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Efficient Quantum Key Distribution Scheme And Proof of Its Unconditional Security
 Cryptology, ISSN: 09332790 (Paper) 14321378 (Online) published online 3 March 2004, (10.1007/s001450040142y). (SpringerVerlag
"... We devise a simple modification that essentially doubles the efficiency of the BB84 quantum key distribution scheme proposed by Bennett and Brassard. We also prove the security of our modified scheme against the most general eavesdropping attack that is allowed by the laws of physics. The first majo ..."
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Cited by 48 (10 self)
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We devise a simple modification that essentially doubles the efficiency of the BB84 quantum key distribution scheme proposed by Bennett and Brassard. We also prove the security of our modified scheme against the most general eavesdropping attack that is allowed by the laws of physics. The first major ingredient of our scheme is the assignment of significantly different probabilities to the different polarization bases during both transmission and reception, thus reducing the fraction of discarded data. A second major ingredient of our scheme is a refined analysis of accepted data: We separate the accepted data into various subsets according to the basis employed and estimate an error rate for each subset separately. We then show that such a refined data analysis guarantees the security of our scheme against the most general eavesdropping strategy, thus generalizing Shor and Preskill’s proof of security of BB84 to our new scheme. Up till now, most proposed proofs of security of singleparticle type quantum key distribution schemes have relied heavily upon the fact that the bases are chosen uniformly, randomly and independently. Our proof removes this symmetry requirement.
Quantum data hiding
 IEEE Trans. Inf. Theory
"... Abstract — We expand on our work on Quantum Data Hiding [1] – hiding classical data among parties who are restricted to performing only local quantum operations and classical communication (LOCC). We review our scheme that hides one bit between two parties using Bell states, and we derive upper and ..."
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Cited by 38 (3 self)
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Abstract — We expand on our work on Quantum Data Hiding [1] – hiding classical data among parties who are restricted to performing only local quantum operations and classical communication (LOCC). We review our scheme that hides one bit between two parties using Bell states, and we derive upper and lower bounds on the secrecy of the hiding scheme. We provide an explicit bound showing that multiple bits can be hidden bitwise with our scheme. We give a preparation of the hiding states as an efficient quantum computation that uses at most one ebit of entanglement. A candidate data hiding scheme that does not use entanglement is presented. We show how our scheme for quantum data hiding can be used in a conditionally secure quantum bit commitment scheme.
An introduction to measurement based quantum computation, ArXiv: quantph/0508124
, 2005
"... In the formalism of measurement based quantum computation we start with a given fixed entangled state of many qubits and perform computation by applying a sequence of measurements to designated qubits in designated bases. The choice of basis for later measurements may depend on earlier measurement o ..."
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Cited by 32 (1 self)
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In the formalism of measurement based quantum computation we start with a given fixed entangled state of many qubits and perform computation by applying a sequence of measurements to designated qubits in designated bases. The choice of basis for later measurements may depend on earlier measurement outcomes and the final result of the computation is determined from the classical data of all the measurement outcomes. This is in contrast to the more familiar gate array model in which computational steps are unitary operations, developing a large entangled state prior to some final measurements for the output. Two principal schemes of measurement based computation are teleportation quantum computation (TQC) and the socalled cluster model or oneway quantum computer (1WQC). We will describe these schemes and show how they are able to perform universal quantum computation. We will outline various possible relationships between the models which serve to clarify their workings. We will also discuss possible novel computational benefits of the measurement based models compared to the gate array model, especially issues of parallelisability of algorithms. 1
Unextendible Product Bases, Uncompletable Product Bases and Bound Entanglement
 COMMUNICATIONS IN MATHEMATICAL PHYSICS
, 2003
"... We report new results and generalizations of our work on unextendible product bases (UPB), uncompletable product bases and bound entanglement. We present a new construction for bound entangled states based on product bases which are only completable in a locally extended Hilbert space. We introduce ..."
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Cited by 25 (3 self)
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We report new results and generalizations of our work on unextendible product bases (UPB), uncompletable product bases and bound entanglement. We present a new construction for bound entangled states based on product bases which are only completable in a locally extended Hilbert space. We introduce a very useful representation of a product basis, an orthogonality graph. Using this representation we give a complete characterization of unextendible product bases for two qutrits. We present several generalizations of UPBs to arbitrary high dimensions and multipartite systems. We present a sufficient condition for sets of orthogonal product states to be distinguishable by separable superoperators. We prove that bound entangled states cannot help increase the distillable entanglement of a state beyond its regularized entanglement of formation assisted by bound entanglement.
