arXiv subjects

Jun-Li Li

Publications and source records attributed to Jun-Li Li.

At least 19 recordsLinked to original sources

arXiv2023

An Effective Way of Characterizing the Quantum Nonlocality

Nonlocality is a distinctive feature of quantum theory, which has been extensively studied for decades. It is found that the uncertainty principle determines the nonlocality of quantum mechanics. Here we show that various degrees of nonlocalities in correlated system can be characterized by the generalized uncertainty principle, by which the complementarity is attributed to the mutual dependence of observables. Concrete examples for different kinds of non-classical phenomena pertaining to different orders of dependence are presented. We obtain the third order ``skewness nonlocality'', and find that the Bell nonlocality turns out to be merely the second order ``variance nonlocality'' and the forth order dependence contains the commutator squares, which hence is related to the quantum contextuality. More applications of the generalized uncertainty principle are expected.

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arXiv2021

The Generalized Uncertainty Principle

The uncertainty principle lies at the heart of quantum physics, and is widely thought of as a fundamental limit on the measurement precisions of incompatible observables. Here we show that the traditional uncertainty relation in fact belongs to the leading order approximation of a generalized uncertainty relation. That is, the leading order linear dependence of observables gives the Heisenberg type of uncertainty relations, while higher order nonlinear dependence may reveal more different and interesting correlation properties. Applications of the generalized uncertainty relation and the high order nonlinear dependence between observables in quantum information science are also discussed.

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arXiv2020

An optimal measurement strategy to beat the quantum uncertainty in correlated system

Uncertainty principle is an inherent nature of quantum system that undermines the precise measurement of incompatible observables and hence the applications of quantum theory. Entanglement, another unique feature of quantum physics, was found may help to reduce the quantum uncertainty. In this paper, we propose a practical method to reduce the one party measurement uncertainty by determining the measurement on the other party of an entangled bipartite system. In light of this method, a family of conditional majorization uncertainty relations in the presence of quantum memory is constructed, which is applicable to arbitrary number of observables. The new family of uncertainty relations implies sophisticated structures of quantum uncertainty and nonlocality, that were usually studied by using scalar measures. Applications to reduce the local uncertainty and to witness quantum nonlocalities are also presented.

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arXiv2020

The Decompositions of Werner and Isotropic States

The decompositions of separable Werner state, and also isotropic state, are well-known tough issues in quantum information theory, in this work we investigate them in the Bloch vector representation, exploring the symmetric informationally complete positive operator-valued measure (SIC-POVM) in the Hilbert space. We successfully get the decomposition for arbitrary $N\times N$ Werner state in terms of regular simplexes. Meanwhile, the decomposition of isotropic state is found to be related to the decomposition of Werner state via partial transposition. It is interesting to note that in the large $N$ limit, while the Werner states are either separable or non-steerably entangled, most of the isotropic states tend to be steerable.

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arXiv2020

Test of Nonlocal Hidden Variable Theory by Leggett Inequality in High Energy Physics

The Leggett inequality is a constraint on the bipartite correlation that admits certain types of non-localities. Existing tests mainly focused on the electromagnetic systems where measurement apparatus are assumed to be projective and sharp. However, in nature there are interactions that do not obey the same conservation laws for photon, and the actual measurements may subject to unavoidable uncertainties due to the fundamental physical principles. In this work, we generalize the Leggett inequality to incorporate the measurements that are unsharp and/or biased. It is found that the parity violation in nature provides a spontaneous implementation of an unsharp measurement for the spin of hyperon. A fine structured Leggett inequality for hyperon decays characterized by the asymmetry parameters is obtained and its violation is found which could be observed with the yet obtained data in experiment, like BESIII and Belle.

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arXiv2020

Nonlocal Correlation of Spin in High Energy Physics

Nonlocality is a key feature of quantum theory and is reflected in the violation of Bell inequalities for entangled systems. The experimental tests beyond the electromagnetism and massless quanta are of great importance for understanding the nonlocality in different quantum interactions. In this work, we develop a generalized Clauser-Horne inequality pertaining especially to the high energy physics processes, which is quantum mechanical intervene free. We find, in the process of pseudoscalar quarkonium exclusive decay to entangled $Λ\barΛ$ pairs, the inequality could be violated and is verifiable in high energy experiments, like BES III or BELLE II.

