Debbie Leung

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Patrick Hayden,1, 2, ∗ Debbie Leung,1, 2, † Peter W. Shor,3, ‡ and Andreas Winter4, 2, § Institute for Quantum Information, Caltech 107–81, Pasadena, CA 91125, USA Mathematical Sciences Research Institute, 1000 Centennial Drive, Berkeley, CA 94720, USA AT & T Labs Research, Florham Park, NJ 07922, USA Department of Computer Science, University of Bristol,(More)
Quantum information theory is concerned with identifying how quantum mechanical resources (such as entangled quantum states) can be utilized for a number of information processing tasks, including data storage, computation, communication, and cryptography. Efficient quantum algorithms and protocols have been developed for performing some tasks (e.g.,(More)
We describe a method for nonobliviously communicating a 2l-qubit quantum state by physically transmitting l+o(l) qubits, and by consuming l ebits of entanglement plus some shared random bits. In the nonoblivious scenario, the sender has a classical description of the state to be communicated. Our method can be used to communicate states that are pure or(More)
We show that any number of parties can coherently exchange any one pure quantum state for another, without communication, given prior shared entanglement. Two applications of this fact to the study of multi-prover quantum interactive proof systems are given. First, we prove that there exists a one-round two-prover quantum interactive proof system for which(More)
Toby Cubitt,1 Aram W. Harrow,2 Debbie Leung,3 Ashley Montanaro,2 and Andreas Winter1, 4 Department of Mathematics, University of Bristol, Bristol BS8 1TW, U.K. Department of Computer Science, University of Bristol, Bristol BS8 1UB, U.K. Insitute for Quantum Computing, University of Waterloo, Waterloo N2L 3G1, Ontario, Canada Centre for Quantum Technologies,(More)
We study the power of closed timelike curves (CTCs) and other nonlinear extensions of quantum mechanics for distinguishing nonorthogonal states and speeding up hard computations. If a CTC-assisted computer is presented with a labeled mixture of states to be distinguished--the most natural formulation--we show that the CTC is of no use. The apparent(More)
This thesis develops restrictions governing how a quantum system, jointly held by two parties, can be altered by the local actions of those parties, under assumptions about how they may communicate. These restrictions are expressed as constraints involving the eigenvalues of the density matrix of one of the parties. The thesis is divided into two parts.(More)
We study two basic graph parameters, the chromatic number and the orthogonal rank, in the context of classical and quantum exact communication complexity. In particular, we consider two types of communication problems that we call promise equality and list problems. For both of these, it was already known that the one-round classical and one-round quantum(More)
A unitary 2-design can be viewed as a quantum analogue of a 2-universal hash function: it is indistinguishable from a truly random unitary by any procedure that queries it twice. We show that exact unitary 2-designs on n qubits can be implemented by quantum circuits consisting of Õ(n) elementary gates in logarithmic depth. This is essentially a quadratic(More)
How entangled is a randomly chosen bipartite stabilizer state? We show that if the number of qubits each party holds is large, the state will be close to maximally entangled with probability exponentially close to 1. We provide a similar tight characterization of the entanglement present in the maximally mixed state of a randomly chosen stabilizer code.(More)