between successive measurements is an essential requirement that should be accomplished in any test of quantum contextuality and that is difficult to achieve in practice. Here, we introduce an optimal quantum state-independent contextuality inequality in which the deviation from the classical bound is maximal. We then experimentally test it using single photons generated from a defect in a bulk silicon carbide, while satisfying the requirement of no-signaling within the experimental error. Our results shed new light on the study of quantum contextuality under no-signaling conditions.
Xiao, Ya; Xu, Zhen-Peng; Li, Qiang; Su, Hong-Yi; Sun, Kai; Cabello, Adán; Xu, Jin-Shi; Chen, Jing-Ling; Li, Chuan-Feng; Guo, Guang-Can
Experimental test of quantum correlations from Platonic graphs
Optica 5, 718-722 (2018)
Great effort has been made in the investigation of contextual correlations between compatible observables due to their both fundamental and practical importance. The graph-theoretic approach to correlate events has been proved to be an effective method in the characterization of quantum contextuality, which implies that quantum violations of noncontextual inequalities derived in the noncontextual hidden-variable models should be achievable. Finding experimentally more friendly and theoretically more powerful noncontextual inequalities associated with specific graphs is of particular interest. Here we consider Platonic graphs to vindicate the quantum maximum predicted by graph theory and test the quantum violation against the mixedness of the state. Among these solids we refer particularly to the icosahedron to build the experiment, as it gives rise to the largest quantum-classical difference. The contextual correlations are demonstrated on quantum four-dimensional states encoded in the spatial modes of single photons generated from a defect in a bulk silicon carbide. Our results shed new light on the conflict between quantum and classical physics and may promote deep understanding of the connection between quantum theory, graph theory, and operator theory.
Jiang, Shu-Han; Xu, Zhen-Peng; Su, Hong-Yi; Pati, Arun Kumar; Chen, Jing-Ling
Generalized Hardy's Paradox
Phys. Rev. Lett. 120, 50403 (2018)
Here, we present the most general framework for n-particle Hardy’s paradoxes, which include Hardy’s original one and Cereceda’s extension as special cases. Remarkably, for any n≥3, we demonstrate that there always exist generalized paradoxes (with the success probability as high as 1/2n−1) that are stronger than the previous ones in showing the conflict of quantum mechanics with local realism. An experimental proposal to observe the stronger paradox is also presented for the case of three qubits. Furthermore, from these paradoxes we can construct the most general Hardy’s inequalities, which enable us to detect Bell’s nonlocality for more quantum states.
Cabello, Adán; Gu, Mile; Gühne, Otfried; Xu, Zhen-Peng
Optimal Classical Simulation of State-Independent Quantum Contextuality
Phys. Rev. Lett. 120, 130401 (2018)
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 log224≈4.585 bits, simulating a single qutrit tested with the Yu-Oh set requires, at least, 5.740 bits.
Xu, Zhen-Peng; Cabello, Adán
Quantum correlations with a gap between the sequential and spatial cases
Phys. Rev. A 96, 12122 (2017)
We address the problem of whether parties who cannot communicate but share nonsignaling quantum correlations between the outcomes of sharp measurements can distinguish, just from the value of a correlation observable, whether their outcomes were produced by sequential compatible measurements on single systems or by measurements on spatially separated subsystems. We show that there are quantum correlations between the outcomes of sequential measurements which cannot be attained with spatially separated systems. We present examples of correlations between spatially separated systems whose quantum maximum tends to the sequential maximum as the number of parties increases and examples of correlations between spatially separated systems whose quantum maximum fails to violate the noncontextual bound while its corresponding sequential version does.
Su, Hong-Yi; Ren, Changliang; Chen, Jing-Ling; Zhang, Fu-Lin; Wu, Chunfeng; Xu, Zhen-Peng; Gu, Mile; Vinjanampathy, Sai; Kwek, L. C.
Beating the Clauser-Horne-Shimony-Holt and the Svetlichny games with optimal states
Phys. Rev. A 93, 22110 (2016)
We study the relation between the maximal violation of Svetlichny's inequality and the mixedness of quantum states and obtain the optimal state (i.e., maximally nonlocal mixed states, or MNMS, for each value of linear entropy) to beat the Clauser-Horne-Shimony-Holt and the Svetlichny games. For the two-qubit and three-qubit MNMS, we showed that these states are also the most tolerant state against white noise, and thus serve as valuable quantum resources for such games. In particular, the quantum prediction of the MNMS decreases as the linear entropy increases, and then ceases to be nonlocal when the linear entropy reaches the critical points 2/3 and 9/14 for the two- and three-qubit cases, respectively. The MNMS are related to classical errors in experimental preparation of maximally entangled states.
