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Quantum information theory
, 1998
"... We survey the field of quantum information theory. In particular, we discuss the fundamentals of the field, source coding, quantum errorcorrecting codes, capacities of quantum channels, measures of entanglement, and quantum cryptography. ..."
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Cited by 99 (3 self)
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We survey the field of quantum information theory. In particular, we discuss the fundamentals of the field, source coding, quantum errorcorrecting codes, capacities of quantum channels, measures of entanglement, and quantum cryptography.
Quantum entanglement and the communication complexity of the inner product function
 IN PROCEEDINGS OF 1ST NASA QCQC CONFERENCE, VOLUME 1509 OF LECTURE NOTES IN COMPUTER SCIENCE
, 1998
"... We consider the communication complexity of the binary inner product function in a variation of the twoparty scenario where the parties have an apriori supply of particles in an entangled quantum state. We prove linear lower bounds for both exact protocols, as well as for protocols that determine ..."
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Cited by 94 (10 self)
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We consider the communication complexity of the binary inner product function in a variation of the twoparty scenario where the parties have an apriori supply of particles in an entangled quantum state. We prove linear lower bounds for both exact protocols, as well as for protocols that determine the answer with boundederror probability. Our proofs employ a novel kind of “quantum” reduction from a quantum information theory problem to the problem of computing the inner product. The communication required for the former problem can then be bounded by an application of Holevo’s theorem. We also give a specific example of a probabilistic scenario where entanglement reduces the communication complexity of the inner product function by one bit.
Exponential Separation of Quantum and Classical Communication Complexity
, 1999
"... Communication complexity has become a central complexity model. In that model, we count the amount of communication bits needed between two parties in order to solve certain computational problems. We show that for certain communication complexity problems quantum communication protocols are expo ..."
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Cited by 93 (2 self)
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Communication complexity has become a central complexity model. In that model, we count the amount of communication bits needed between two parties in order to solve certain computational problems. We show that for certain communication complexity problems quantum communication protocols are exponentially faster than classical ones. More explicitly, we give an example for a communication complexity relation (or promise problem) P such that: 1. The quantum communication complexity of P is O(log m). 2. The classical probabilistic communication complexity of P is \Omega\Gamma m 1=4 = log m). (where m is the length of the inputs). This gives an exponential gap between quantum communication complexity and classical probabilistic communication complexity. Only a quadratic gap was previously known. Our problem P is of geometrical nature, and is a finite precision variation of the following problem: Player I gets as input a unit vector x 2 R n and two orthogonal subspaces M 0 ...
A lambda calculus for quantum computation
 SIAM Journal of Computing
"... The classical lambda calculus may be regarded both as a programming language and as a formal algebraic system for reasoning about computation. It provides a computational model equivalent to the Turing machine, and continues to be of enormous benefit in the classical theory of computation. We propos ..."
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Cited by 71 (1 self)
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The classical lambda calculus may be regarded both as a programming language and as a formal algebraic system for reasoning about computation. It provides a computational model equivalent to the Turing machine, and continues to be of enormous benefit in the classical theory of computation. We propose that quantum computation, like its classical counterpart, may benefit from a version of the lambda calculus suitable for expressing and reasoning about quantum algorithms. In this paper we develop a quantum lambda calculus as an alternative model of quantum computation, which combines some of the benefits of both the quantum Turing machine and the quantum circuit models. The calculus turns out to be closely related to the linear lambda calculi used in the study of Linear Logic. We set up a computational model and an equational proof system for this calculus, and we argue that it is equivalent to the quantum Turing machine.
Experimental quantum teleportation
 Nature
, 1997
"... Quantum entanglement lies at the heart of new proposals for quantum communication and computation. Here we describe the recent experimental realization of quantum teleportation. ..."
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Cited by 69 (3 self)
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Quantum entanglement lies at the heart of new proposals for quantum communication and computation. Here we describe the recent experimental realization of quantum teleportation.
Communication complexity lower bounds by polynomials
 In Proc. of the 16th Conf. on Computational Complexity (CCC
, 2001
"... The quantum version of communication complexity allows Alice and Bob to communicate qubits and/or to make use of prior entanglement (shared EPRpairs). Some lower bound techniques are available for qubit communication [17, 11, 2], but except for the inner product function [11], no bounds are known f ..."