Introduction to Quantum Algorithms
, 2001
"... Abstract. These notes discuss the quantum algorithms we know of that can solve problems significantly faster than the corresponding classical algorithms. ..."
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Cited by 23 (0 self)
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Abstract. These notes discuss the quantum algorithms we know of that can solve problems significantly faster than the corresponding classical algorithms.
Toward a software architecture for quantum computing design tools
 Proceedings of the 2nd International Workshop on Quantum Programming Languages (QPL
, 2004
"... Compilers and computeraided design tools are essential for finegrained control of nanoscale quantummechanical systems. A proposed fourphase design flow assists with computations by transforming a quantum algorithm from a highlevel language program into precisely scheduled physical actions. Quan ..."
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Cited by 21 (3 self)
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Compilers and computeraided design tools are essential for finegrained control of nanoscale quantummechanical systems. A proposed fourphase design flow assists with computations by transforming a quantum algorithm from a highlevel language program into precisely scheduled physical actions. Quantum computers have the potential to solve certain computational problems—for example, factoring composite numbers or comparing an unknown image against a large database— more efficiently than modern computers. They are also indispensable in controlling quantummechanical systems in emergent nanotechnology applications, such as secure optical communication, in which modern computers cannot natively operate on quantum data. Despite convincing laboratory demonstrations of
Projective Plane And Planar Quantum Codes
, 1998
"... Cellulations of the projective plane RP 2 define single qubit topological quantum error correcting codes since there is a unique essential cycle in H 1 (RP 2 ; Z 2 ). We construct three of the smallest such codes, show they are inequivalent, and identify one of them as Shor's original 9 qub ..."
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Cited by 20 (2 self)
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Cellulations of the projective plane RP 2 define single qubit topological quantum error correcting codes since there is a unique essential cycle in H 1 (RP 2 ; Z 2 ). We construct three of the smallest such codes, show they are inequivalent, and identify one of them as Shor's original 9 qubit repetition code. We observe that Shor's code can be constructed in a planar domain and generalize to planar constructions of higher genus codes for multiple qubits. PACS numbers: 03.67.Lx, 89.70.+c, 89.80.+h. AMS subject classification: 94Bxx, 81P99, 57M20. KEY WORDS: topological code, quantum error correction, planar code. Projective plane and planar quantum codes Freedman & Meyer Kitaev has constructed a class of quantum error correcting codes using qubits arranged on the edges of square lattices embedded in the two dimensional torus [1]. While these toric codes are not particularly efficientthey do not come close to saturating the quantum Hamming bound [2]they are nevertheless inte...
Twoqubit projective measurements are universal for quantum computation
"... Nielsen showed in quantph/0108020 that universal quantum computation can be performed using projective measurements, quantum memory, and preparation of the 0 〉 state. Furthermore, 4qubit measurements are sufficient. Fenner and Zhang showed in quantph/0111077 that 3qubit measurements are suffici ..."
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Nielsen showed in quantph/0108020 that universal quantum computation can be performed using projective measurements, quantum memory, and preparation of the 0 〉 state. Furthermore, 4qubit measurements are sufficient. Fenner and Zhang showed in quantph/0111077 that 3qubit measurements are sufficient. We prove that 2qubit measurements are sufficient, closing the gap between the upper and lower bound of the number of qubits to be measured jointly. We conclude with some open questions. 1 Introduction and previous work Studying the resources required for universal quantum computation is important not only for its realization but also for our theoretical understanding of what makes it so powerful. In the predominant standard quantum circuit model [1], it suffices to prepare the 0 〉 state, to measure individual qubits in the computation basis, and to well approximate any unitary gate. Any unitary gate
Global Entanglement in Multiparticle Systems
 Journal of Mathematical Physics
"... We define a polynomial measure of multiparticle entanglement which is scalable, i.e., which applies to any number of spin1 2 particles. By evaluating it for three particle states, for eigenstates of the one dimensional Heisenberg antiferromagnet and on quantum error correcting code subspaces, we il ..."
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Cited by 19 (3 self)
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We define a polynomial measure of multiparticle entanglement which is scalable, i.e., which applies to any number of spin1 2 particles. By evaluating it for three particle states, for eigenstates of the one dimensional Heisenberg antiferromagnet and on quantum error correcting code subspaces, we illustrate the extent to which it quantifies global entanglement. We also apply it to track the evolution of entanglement during a quantum computation.
Level reduction and the quantum threshold theorem
 PH.D. THESIS, CALTECH, 2007, EPRINT ARXIV:QUANTPH/0703230
, 2007
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