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Dong Yang

Publications and source records attributed to Dong Yang.

At least 217 records · Page 12Linked to original sources
arXiv2014

Strong converse for the classical capacity of entanglement-breaking and Hadamard channels via a sandwiched Renyi relative entropy

A strong converse theorem for the classical capacity of a quantum channel states that the probability of correctly decoding a classical message converges exponentially fast to zero in the limit of many channel uses if the rate of communication exceeds the classical capacity of the channel. Along with a corresponding achievability statement for rates below the capacity, such a strong converse theorem enhances our understanding of the capacity as a very sharp dividing line between achievable and unachievable rates of communication. Here, we show that such a strong converse theorem holds for the classical capacity of all entanglement-breaking channels and all Hadamard channels (the complementary channels of the former). These results follow by bounding the success probability in terms of a "sandwiched" Renyi relative entropy, by showing that this quantity is subadditive for all entanglement-breaking and Hadamard channels, and by relating this quantity to the Holevo capacity. Prior results regarding strong converse theorems for particular covariant channels emerge as a special case of our results.

quant-ph↗
arXiv2014

Collaborative Discriminant Locality Preserving Projections With its Application to Face Recognition

We present a novel Discriminant Locality Preserving Projections (DLPP) algorithm named Collaborative Discriminant Locality Preserving Projection (CDLPP). In our algorithm, the discriminating power of DLPP are further exploited from two aspects. On the one hand, the global optimum of class scattering is guaranteed via using the between-class scatter matrix to replace the original denominator of DLPP. On the other hand, motivated by collaborative representation, an $L_2$-norm constraint is imposed to the projections to discover the collaborations of dimensions in the sample space. We apply our algorithm to face recognition. Three popular face databases, namely AR, ORL and LFW-A, are employed for evaluating the performance of CDLPP. Extensive experimental results demonstrate that CDLPP significantly improves the discriminating power of DLPP and outperforms the state-of-the-arts.

cs.CV↗
arXiv2014

Homotopy categories, Leavitt path algebras and Gorenstein projective modules

For a finite quiver without sources or sinks, we prove that the homotopy category of acyclic complexes of injective modules over the corresponding finite dimensional algebra with radical square zero is triangle equivalent to the derived category of the Leavitt path algebra viewed as a differential graded algebra with trivial differential, which is further triangle equivalent to the stable category of Gorenstein projective modules over the trivial extension algebra of a von Neumann regular algebra by an invertible bimodule. A related, but different, result for the homotopy category of acyclic complexes of projective modules is given. Restricting these equivalences to compact objects, we obtain various descriptions of the singularity category of a finite dimensional algebra with radical square zero, which contain previous results.

math.RT↗
arXiv2013

Glueing silting objects

Recent results by Keller and Nicol{á}s and by Koenig and Yang have shown bijective correspondences between suitable classes of t-structures and co-t-structures with certain objects of the derived category: silting objects. On the other hand, the techniques of glueing (co-)t-structures along a recollement play an important role in the understanding of derived module categories. Using the above correspondence with silting objects we present explicit constructions of glueing of silting objects, and, furthermore, we answer the question of when is the glued silting tilting.

math.RT↗
arXiv2013

Silting objects, simple-minded collections, $t$-structures and co-$t$-structures for finite-dimensional algebras

Bijective correspondences are established between (1) silting objects, (2) simple-minded collections, (3) bounded $t$-structures with length heart and (4) bounded co-$t$-structures. These correspondences are shown to commute with mutations. The results are valid for finite-dimensional algebras. A concrete example is given to illustrate how these correspondences help to compute the space of Bridgeland's stability conditions.

math.RT↗
arXiv2013

Entangled inputs cannot make imperfect quantum channels perfect

Entangled inputs can enhance the capacity of quantum channels, this being one of the consequences of the celebrated result showing the non-additivity of several quantities relevant for quantum information science. In this work, we answer the converse question (whether entangled inputs can ever render noisy quantum channels have maximum capacity) to the negative: No sophisticated entangled input of any quantum channel can ever enhance the capacity to the maximum possible value; a result that holds true for all channels both for the classical as well as the quantum capacity. This result can hence be seen as a bound as to how "non-additive quantum information can be". As a main result, we find first practical and remarkably simple computable single-shot bounds to capacities, related to entanglement measures. As examples, we discuss the qubit amplitude damping and identify the first meaningful bound for its classical capacity.

quant-ph↗
arXiv2011

Sparseness of t-structures and negative Calabi-Yau dimension in triangulated categories generated by a spherical object

Let k be an algebraically closed field and let T be the k-linear algebraic triangulated category generated by a w-spherical object for an integer w. For certain values of w this category is classical. For instance, if w = 0 then it is the compact derived category of the dual numbers over k. As main results of the paper we show that for w \leq 0, the category T has no non-trivial t-structures, but does have one family of non-trivial co-t-structures, whereas for w \geq 1 the opposite statement holds. Moreover, without any claim to originality, we observe that for w \leq -1, the category T is a candidate to have negative Calabi-Yau dimension since Σ^w is the unique power of the suspension functor which is a Serre functor.