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Cited by 69 (13 self)
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The quantum version of communication complexity allows Alice and Bob to communicate qubits and/or to make use of prior entanglement (shared EPRpairs). Some lower bound techniques are available for qubit communication [17, 11, 2], but except for the inner product function [11], no bounds are known for the model with unlimited prior entanglement. We show that the “log rank ” lower bound extends to the strongest model (qubit communication + prior entanglement). By relating the rank of the communication matrix to properties of polynomials, we are able to derive some strong bounds for exact protocols. In particular, we prove both the “logrank conjecture ” and the polynomial equivalence of quantum and classical communication complexity for various classes of functions. We also derive some weaker bounds for boundederror protocols. 1
Unknown quantum states: the quantum de Finetti representation
 J. Math. Phys
"... We present an elementary proof of the quantum de Finetti representation theorem, a quantum analogue of de Finetti’s classical theorem on exchangeable probability assignments. This contrasts with the original proof of Hudson and Moody [Z. Wahrschein. verw. Geb. 33, 343 (1976)], which relies on advanc ..."
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Cited by 67 (9 self)
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We present an elementary proof of the quantum de Finetti representation theorem, a quantum analogue of de Finetti’s classical theorem on exchangeable probability assignments. This contrasts with the original proof of Hudson and Moody [Z. Wahrschein. verw. Geb. 33, 343 (1976)], which relies on advanced mathematics and does not share the same potential for generalization. The classical de Finetti theorem provides an operational definition of the concept of an unknown probability in Bayesian probability theory, where probabilities are taken to be degrees of belief instead of objective states of nature. The quantum de Finetti theorem, in a closely analogous fashion, deals with exchangeable densityoperator assignments and provides an operational definition of the concept of an “unknown quantum state ” in quantumstate tomography. This result is especially important for informationbased interpretations of quantum mechanics, where quantum states, like probabilities, are taken to be states of knowledge rather than states of nature. We further demonstrate that the theorem fails for real Hilbert spaces and discuss the significance of this point. I.
Improved simulation of stabilizer circuits
 Phys. Rev. Lett
"... The GottesmanKnill theorem says that a stabilizer circuit—that is, a quantum circuit consisting solely of CNOT, Hadamard, and phase gates—can be simulated efficiently on a classical computer. This paper improves that theorem in several directions. • By removing the need for Gaussian elimination, we ..."
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Cited by 65 (6 self)
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The GottesmanKnill theorem says that a stabilizer circuit—that is, a quantum circuit consisting solely of CNOT, Hadamard, and phase gates—can be simulated efficiently on a classical computer. This paper improves that theorem in several directions. • By removing the need for Gaussian elimination, we make the simulation algorithm much faster at the cost of a factor2 increase in the number of bits needed to represent a state. We have implemented the improved algorithm in a freelyavailable program called CHP (CNOTHadamardPhase), which can handle thousands of qubits easily. • We show that the problem of simulating stabilizer circuits is complete for the classical complexity class ⊕L, which means that stabilizer circuits are probably not even universal for classical computation. • We give efficient algorithms for computing the inner product between two stabilizer states, putting any nqubit stabilizer circuit into a “canonical form ” that requires at most O ( n 2 /log n) gates, and other useful tasks. • We extend our simulation algorithm to circuits acting on mixed states, circuits containing a limited number of nonstabilizer gates, and circuits acting on general tensorproduct initial states but containing only a limited number of measurements. 1
Authentication of Quantum Messages
, 2002
"... Authentication is a wellstudied area of classical cryptography: a sender A and a receiver B sharing a classical private key want to exchange a classical message with the guarantee that the message has not been modified or replaced by a dishonest party with control of the communication line. In th ..."
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Cited by 61 (10 self)
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Authentication is a wellstudied area of classical cryptography: a sender A and a receiver B sharing a classical private key want to exchange a classical message with the guarantee that the message has not been modified or replaced by a dishonest party with control of the communication line. In this paper we study the authentication of messages composed of quantum states.
Limitations of Quantum Advice and OneWay Communication
 Theory of Computing
, 2004
"... Although a quantum state requires exponentially many classical bits to describe, the laws of quantum mechanics impose severe restrictions on how that state can be accessed. This paper shows in three settings that quantum messages have only limited advantages over classical ones. ..."
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Cited by 59 (16 self)
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Although a quantum state requires exponentially many classical bits to describe, the laws of quantum mechanics impose severe restrictions on how that state can be accessed. This paper shows in three settings that quantum messages have only limited advantages over classical ones.