arXiv subjects
Publications and source records attributed to Naihuan Jing.
In this paper, vertex representations of the 2-toroidal Lie superalgebras of type $D(m, n)$ are constructed using both bosonic fields and vertex operators based on their loop algebraic presentation.
The exact solutions of the super quantum discord are derived for general two qubit X states in terms of a one-variable function. Several exact solutions of the super quantum discord are given for the general X-state over nontrivial regions of a seven dimensional manifold. It is shown that the super quantum discord of the X state may increase or decreases under the phase damping channel.
The uncertainty principle restricts potential information one gains about physical properties of the measured particle. However, if the particle is prepared in entanglement with a quantum memory, the corresponding entropic uncertainty relation will vary. Based on the knowledge of correlations between the measured particle and quantum memory, we have investigated the entropic uncertainty relations for two and multiple measurements, and generalized the lower bounds on the sum of Shannon entropies without quantum side information to those that allow quantum memory. In particular, we have obtained generalization of Kaniewski-Tomamichel-Wehner's bound for effective measures and majorization bounds for noneffective measures to allow quantum side information. Furthermore, we have derived several strong bounds for the entropic uncertainty relations in the presence of quantum memory for two and multiple measurements. Finally, potential applications of our results to entanglement witnesses are discussed via the entropic uncertainty relation in the absence of quantum memory.
The multiparameter quantum Pfaffian of the $(p, λ)$-quantum group is introduced and studied together with the quantum determinant, and an identity relating the two invariants is given. Generalization to the multiparameter hyper-Pfaffian and relationship with the quantum minors are also considered.
The notion of generalized quantum monoids is introduced. It is proved that the quantum coordinate ring of the monoid can be lifted to a quantum hyper-algebra, in which the quantum determinant and quantum Pfaffian are sent to the quantum hyperdeterminant and quantum hyper-Pfaffian respectively. The quantum hyperdeterminant in even dimension is shown to be a $q$-analog of Cayley's first hyperdeterminant.
In Coles-Piani's recent remarkable version of the entropic uncertainty principle, the entropic sum is controlled by the first and second maximum overlaps between the two projective measurements. We generalize the entropic uncertainty relation in the presence of quantum memory and find the exact dependence on all $d$ largest overlaps between two measurements on any $d$-dimensional Hilbert space. The corresponding entropic uncertainty principle in the absence of quantum memory is also derived. Our bounds are strictly tighter than previous entropic bounds in the presence of quantum memory, which have potential applications to quantum cryptography with entanglement witnesses and quantum key distributions.
We study universal uncertainty relations and present a method called joint probability distribution diagram to improve the majorization bounds constructed independently in [Phys. Rev. Lett. 111, 230401 (2013)] and [J. Phys. A. 46, 272002 (2013)]. The results give rise to state independent uncertainty relations satisfied by any nonnegative Schur-concave functions. On the other hand, a remarkable recent result of entropic uncertainty relation is the direct-sum majorization relation. In this paper, we illustrate our bounds by showing how they provide a complement to that in [Phys. Rev. A. 89, 052115 (2014)].
The uncertainty principle is one of the characteristic properties of quantum theory based on incompatibility. Apart from the incompatible relation of quantum states, mutually exclusiveness is another remarkable phenomenon in the information-theoretic foundation of quantum theory. We investigate the role of mutual exclusive physical states in the recent work of stronger uncertainty relations for all incompatible observables by Mccone and Pati and generalize the weighted uncertainty relation to the product form as well as their multi-observable analogues. The new bounds capture both incompatibility and mutually exclusiveness, and are tighter compared with the existing bounds.
We describe generating functions for several important families of classical symmetric functions and shifted Schur functions. The approach is originated from vertex operator realization of symmetric functions and offers a unified method to treat various families of symmetric functions and their shifted analogues.
We establish Drinfeld realization for the two-parameter twisted quantum affine algebras using a new method. The Hopf algebra structure for Drinfeld generators is given for both untwisted and twisted two-parameter quantum affine algebras, which include the quantum affine algebras as special cases.
Quantum determinants and Pfaffians or permanents and Hafnians are introduced on the two parameter quantum general linear group. Fundamental identities among quantum Pf, Hf, and det are proved in the general setting. We show that there are two special quantum algebras among the quantum groups, where the quantum Pfaffians have integral Laurent polynomials as coefficients. As a consequence, the quantum Hafnian is computed by a closely related quantum permanent and identical to the quantum Pfaffian on this special quantum algebra.
We solve the quantum discord completely as an optimization of certain one variable function for arbitrary two qubit X state. Exact solutions of the quantum discord are obtained for several nontrivial regions of the five parametric space for the quantum state. Exceptional solutions are determined via an iterative algorithm.
In Hall's reformulation of the uncertainty principle, the entropic uncertainty relation occupies a core position and provides the first nontrivial bound for the information exclusion principle. Based upon recent developments on the uncertainty relation, we present new bounds for the information exclusion relation using majorization theory and combinatoric techniques, which reveal further characteristic properties of the overlap matrix between the measurements.
The homogeneous Rota-Baxter operators on the Witt and Virasoro algebras are classified. As applications, the induced solutions of the classical Yang-Baxter equation and the induced pre-Lie and PostLie algebra structures are obtained.
We study the fully entangled fraction of a quantum state. An upper bound is obtained for arbitrary bipartite system. This upper bound only depends on the Frobenius norm of the state.
The Drinfled realization of quantum affine algebras has been tremendously useful since its discovery. Combining techniques of Beck and Nakajima with our previous approach, we give a complete and conceptual proof of the Drinfeld realization for the twisted quantum affine algebras using Lusztig's twisted braid group action.
Toroidal Lie algebras are generalizations of affine Lie algebras. In 1990, Moody, Rao and Yokonuma gave a presentation for untwisted toroidal Lie algebras. In this paper we give a presentation for the twisted toroidal Lie algebras of type $A$ and $D$ constructed by Fu and Jiang.
The correspondence between local unitary equivalence of bipartite quantum states and simultaneous orthogonal equivalence is thoroughly investigated and strengthened. It is proved that local unitary equivalence can be studied through simultaneous similarity under projective orthogonal transformations, and four parametrization independent algorithms are proposed to judge when two density matrices on $\mathbb C^{d_1}\otimes \mathbb C^{d_2}$ are locally unitary equivalent in connection with trace identities, Weierstrass pencils, Albert determinants and Smith normal forms.