arXiv subjects

Zhen-Peng Xu

Publications and source records attributed to Zhen-Peng Xu.

51 records · Page 3Linked to original sources

arXiv2018

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.

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arXiv2018

Generalized Hardy's Paradox

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 $n\ge 3$ we demonstrate that there always exist generalized paradoxes (with the success probability as high as $1/2^{n-1}$) 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.

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arXiv2017

Quantum correlations with a gap between the sequential and spatial cases

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.

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arXiv2016

Maximum nonlocality in the (3,2,2) scenario

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.

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arXiv2016

Reformulating noncontextuality inequalities in an operational approach

A new theory-independent noncontextuality inequality is presented [Phys. Rev. Lett. 115, 110403 (2015)] based on Kochen-Specker (KS) set without imposing the assumption of determinism. By proposing novel noncontextuality inequalities, we show that such result can be generalized from KS set to the noncontextuality inequalities not only for state-independent but also for state-dependent scenario. The YO-13 ray and $n$ cycle ray are considered as examples.

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arXiv2016

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.

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arXiv2016

On realizing Lovász-optimum orthogonal representation in the real Hilbert space

Quantum contextuality is usually revealed by the non-contextual inequality, which can always be associated with an exclusivity graph. The quantum upper bound of the inequality is nothing but the Lovász number of the graph. In this work, we show that if there is a Lovász-optimum orthogonal representation realized in the $d$-dimensional complex Hilbert space, then there always exists a corresponding Lovász-optimum orthogonal representation in the $(2d-1)$-dimensional real Hilbert space. This in turn completes the proof that the Lovász-optimum orthogonal representation for any exclusivity graph can always be realized in the real Hilbert space of suitable dimension.

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arXiv2016

Beating the Clauser-Horne-Shimony-Holt and the Svetlichny games with Optimal States

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.

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arXiv2015

Optimal GHZ Paradox for Three Qubits

Quatum nonlocality as a valuable resource is of vital importance in quantum information processing. The characterization of the resource has been extensively investigated mainly for pure states, while relatively less is know for mixed states. Here we prove the existence of the optimal GHZ paradox by using a novel and simple method to extract an optimal state that can saturate the tradeoff relation between quantum nonlocality and the state purity. In this paradox, the logical inequality which is formulated by the GHZ-typed event probabilities can be violated maximally by the optimal state for any fixed amount of purity (or mixedness). Moreover, the optimal state can be described as a standard GHZ state suffering flipped color noise. The maximal amount of noise that the optimal state can resist is 50%. We suggest our result to be a step toward deeper understanding of the role played by the AVN proof of quantum nonlocality as a useful physical resource.

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arXiv2015

Quantum contextuality of a qutrit state

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 does 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.

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arXiv2015

Beyond Gisin's Theorem and its Applications: Violation of Local Realism by Two-Party Einstein-Podolsky-Rosen Steering

We demonstrate here that for a given mixed multi-qubit state if there are at least two observers for whom mutual Einstein-Podolsky-Rosen steering is possible, i.e. each observer is able to steer the other qubits into two different pure states by spontaneous collapses due to von Neumann type measurements on his/her qubit, then nonexistence of local realistic models is fully equivalent to quantum entanglement (this is not so without this condition). This result leads to an enhanced version of Gisin's theorem (originally: all pure entangled states violate local realism). Local realism is violated by all mixed states with the above steering property. The new class of states allows one e.g. to perform three party secret sharing with just pairs of entangled qubits, instead of three qubit entanglements (which are currently available with low fidelity). This significantly increases the feasibility of having high performance versions of such protocols. Finally, we discuss some possible applications.

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arXiv2015

State-independent contextuality sets for a qutrit

We present a generalized set of complex rays for a qutrit in terms of parameter $q=e^{i2π/k}$, 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.

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arXiv2015

Dimension-Independent Bounds for Hardy's Experiment

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.

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arXiv2015

Quantum Nonlocality Enhanced by Homogenization

Homogenization proposed in [Y.-C Wu and M. Żukowski, 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.

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arXiv2013

Hardy's Paradox for High-Dimensional Systems: Beyond Hardy's Limit

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.

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