López-Rosa, Sheila; Xu, Zhen-Peng; Cabello, Adán
Maximum nonlocality in the (3,2,2) scenario
Phys. Rev. A 94, 62121 (2016)
We identify the simplest combinations of entanglement and incompatibility giving the maximum quantum violation for each of the 46 classes of tight Bell inequalities for the (3,2,2) scenario, i.e., three parties, two measurements per party, and two outcomes per measurement. This allows us to classify the maximum quantum nonlocality according to the simplest resources needed to achieve it. We show that entanglement and incompatibility only produce maximum nonlocality when they are combined in specific ways. For each entanglement class there is, in most cases, just one incompatibility class leading to maximum nonlocality. We also identify two interesting cases. We show that the maximum quantum violation of Śliwa inequality 23 only occurs when the third party measures the identity, so nonlocality cannot increase when we add a third party to the bipartite case. Almost quantum correlations predict that adding a new party increases nonlocality. This points out that either almost quantum correlations violate a fundamental principle or that there is a form of tripartite entanglement which quantum theory cannot account for. The other interesting case is the maximum quantum violation of Śliwa inequality 26, which, like the Mermin inequality, requires maximum incompatibility for all parties. In contrast, it requires a specific entangled state which has the same tripartite negativity as the W state.
Xu, Zhen-Peng; Saha, Debashis; Su, Hong-Yi; Pawłowski, Marcin; Chen, Jing-Ling
Reformulating noncontextuality inequalities in an operational approach
Phys. Rev. A 94, 62103 (2016)
A new theory-independent noncontextuality inequality is presented [R. Kunjwal and R. W. Spekkens, Phys. Rev. Lett. 115, 110403 (2015)] based on a Kochen-Specker (KS) set without imposing the assumption of determinism. By proposing noncontextuality inequalities, we show that such result can be generalized from a KS set to the noncontextuality inequalities not only for a state-independent scenario but also for a state-dependent scenario. The YO-13 ray and n cycle ray are considered as examples.
Chen, Jing-Ling; Su, Hong-Yi; Xu, Zhen-Peng; Pati, Arun Kumar
Sharp Contradiction for Local-Hidden-State Model in Quantum Steering
Sci. Rep. 6, 32075 (2016)
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.
Chen, Jing-Ling; Su, Hong-Yi; Xu, Zhen-Peng; Wu, Yu-Chun; Wu, Chunfeng; Ye, Xiang-Jun; Żukowski, Marek; Kwek, L. C.
Beyond Gisin’s Theorem and its Applications: Violation of Local Realism by Two-Party Einstein-Podolsky-Rosen Steering
Sci. Rep. 5, 11624 (2015)
Ren, Changliang; Su, Hong-Yi; Xu, Zhen-Peng; Wu, Chunfeng; Chen, Jing-Ling
Optimal GHZ Paradox for Three Qubits
Sci. Rep. 5, 13080 (2015)
Xu, Zhen-Peng; Su, Hong-Yi; Chen, Jing-Ling
Quantum contextuality of a qutrit state
Phys. Rev. A 92, 12104 (2015)
We present a study of quantum contextuality of three-dimensional mixed states for the Klyachko-Can-Binicioğlu-Shumovsky (KCBS) and the Kurzyński-Kaszlikowski (KK) noncontextuality inequalities. For any class of states whose eigenvalues are arranged in decreasing order, a universal set of measurements always exists for the KK inequality, whereas none exists for the KCBS inequality. This difference can be reflected from the spectral distribution of the overall measurement matrix. Our results would facilitate the error analysis for experimental setups, and our spectral method in the paper combined with graph theory could be useful in future studies on quantum contextuality.
Xu, Zhen-Peng; Chen, Jing-Ling; Su, Hong-Yi
State-independent contextuality sets for a qutrit
Physics Letters A 379, 1868-1870 (2015)
We present a generalized set of complex rays for a qutrit in terms of parameter q = e i 2 π / 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 = 3 m and k = 4 are SIC sets, while the set with k = 5 is not. Our generalized set of rays will theoretically enrich the study of SIC proofs, and stimulate the novel application to quantum information processing.
Xu, Zhen-Peng; Su, Hong-Yi; Chen, Jing-Ling
Dimension-independent bounds for Hardy's experiment
Int. J. Quantum Inform. 12, 1450039 (2014)
Hardy's paradox is of fundamental importance in quantum information theory. So far, there have been two types of its extensions into higher dimensions: in the first type the maximum probability of nonlocal events is roughly 9% and remains the same as the dimension changes (dimension-independent), while in the second type the probability becomes larger as the dimension increases, reaching approximately 40% in the infinite limit. Here, we (i) give an alternative proof of the first type, (ii) study the situation in which the maximum probability of nonlocal events can also be dimension-independent in the second type and (iii) conjecture how the situation could be changed in order that (ii) still holds.
Chen, Xu; Su, Hong-Yi; Xu, Zhen-Peng; Wu, Yu-Chun; Chen, Jing-Ling
Quantum nonlocality enhanced by homogenization
Int. J. Quantum Inform. 12, 1450040 (2014)
Homogenization proposed in [Y.-C Wu and M. Żukowski, Phys. Rev. A85 (2012) 022119] 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.
Chen, Jing-Ling; Cabello, Adán; Xu, Zhen-Peng; Su, Hong-Yi; Wu, Chunfeng; Kwek, L. C.
Hardy's paradox for high-dimensional systems
Phys. Rev. A 88, 62116 (2013)
Hardy's proof is considered the simplest proof of nonlocality. Here we introduce an equally simple proof that (i) has Hardy's as a particular case, (ii) shows that the probability of nonlocal events grows with the dimension of the local systems, and (iii) is always equivalent to the violation of a tight Bell inequality. Our proof has all the features of Hardy's and adds the only ingredient of the Einstein-Podolsky-Rosen scenario missing in Hardy's proof: It applies to measurements with an arbitrarily large number of outcomes.