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We present an infinite family of protocols to distill magic states for $T$-gates that has a low space overhead and uses an asymptotic number of input magic states to achieve a given target error that is conjectured to be optimal. The space…
Two parts of an entangled quantum state can have a correlation in their joint behavior under measurements that is unexplainable by shared classical information. Such correlations are called non-local and have proven to be an interesting…
We analyze the distinguishability norm on the states of a multi-partite system, defined by local measurements. Concretely, we show that the norm associated to a tensor product of sufficiently symmetric measurements is essentially equivalent…
This is a note from a series of lectures at Encuentro Colombiano de Computacion Cuantica, Universidad de los Andes, Bogota, Colombia, 2015. The purpose is to introduce additive quantum error correcting codes, with emphasis on the use of…
In this paper, we develop a novel local graph pooling method, namely the Separated Subgraph-based Hierarchical Pooling (SSHPool), for graph classification. We commence by assigning the nodes of a sample graph into different clusters,…
It is known that every (single-qudit) Clifford operator maps the full set of generalized Pauli matrices (GPMs) to itself under unitary conjugation, which is an important quantum operation and plays a crucial role in quantum computation and…
Quantum secret sharing (QSS) is a typical multipartite cryptographic primitive, which is an important part of quantum communication network. Existing QSS protocols generally require basis selection and matching, which would increase the…
Hashing methods have been widely used for efficient similarity retrieval on large scale image database. Traditional hashing methods learn hash functions to generate binary codes from hand-crafted features, which achieve limited accuracy…
We propose a protocol for local implementation of two consecutive nonlocal operations by three parters. It consumes one shared GHZ state in this protocol. We also demonstrate that these resources are sufficient and necessary to locally…
We can only perform a finite rounds of measurements in protocols with local operations and classical communication (LOCC). In this paper, we propose a set of product states, which require infinite rounds of measurements in order to…
Methods for distilling maximally entangled tripartite (GHZ) states from arbitrary entangled tripartite pure states are described. These techniques work for virtually any input state. Each technique has two stages which we call primary and…
The partition function is an essential quantity in statistical mechanics, and its accurate computation is a key component of any statistical analysis of quantum system and phenomenon. However, for interacting many-body quantum systems, its…
Recently, a protocol for quantum state discrimination (QSD) in a multi-party scenario has been introduced [Phys. Rev. Lett. 111, 100501 (2013)]. In this protocol, Alice generates a quantum system in one of two pre-defined non-orthogonal…
We propose a novel protocol for computing a circuit which implements the multi-party private set intersection functionality (PSI). Circuit-based approach has advantages over using custom protocols to achieve this task, since many…
This paper introduces a novel abstraction for programming quantum operations, specifically projective Cliffords, as functions over the qudit Pauli group. Generalizing the idea behind Pauli tableaux, we introduce a type system and lambda…
We describe stabilizer states and Clifford group operations using linear operations and quadratic forms over binary vector spaces. We show how the n-qubit Clifford group is isomorphic to a group with an operation that is defined in terms of…
We present a general technique for hiding a classical bit in multipartite quantum states. The hidden bit, encoded in the choice of one of two possible density operators, cannot be recovered by local operations and classical communication…
Verification of quantum computations is crucial as experiments advance toward fault-tolerant quantum computing. Yet, no efficient protocol exists for certifying states generated in the Magic-State Injection model -- the foundation of…
We introduce an error resilient distributed computing method based on an extension of the channel polarization phenomenon to distributed algorithms. The method leverages an algorithmic split operation that transforms two identical compute…
Channel state information (CSI) reporting is important for multiple-input multiple-output (MIMO) transmitters to achieve high capacity and energy efficiency in frequency division duplex (FDD) mode. CSI reporting for massive MIMO systems…