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arXiv2019

Experimental investigation of the uncertainty relations with coherent light

Taking advantage of coherent light beams, we experimentally investigate the variancebased uncertainty relations and the optimal majorization uncertainty relation for the two-dimensional quantum mechanical system.Different from most of the experiments which devoted to record each individual quantum, we examine the uncertainty relations by measuring an ensemble of photons with two polarization degree of freedom characterized by the Stokes parameters which allow us to determine the polarization density matrix with high precision. The optimality of the recently proposed direct-sum majorization uncertainty relation is verified by measuring the Lorenz curves. Results show that the Lorenz curve method represents a faithful verification of the majorization uncertainty relation and the uncertainty relation is indeed an ensemble property of quantum system.

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arXiv2019

Characterizing the Quantum Non-locality by the Mathematics of Magic Square

By constructing the quantum state in high-dimensional probability tensor, we find the quantum magic square(QMS) may stand as an ideal means of characterizing the non-local phenomena, i.e. the separability, entanglement, two/one-way steering, and Bell non-locality, etc. In this scheme, different types of non-locality exhibit distinctive inner structures of the probability tensor, which are observable in form of the partial sum of the tensor components. In application, we prove the Bell and GHZ theorems, and demonstrate that the uncertainty relation may rate the non-locality, from Bell locality to separability. We derive a conditional majorization uncertainty relation, which is superior to the steering criterion previously thought to be optimal for the uncertainty relation.

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arXiv2019

The Optimal Uncertainty Relation

Employing the lattice theory on majorization, we investigate the universal quantum uncertainty relation for any number observables and general measurement. We find: 1. The least bounds of the universal uncertainty relations can only be properly defined in the lattice theory; 2. Contrary to variance and entropy, the metric induced by the majorization lattice implies an intrinsic structure of the quantum uncertainty; 3. The lattice theory correlates the optimization of uncertainty relation with the entanglement transformation under local quantum operation and classical communication. Interestingly, the optimality of the universal uncertainty relation is found can be mimicked by the Lorenz curve, initially introduced in economics to measure the wealth concentration degree of a society.

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arXiv2019

Tight $N$-observable uncertainty relations and their experimental demonstrations

The uncertainty relation, as one of the fundamental principles of quantum physics, captures the incompatibility of noncommuting observables in the preparation of quantum states. In this work, we derive two strong and universal uncertainty relations for $N(N\ge2)$ observables with discrete and bounded spectra, one in multiplicative form and the other in additive form. To verify their validity, for illustration, we implement in the spin-1/2 system an experiment with single-photon measurement. The experimental results exhibit the validity and robustness of these uncertainty relations, and indicate the existence of stringent lower bounds.

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arXiv2018

Separable Decompositions of Bipartite Mixed States

We present a practical scheme for the decomposition of a bipartite mixed state into a sum of direct products of local density matrices, using the technique developed in Li and Qiao (Sci. Rep. 8: 1442, 2018). In the scheme, the correlation matrix which characterizes the bipartite entanglement is first decomposed into two matrices composed of the Bloch vectors of local states. Then we show that the symmetries of Bloch vectors are consistent with that of the correlation matrix, and the magnitudes of the local Bloch vectors are lower bounded by the correlation matrix. Concrete examples for the separable decompositions of bipartite mixed states are presented for illustration.

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arXiv2018

State-independent Uncertainty Relations and Entanglement Detection

The uncertainty relation is one of the key ingredients of quantum theory. Despite the great efforts devoted to this subject, most of the variance-based uncertainty relations are state-dependent and suffering from the triviality problem of zero lower bounds. Here we develop a method to get uncertainty relations with state-independent lower bounds. The method works by exploring the eigenvalues of a Hermitian matrix composed by Bloch vectors of incompatible observables and is applicable for both pure and mixed states and for arbitrary number of N- dimensional observables. The uncertainty relation for incompatible observables can be explained by geometric relations related to the parallel postulate and the inequalities in Horn's conjecture on Hermitian matrix sum. Practical entanglement criteria are also presented based on the derived uncertainty relations.

