Any 2⊗n2\otimes n subspace is locally distinguishable

A subspace of a multipartite Hilbert space is called \textit{locally indistinguishable} if any orthogonal basis of this subspace cannot be perfectly distinguished by local operations and classical communication. Previously it was shown that any $m\otimes n$ bipartite system such that $m>2$ and $n>2$ has a locally indistinguishable subspace. However, it has been an open problem since 2005 whether there is a locally indistinguishable bipartite subspace with a qubit subsystem. We settle this problem by showing that any $2\otimes n$ bipartite subspace is locally distinguishable in the sense it contains a basis perfectly distinguishable by LOCC. As an interesting application, we show that any quantum channel with two Kraus operations has optimal environment-assisted classical capacity.Comment: 3 pages (Revtex 4).Comments are welcome

Optimal Simulation of a Perfect Entangler

A $2\otimes 2$ unitary operation is called a perfect entangler if it can generate a maximally entangled state from some unentangled input. We study the following question: How many runs of a given two-qubit entangling unitary operation is required to simulate some perfect entangler with one-qubit unitary operations as free resources? We completely solve this problem by presenting an analytical formula for the optimal number of runs of the entangling operation. Our result reveals an entanglement strength of two-qubit unitary operations.Comment: 4 pages, Comments are welcomed;v2 : more discussions with previous related works, main results unchanged, submitted to PR

Distinguishability of quantum states by positive operator-valued measures with positive partial transpose

We study the distinguishability of bipartite quantum states by positive operator-valued measures with positive partial transpose (PPT POVMs). The contributions of this paper include: 1) we give a negative answer to an open problem of showing a limitation of a previous known method for detecting nondistinguishability; 2) we show that a maximally entangled state and its orthogonal complement, no matter how many copies are supplied, cannot be distinguished by the PPT POVMs, even unambiguously. This result is much stronger than the previous known ones; and 3) we study the entanglement cost of distinguishing quantum states. It is proved that √2/3|00〉 + √1/3|11〉 is sufficient and necessary for distinguishing three Bell states by the PPT POVMs. An upper bound of entanglement cost of distinguishing a d ⊗ d pure state and its orthogonal complement is obtained for separable operations. Based on this bound, we are able to construct two orthogonal quantum states, which cannot be distinguished unambiguously by separable POVMs, but finite copies would make them perfectly distinguishable by local operations and classical communication. We further observe that a two-qubit maximally entangled state is always enough for distinguishing a d ⊗ d pure state and its orthogonal complement by the PPT POVMs, no matter the value of d. In sharp contrast, an entangled state with Schmidt number at least d is always needed for distinguishing such two states by separable POVMs. As an application, we show that the entanglement cost of distinguishing a d ⊗ d maximally entangled state and its orthogonal complement must be a maximally entangled state for d = 2, which implies that teleportation is optimal, and in general, it could be chosen as O{script} (log d/d). © 1963-2012 IEEE

Five two-qubit gates are necessary for implementing the Toffoli gate

In this Rapid Communication, we consider the open problem of the minimum cost of two-qubit gates for simulating the Toffoli gate and show that five two-qubit gates are necessary. Before our work, it was known that five two-qubit gates are sufficient to

Four Locally Indistinguishable Ququad-Ququad Orthogonal Maximally Entangled States

We explicitly exhibit a set of four ququad-ququad orthogonal maximally entangled states that cannot be perfectly distinguished by means of local operations and classical communication. Before our work, it was unknown whether there is a set of $d$ locally indistinguishable $d\otimes d$ orthogonal maximally entangled states for some positive integer $d$. We further show that a $2\otimes 2$ maximally entangled state can be used to locally distinguish this set of states without being consumed, thus demonstrate a novel phenomenon of "Entanglement Discrimination Catalysis". Based on this set of states, we construct a new set $\mathrm{K}$ consisting of four locally indistinguishable states such that $\mathrm{K}^{\otimes m}$ (with $4^m$ members) is locally distinguishable for some $m$ greater than one. As an immediate application, we construct a noisy quantum channel with one sender and two receivers whose local zero-error classical capacity can achieve the full dimension of the input space but only with a multi-shot protocol.Comment: 6 pages. Comments are welcom

MHLAT: Multi-hop Label-wise Attention Model for Automatic ICD Coding

International Classification of Diseases (ICD) coding is the task of assigning ICD diagnosis codes to clinical notes. This can be challenging given the large quantity of labels (nearly 9,000) and lengthy texts (up to 8,000 tokens). However, unlike the single-pass reading process in previous works, humans tend to read the text and label definitions again to get more confident answers. Moreover, although pretrained language models have been used to address these problems, they suffer from huge memory usage. To address the above problems, we propose a simple but effective model called the Multi-Hop Label-wise ATtention (MHLAT), in which multi-hop label-wise attention is deployed to get more precise and informative representations. Extensive experiments on three benchmark MIMIC datasets indicate that our method achieves significantly better or competitive performance on all seven metrics, with much fewer parameters to optimize.Comment: 5 pages, 1 figure, accepted in ICASSP 202

Existence of Universal Entangler

A gate is called entangler if it transforms some (pure) product states to entangled states. A universal entangler is a gate which transforms all product states to entangled states. In practice, a universal entangler is a very powerful device for generating entanglements, and thus provides important physical resources for accomplishing many tasks in quantum computing and quantum information. This Letter demonstrates that a universal entangler always exists except for a degenerated case. Nevertheless, the problem how to find a universal entangler remains open.Comment: 4 page