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469
Mixed state entanglement and quantum error correction
 Phys. Rev., A
, 1996
"... Entanglement purification protocols (EPP) and quantum errorcorrecting codes (QECC) provide two ways of protecting quantum states from interaction with the environment. In an EPP, perfectly entangled pure states are extracted, with some yield D, from a bipartite mixed state M; with a QECC, an arbitra ..."
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Cited by 156 (8 self)
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Entanglement purification protocols (EPP) and quantum errorcorrecting codes (QECC) provide two ways of protecting quantum states from interaction with the environment. In an EPP, perfectly entangled pure states are extracted, with some yield D, from a bipartite mixed state M; with a QECC, an arbitrary quantum state ξ〉 can be transmitted at some rate Q through a noisy channel χ without degradation. We prove that an EPP involving oneway classical communication and acting on mixed state ˆ M(χ) (obtained by sharing halves of EPR pairs through a channel χ) yields a QECC on χ with rate Q = D, and vice versa. We compare the amount of entanglement E(M) required to prepare a mixed state M by local actions with the amounts D1(M) and D2(M) that can be locally distilled from it by EPPs using one and twoway classical communication respectively, and give an exact expression for E(M) when M is Belldiagonal. While EPPs require classical communication, quantum channel coding does not, and we prove Q is not increased by adding oneway classical communication. However, both D and Q can be increased by adding twoway communication. We show that certain noisy quantum channels, for example a 50 % depolarizing channel, can be used for reliable transmission of quantum states if twoway communication is available, but cannot be used if only oneway communication is available. We exhibit a family of codes based on universal hashing able to achieve an asymptotic Q (or D) of 1S for simple noise models, where S is the error entropy. We also obtain a specific, simple 5bit singleerrorcorrecting quantum block code. We prove that iff a QECC results in perfect fidelity for the case of the noerror error syndrome the QECC can be recast into a form where the encoder is the matrix inverse of the decoder. 1 PACS numbers: 03.65.Bz, 42.50.Dv, 89.70.+c 1
Quantum cryptography
 Rev. Mod. Phys
, 2002
"... Quantum cryptography could well be the first application of quantum mechanics at the individual quanta level. The very fast progress in both theory and experiments over the recent years are reviewed, with emphasis on open questions and technological issues. Contents I ..."
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Cited by 93 (3 self)
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Quantum cryptography could well be the first application of quantum mechanics at the individual quanta level. The very fast progress in both theory and experiments over the recent years are reviewed, with emphasis on open questions and technological issues. Contents I
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 89 (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.
A Quantum Bit Commitment Scheme Provably Unbreakable by both Parties
, 1993
"... Assume that a party, Alice, has a bit x in mind, to which she would like to be committed toward another party, Bob. That is, Alice wishes, through a procedure commit(x), to provide Bob with a piece of evidence that she has a bit x in mind and that she cannot change it. Meanwhile, Bob should not be ..."
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Cited by 68 (12 self)
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Assume that a party, Alice, has a bit x in mind, to which she would like to be committed toward another party, Bob. That is, Alice wishes, through a procedure commit(x), to provide Bob with a piece of evidence that she has a bit x in mind and that she cannot change it. Meanwhile, Bob should not be able to tell from that evidence what x is. At a later time, Alice can reveal, through a procedure unveil(x), the value of x and prove to Bob that the piece of evidence sent earlier really corresponded to that bit. Classical bit commitment schemes (by which Alice's piece of evidence is classical information such as a bit string) cannot be secure against unlimited computing power and none have been proven secure against algorithmic sophistication. Previous quantum bit commitment schemes (by which Alice's piece of evidence is quantum information such as a stream of polarized photons) were known to be invulnerable to unlimited computing power and algorithmic sophistication, but not to arbitrary...
Resilient quantum computation
 Science
, 1998
"... This article is a short introduction to and review of the clusterstate model of quantum computation, in which coherent quantum information processing is accomplished via a sequence of singlequbit measurements applied to a fixed quantum state known as a cluster state. We also discuss a few novel pr ..."
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Cited by 64 (3 self)
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This article is a short introduction to and review of the clusterstate model of quantum computation, in which coherent quantum information processing is accomplished via a sequence of singlequbit measurements applied to a fixed quantum state known as a cluster state. We also discuss a few novel properties of the model, including a proof that the cluster state cannot occur as the exact ground state of any naturally occurring physical system, and a proof that measurements on any quantum state which is linearly prepared in one dimension can be efficiently simulated on a classical computer, and thus are not candidates for use as a substrate for quantum computation. Key words: quantum computation, cluster states, oneway quantum computer 1.
Quantum mechanics as quantum information (and only a little more), Quantum Theory: Reconsideration of Foundations
, 2002
"... In this paper, I try once again to cause some goodnatured trouble. The issue remains, when will we ever stop burdening the taxpayer with conferences devoted to the quantum foundations? The suspicion is expressed that no end will be in sight until a means is found to reduce quantum theory to two or ..."
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Cited by 61 (6 self)
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In this paper, I try once again to cause some goodnatured trouble. The issue remains, when will we ever stop burdening the taxpayer with conferences devoted to the quantum foundations? The suspicion is expressed that no end will be in sight until a means is found to reduce quantum theory to two or three statements of crisp physical (rather than abstract, axiomatic) significance. In this regard, no tool appears better calibrated for a direct assault than quantum information theory. Far from a strained application of the latest fad to a timehonored problem, this method holds promise precisely because a large part—but not all—of the structure of quantum theory has always concerned information. It is just that the physics community needs reminding. This paper, though takingquantph/0106166 as its core, corrects one mistake and offers several observations beyond the previous version. In particular, I identify one element of quantum mechanics that I would not label a subjective term in the theory—it is the integer parameter D traditionally ascribed to a quantum system via its Hilbertspace dimension. 1
A functional quantum programming language
 In: Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
, 2005
"... This thesis introduces the language QML, a functional language for quantum computations on finite types. QML exhibits quantum data and control structures, and integrates reversible and irreversible quantum computations. The design of QML is guided by the categorical semantics: QML programs are inte ..."
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Cited by 46 (12 self)
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This thesis introduces the language QML, a functional language for quantum computations on finite types. QML exhibits quantum data and control structures, and integrates reversible and irreversible quantum computations. The design of QML is guided by the categorical semantics: QML programs are interpreted by morphisms in the category FQC of finite quantum computations, which provides a constructive operational semantics of irreversible quantum computations, realisable as quantum circuits. The quantum circuit model is also given a formal categorical definition via the category FQC. QML integrates reversible and irreversible quantum computations in one language, using first order strict linear logic to make weakenings, which may lead to the collapse of the quantum wavefunction, explicit. Strict programs are free from measurement, and hence preserve superpositions and entanglement. A denotational semantics of QML programs is presented, which maps QML terms
Finite precision measurement nullifies the KochenSpecker theorem
, 1999
"... Only finite precision measurements are experimentally reasonable, and they cannot distinguish a dense subset from its closure. We show that the rational vectors, which are dense in S 2, can be colored so that the contradiction with hidden variable theories provided by KochenSpecker constructions do ..."
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Cited by 32 (1 self)
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Only finite precision measurements are experimentally reasonable, and they cannot distinguish a dense subset from its closure. We show that the rational vectors, which are dense in S 2, can be colored so that the contradiction with hidden variable theories provided by KochenSpecker constructions does not obtain. Thus, in contrast to violation of the Bell inequalities, no quantumoverclassical advantage for information processing can be derived from the KochenSpecker theorem alone.
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 31 (13 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...