math.RT↗
arXiv2011

Endomorphism algebras of maximal rigid objects in cluster tubes

Given a maximal rigid object $T$ of the cluster tube, we determine the objects finitely presented by $T$. We then use the method of Keller and Reiten to show that the endomorphism algebra of $T$ is Gorenstein and of finite representation type, as first shown by Vatne. This algebra turns out to be the Jacobian algebra of a certain quiver with potential, when the characteristic of the base field is not 3. We study how this quiver with potential changes when $T$ is mutated. We also provide a derived equivalence classification for the endomorphism algebras of maximal rigid objects.

math.RT↗
arXiv2011

Blocks of group algebras are derived simple

A derived version of Maschke's theorem for finite groups is proved: the derived categories, bounded or unbounded, of all blocks of the group algebra of a finite group are simple, in the sense that they admit no nontrivial recollements. This result is independent of the characteristic of the base field.

math.RT↗
arXiv2011

The Ringel--Hall Lie algebra of a spherical object

For an integer $w$, let $\cs_w$ be the algebraic triangulated category generated by a $w$-spherical object. We determine the Picard group of $\cs_w$ and show that each orbit category of $\cs_w$ is triangulated and is triangle equivalent to a certain orbit category of the bounded derived category of a standard tube. When $n=2$, the orbit category $\cs_w/Σ^2$ is 2-periodic triangulated, and we characterize the associated Ringel--Hall Lie algebra in the sense of Peng and Xiao.

math.RT↗
arXiv2010

On tilting complexes providing derived equivalences that send simple-minded objects to simple objects

Given a set of 'simple-minded' objects in a derived category, Rickard constructed a complex, which over a symmetric algebra provides a derived equivalence sending the 'simple-minded' objects to simple ones. We characterise in terms of t-structures, when this complex is a tilting complex, show that there is an associated natural $t$-structure and we provide an alternative construction of this complex in terms of A-infinity-structures. Our approach is similar to that of Keller--Nicolás.

math.RT↗
arXiv2010

Recollements from generalized tilting

Let $\ca$ be a small dg category over a field $k$ and let $\cu$ be a small full subcategory of the derived category $\cd\ca$ which generate all free dg $\ca$-modules. Let $(\cb,X)$ be a standard lift of $\cu$. We show that there is a recollement such that its middle term is $\cd\cb$, its right term is $\cd\ca$, and the three functors on its right side are constructed from $X$. This applies to the pair $(A,T)$, where $A$ is a $k$-algebra and $T$ is a good $n$-tilting module, and we obtain a result of Bazzoni--Mantese--Tonolo. This also applies to the pair $(\ca,\cu)$, where $\ca$ is an augmented dg category and $\cu$ is the category of `simple' modules, e.g. $\ca$ is a finite-dimensional algebra or the Kontsevich--Soibelman $A_\infty$-category associated to a quiver with potential.

math.CT↗
arXiv2009

Entanglement combing

We show that all multi-partite pure states can, under local operations, be transformed into bi-partite pairwise entangled states in a "lossless fashion": An arbitrary distinguished party will keep pairwise entanglement with all other parties after the asymptotic protocol - decorrelating all other parties from each other - in a way that the degree of entanglement of this party with respect to the rest will remain entirely unchanged. The set of possible entanglement distributions of bi-partite pairs is also classified. Finally, we point out several applications of this protocol as a useful primitive in quantum information theory.

quant-ph↗
arXiv2009

Derived equivalences from mutations of quivers with potential

We show that Derksen-Weyman-Zelevinsky's mutations of quivers with potential yield equivalences of suitable 3-Calabi-Yau triangulated categories. Our approach is related to that of Iyama-Reiten and Koszul dual to that of Kontsevich-Soibelman. It improves on previous work by Vitoria. In the appendix, the first-named author studies pseudo-compact derived categories of certain pseudo-compact dg algebras.

math.RT↗
arXiv2009

Squashed entanglement for multipartite states and entanglement measures based on the mixed convex roof

New measures of multipartite entanglement are constructed based on two definitions of multipartite information and different methods of optimizing over extensions of the states. One is a generalization of the squashed entanglement where one takes the mutual information of parties conditioned on the state's extension and takes the infimum over such extensions. Additivity of the multipartite squashed entanglement is proved for both versions of the multipartite information which turn out to be related. The second one is based on taking classical extensions. This scheme is generalized, which enables to construct measures of entanglement based on the {\it mixed convex roof} of a quantity, which in contrast to the standard convex roof method involves optimization over all decompositions of a density matrix rather than just the decompositions into pure states. As one of the possible applications of these results we prove that any multipartite monotone is an upper bound on the amount of multipartite distillable key. The findings are finally related to analogous results in classical key agreement.

quant-ph↗
arXiv2008

An additive and operational entanglement measure: conditional entanglement of mutual information

Based on the monogamy of entanglement, we develop the technique of quantum conditioning to build an {\it additive} entanglement measure: the conditional entanglement of mutual information. Its {\it operational} meaning is elaborated to be the minimal net "flow of qubits" in the process of partial state merging. The result and conclusion can also be generalized to multipartite entanglement cases.

quant-ph↗
arXiv2007

Multipartite quantum correlation and entanglement in four-qubit pure states

Based on the quantitative complementarity relations, we analyze thoroughly the properties of multipartite quantum correlations and entanglement in four-qubit pure states. We find that, unlike the three-qubit case, the single residual correlation, the genuine three- and four-qubit correlations are not suited to quantify entanglement. More interestingly, from our qualitative and numerical analysis, it is conjectured that the sum of all the residual correlations may constitute a good measure for the total multipartite entanglement in the system.

quant-ph↗