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arXiv2018

A Necessary and Sufficient Criterion for the Separability of Quantum State

Quantum entanglement has been regarded as one of the key physical resources in quantum information sciences. However, the determination of whether a mixed state is entangled or not is generally a hard issue, even for the bipartite system. In this work we propose an operational necessary and sufficient criterion for the separability of an arbitrary bipartite mixed state, by virtue of the multiplicative Horn's problem. The work follows the work initiated by Horodecki {\it et. al.} and uses the Bloch vector representation introduced to the separability problem by J. De Vicente. In our criterion, a complete and finite set of inequalities to determine the separability of compound system is obtained, which may be viewed as trade-off relations between the quantumness of subsystems. We apply the obtained result to explicit examples, e.g. the separable decomposition of arbitrary dimension Werner state and isotropic state.

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arXiv2018

The Diminished Quantum Uncertainty in Multipartite Entanglement

The uncertainty principle and entanglement are two fundamental, but yet not well understood, features of quantum theory. The uncertainty relation reflects the capability limit in acquiring the knowledge of different physical properties of a particle simultaneously, while on the other side, the quantum entanglement renders the entangled quanta lose their independence, including measurements imposed on them. By virtue of the majorization, here we establish a general correlation relation for quantum uncertainty and multipartite entanglement. Within this scheme, the optimization problems for entropy and majorization uncertainty relation are solved. We obtain a diminished uncertainty relation in the presence of multipartite entanglement, where the lower bound is connected with the entanglement class. This result is inspiring, reveals the intrinsic quantitative connection between uncertainty relation and entanglement, and may have a deep impact on quantum measurement in application.

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arXiv2018

Classification of the Entangled States $2 \times M \times N$

We extend the matrix decomposition method(MDM) in classifying the $2\times N\times N$ truly entangled states to $2\times M\times N$ system under the condition of stochastic local operations and classical communication. It is found that the MDM is quite practical and convenient in operation for the asymmetrical tripartite states, and an explicit example of the classification of $2\times 6\times 7$ quantum system is presented.

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arXiv2018

Classification of the Entangled States of $2 \times L \times M \times N$

We present a practical entanglement classification scheme for pure state in form of $2\times L\times M\times N$ under the stochastic local operation and classical communication (SLOCC), where every inequivalent class of the entangled quantum states may be sorted out according to its standard form and the corresponding transformation matrix. This provides a practical method for determining the interconverting matrix between two SLOCC equivalent entangled states, and classification examples for some $2\times 4\times M\times N$ systems are also presented.

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arXiv2018

Quantum State Concentration and Classification of Multipartite Entanglement

Entanglement is a unique nature of quantum theory and has tremendous potential for application. Nevertheless, the complexity of quantum entanglement grows exponentially with an increase in the number of entangled particles. Here we introduce a quantum state concentration scheme which decomposes the multipartite entangled state into a set of bipartite and tripartite entangled states. It is shown that the complexity of the entanglement induced by the large number of particles is transformed into the high dimensions of bipartite and tripartite entangled states for pure quantum systems. The results not only simplify the tedious work of verifying the (in)equivalence of multipartite entangled states, but also are instructive to the quantum many-body problem involving multipartite entanglement.

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arXiv2017

Experimental investigation of multi-observable uncertainty relations

The uncertainty relation is a distinguishing feature of quantum theory, characterizing the incompatibility of noncommuting observables in the preparation of quantum states. Recently, many uncertainty relations were proposed with improved lower bounds and were deemed capable of incorporating multiple observables. Here we report an experimental verification of seven uncertainty relations of this type with single-photon measurements. The results, while confirming these uncertainty relations, show as well the relative stringency of various uncertainty lower bounds.

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