Reformulating the Quantum Uncertainty Relation

Uncertainty principle is one of the cornerstones of quantum theory. In the literature, there are two types of uncertainty relations, the operator form concerning the variances of physical observables and the entropy form related to entropic quantities. Both these forms are inequalities involving pairwise observables, and are found to be nontrivial to incorporate multiple observables. In this work we introduce a new form of uncertainty relation which may give out complete trade-off relations for variances of observables in pure and mixed quantum systems. Unlike the prevailing uncertainty relations, which are either quantum state dependent or not directly measurable, our bounds for variances of observables are quantum state independent and immune from the "triviality" problem of having zero expectation values. Furthermore, the new uncertainty relation may provide a geometric explanation for the reason why there are limitations on the simultaneous determination of different observables in $N$-dimensional Hilbert space.Comment: 15 pages, 2 figures; published in Scientific Report

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.Comment: 33 pages; published in Scientific Report

Equivalence theorem of uncertainty relations

We present an equivalence theorem to unify the two classes of uncertainty relations, i.e., the variance-based ones and the entropic forms, which shows that the entropy of an operator in a quantum system can be built from the variances of a set of commutative operators. That means an uncertainty relation in the language of entropy may be mapped onto a variance-based one, and vice versa. Employing the equivalence theorem, alternative formulations of entropic uncertainty relations stronger than existing ones in the literature are obtained for qubit system, and variance based uncertainty relations for spin systems are reached from the corresponding entropic uncertainty relations.Comment: 18 pages, 1 figure; published in J. Phys. A: Math. Theo

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.Comment: 22 pages; published in Quantum Inf. Proces

Generation of Einstein-Podolsky-Rosen State via Earth's Gravitational Field

Although various physical systems have been explored to produce entangled states involving electromagnetic, strong, and weak interactions, the gravity has not yet been touched in practical entanglement generation. Here, we propose an experimentally feasible scheme for generating spin entangled neutron pairs via the Earth's gravitational field, whose productivity can be one pair in every few seconds with the current technology. The scheme is realized by passing two neutrons through a specific rectangular cavity, where the gravity adjusts the neutrons into entangled state. This provides a simple and practical way for the implementation of the test of quantum nonlocality and statistics in gravitational field.Comment: 12 pages, 9 figure

Quantum Entanglement of Neutrino Pairs

It is practically shown that a pair of neutrinos from tau decay can form a flavor entangled state. With this kind of state we show that the locality constrains imposed by Bell inequality are violated by the quantum mechanics, and an experimental test of this effect is feasible within the earth's length scale. Theoretically, the quantum entanglement of neutrino pairs can be employed to the use of long distance cryptography distribution in a protocol similar to the BB84.Comment: 7 pages, 5 eps figures; This paper has been withdrawn by the author due to the efficiency of detection

The Feasibility of Testing LHVTs in Charm Factory

It is commonly believed that the LHVTs can be tested through measuring the Bell's inequalities. This scheme, for the massive particle system, was originally set up for the entangled K^0\bar{K^0} pair system from the \phi factory. In this Letter we show that the J/\Psi -> K^0\bar{K^0} process is even more realistic for this goal. We analyze the unique properties of J/\Psi in the detection of basic quantum effects, and find that it is possible to use J/\Psi decay as a test of LHVTs in the future \tau-Charm factory. Our analyses and conclusions are generally also true for other heavy Onium decays.Comment: 8 pages in LaTex, 3 eps form figures. To appear in PR

Connection between Measurement Disturbance Relation and Multipartite Quantum Correlation

It is found that the measurement disturbance relation (MDR) determines the strength of quantum correlation and hence is one of the essential facets of the nature of quantum nonlocality. In reverse, the exact form of MDR may be ascertained through measuring the correlation function. To this aim, an optical experimental scheme is proposed. Moreover, by virtue of the correlation function, we find that the quantum entanglement, the quantum non-locality, and the uncertainty principle can be explicitly correlated.Comment: 27 pages, 7 figures; published in Phys. Rev.

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.Comment: 15 pages, no figure

Ascertaining the Uncertainty Relations via Quantum Correlations

We propose a new scheme to express the uncertainty principle in form of inequality of the bipartite correlation functions for a given multipartite state, which provides an experimentally feasible and model-independent way to verify various uncertainty and measurement disturbance relations. By virtue of this scheme the implementation of experimental measurement on the measurement disturbance relation to a variety of physical systems becomes practical. The inequality in turn also imposes a constraint on the strength of correlation, i.e. it determines the maximum value of the correlation function for two-body system and a monogamy relation of the bipartite correlation functions for multipartite system.Comment: 18 pages, 2 figures; published in J. Phys. A: Math. Theo