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Quantum entanglement
, 2007
"... Contents All our former experience with application of quantum theory seems to say: what is predicted by quantum formalism must occur in laboratory. But the essence of quantum formalism — entanglement, recognized by Einstein, Podolsky, Rosen and Schrödinger — waited over 70 years to enter to laborat ..."
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Cited by 88 (1 self)
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Contents All our former experience with application of quantum theory seems to say: what is predicted by quantum formalism must occur in laboratory. But the essence of quantum formalism — entanglement, recognized by Einstein, Podolsky, Rosen and Schrödinger — waited over 70 years to enter to laboratories as a new resource as real as energy.
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 68 (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
Private Quantum Channels
 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
, 2000
"... We investigate how a classical private key can be used by two players, connected by an insecure oneway quantum channel, to perform private communication of quantum information. In particular we show that in order to transmit n qubits privately, 2n bits of shared private key are necessary and sucien ..."
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Cited by 54 (0 self)
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We investigate how a classical private key can be used by two players, connected by an insecure oneway quantum channel, to perform private communication of quantum information. In particular we show that in order to transmit n qubits privately, 2n bits of shared private key are necessary and sucient. This result may be viewed as the quantum analogue of the classical onetime pad encryption scheme. 1 Introduction Secure transmission of classical information is a well studied topic. Suppose Alice wants to send an nbit message M to Bob over an insecure (i.e. spiedon) channel, in such a way that the eavesdropper Eve cannot obtain any information about M from tapping the channel. If Alice and Bob share some secret nbit key K, then here is a simple way for them to achieve their goal: Alice exclusiveors M with K and sends the result M 0 = M K over the channel, Bob then xors M 0 again with K and obtains the original message M 0 K = M . Eve may see the encoded message M 0 , ...
Quantum Communication and Complexity
 Theoretical Computer Science
, 2000
"... In the setting of communication complexity, two distributed parties want to compute a function depending on both their inputs, using as little communication as possible. The required communication can sometimes be significantly lowered if we allow the parties the use of quantum communication. We sur ..."
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Cited by 37 (15 self)
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In the setting of communication complexity, two distributed parties want to compute a function depending on both their inputs, using as little communication as possible. The required communication can sometimes be significantly lowered if we allow the parties the use of quantum communication. We survey the main results of the young area of quantum communication complexity: its relation to teleportation and dense coding, the main examples of fast quantum communication protocols, lower bounds, and some applications. 1 Introduction The area of communication complexity deals with the following type of problem. There are two separated parties, called Alice and Bob. Alice receives some input x 2 X, Bob receives some y 2 Y , and together they want to compute some function f(x; y). As the value f(x; y) will generally depend on both x and y, neither Alice nor Bob will have sufficient information to do the computation by themselves, so they will have to communicate in order to achieve their go...
Improved quantum communication complexity bounds for disjointness and equality
 In Proc. Intl. Symp. on Theoretical Aspects of Computer Science (STACS
, 2002
"... Abstract. We prove new bounds on the quantum communication complexity of the disjointness and equality problems. For the case of exact and nondeterministic protocols we show that these complexities are all equal to n+1, the previous best lower bound being n/2. We show this by improving a general bo ..."
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Cited by 30 (5 self)
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Abstract. We prove new bounds on the quantum communication complexity of the disjointness and equality problems. For the case of exact and nondeterministic protocols we show that these complexities are all equal to n+1, the previous best lower bound being n/2. We show this by improving a general bound for nondeterministic protocols of de Wolf. We also give an O ( √ n·c log ∗ n)qubit boundederror protocol for disjointness, modifying and improving the earlier O ( √ n log n) protocol of Buhrman, Cleve, and Wigderson, and prove an Ω ( √ n) lower bound for a class of protocols that includes the BCWprotocol as well as our new protocol. 1
On Quantum Coding for Ensembles of Mixed States
"... We consider the problem of optimal asymptotically faithful compression for ensembles of mixed quantum states. Although the optimal rate is unknown, we prove upper and lower bounds and describe a series of illustrative examples of compression of mixed states. We also discuss a classical analogue of ..."
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Cited by 20 (3 self)
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We consider the problem of optimal asymptotically faithful compression for ensembles of mixed quantum states. Although the optimal rate is unknown, we prove upper and lower bounds and describe a series of illustrative examples of compression of mixed states. We also discuss a classical analogue of the problem.
On the communication complexity of XOR functions
, 2010
"... An XOR function is a function of the form g(x, y) = f(x ⊕ y), for some boolean function f on n bits. We study the quantum and classical communication complexity of XOR functions. In the case of exact protocols, we completely characterise oneway communication complexity for all f. We also show that ..."
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Cited by 5 (0 self)
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An XOR function is a function of the form g(x, y) = f(x ⊕ y), for some boolean function f on n bits. We study the quantum and classical communication complexity of XOR functions. In the case of exact protocols, we completely characterise oneway communication complexity for all f. We also show that, when f is monotone, g’s quantum and classical complexities are quadratically related, and that when f is a linear threshold function, g’s quantum complexity is Θ(n). More generally, we make a structural conjecture about the Fourier spectra of boolean functions which, if true, would imply that the quantum and classical exact communication complexities of all XOR functions are asymptotically equivalent. We give two randomised classical protocols for general XOR functions which are efficient for certain functions, and a third protocol for linear threshold functions with high margin. These protocols operate in the symmetric message passing model with shared randomness. 1
Universal Compression of Ergodic Quantum Sources
, 2003
"... 1) For a real r> 0, let F(r) be the family of all stationary ergodic quantum sources with von Neumann entropy rate less than r. We prove that, for any r> 0, there exists a blind, sourceindependent block compression scheme which compresses every source from F(r) to rn qubits per input block of ..."
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Cited by 3 (0 self)
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1) For a real r> 0, let F(r) be the family of all stationary ergodic quantum sources with von Neumann entropy rate less than r. We prove that, for any r> 0, there exists a blind, sourceindependent block compression scheme which compresses every source from F(r) to rn qubits per input block of size n with arbitrary high fidelity for all large enough n. 2) We show that the stationarity and the ergodicity of a quantum source {ρm} ∞ m=1 are preserved by any tracepreserving completely positive linear map of the tensor product form E⊗m, where a copy of E acts locally on each spin lattice site. We also establish ergodicity criteria for so called classicallycorrelated quantum sources.
On Lossless quantum data compression with a classical helper
 IEEE TRANS. INF. THEORY
"... After K. Boström and T. Felbinger observed that lossless quantum data compression does not exist unless decoders know the lengths of codewords, they introduced a classical noiseless channel to inform the decoder of a quantum source about the lengths of codewords. In this paper we analyse their codes ..."
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Cited by 2 (1 self)
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After K. Boström and T. Felbinger observed that lossless quantum data compression does not exist unless decoders know the lengths of codewords, they introduced a classical noiseless channel to inform the decoder of a quantum source about the lengths of codewords. In this paper we analyse their codes and present 1) a sufficient and necessary condition for the existence of such codes for given lists of lengths of codes 2) a characterization of the optimal compression rate for their codes. However our main contribution is a more efficient way to use the classical channel. We propose a more general coding scheme. It turned out that the optimal compression can always be achieved by a code obtained by this scheme. A von Neumann entropy lower bound to rates of our codes and a necessary and sufficient condition to achieve the bound are obtained. The gap between this lower bound and the compression rates is also well analysed. For a special family of quantum sources we provide a sharper lower bound in terms of Shannon entropy. Finally we propose some problems for further research.