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200
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 102 (2 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 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.
Braiding operators are universal quantum gates
 New J. Phys
, 2004
"... doi:10.1088/13672630/6/1/134 Abstract. This paper explores the role of unitary braiding operators in quantum computing. We show that a single specific solution R (the Bell basis change matrix) of theYang–Baxter equation is a universal gate for quantum computing, in the presence of local unitary tra ..."
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Cited by 36 (9 self)
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doi:10.1088/13672630/6/1/134 Abstract. This paper explores the role of unitary braiding operators in quantum computing. We show that a single specific solution R (the Bell basis change matrix) of theYang–Baxter equation is a universal gate for quantum computing, in the presence of local unitary transformations.We show that this same R generates a new nontrivial invariant of braids, knots and links. Other solutions of the Yang– Baxter equation are also shown to be universal for quantum computation. The paper discusses these results in the context of comparing quantum and topological points of view. In particular, we discuss quantum computation of link invariants, the relationship between quantum entanglement and topological entanglement, and the structure of braiding in a topological quantum field theory.
Scaling of entanglement close to a quantum phase transition, Nature (London
, 2002
"... Classical phase transitions occur when a physical system reaches a state below a critical temperature characterized by macroscopic order 8 . The role of entanglement at a phase transition is not captured by statistical mechanicsa complete classification of the critical manybody state requires th ..."
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Cited by 35 (0 self)
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Classical phase transitions occur when a physical system reaches a state below a critical temperature characterized by macroscopic order 8 . The role of entanglement at a phase transition is not captured by statistical mechanicsa complete classification of the critical manybody state requires the introduction of concepts from quantum information theory 9 . Here we connect the theory of critical phenomena with quantum information by exploring the entangling resources of a system close to its quantum critical point. We demonstrate, for a class of onedimensional magnetic systems, that entanglement shows scaling behaviour in the vicinity of the transition point. There are various questions that emerge in the study of this problem. Because the groundstate wavefunction undergoes qualitative changes at a quantum phase transition, it is important to understand how its genuine quantum aspects evolve throughout the transition. Will entanglement between distant subsystems be extended over macroscopic regions, as correlations are? Will it carry distinct features of the transition itself and show scaling behaviour? Answering these questions is important for a deeper understanding of quantum phase transitions, and also from the perspective of quantum information theory. So results that bridge these two areas of research are of great relevance. We study a set of localized spins coupled through exchange interaction and subjected to an external magnetic field (we consider only spin1/2 particles), a model central both to condensedmatter and information theory and subject to intense study The system under consideration is a spin1/2 ferromagnetic chain with an exchange coupling J in a transverse magnetic field of
On local invariants of pure threequbit states
 J. Phys. A34
"... We study invariants of threequbit states under local unitary transformations, i.e. functions on the space of entanglement types, which is known to have dimension 6. We show that there is no set of six independent polynomial invariants of degree ≤ 6, and find such a set with maximum degree 8. We des ..."
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Cited by 21 (1 self)
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We study invariants of threequbit states under local unitary transformations, i.e. functions on the space of entanglement types, which is known to have dimension 6. We show that there is no set of six independent polynomial invariants of degree ≤ 6, and find such a set with maximum degree 8. We describe an intrinsic definition of a canonical state on each orbit, and discuss the (nonpolynomial) invariants associated with it. 1 1
Entanglement detection
 Physics Reports
"... How can one prove that a given state is entangled? In this paper we review different methods that have been proposed for entanglement detection. We first explain the basic elements of entanglement theory for two or more particles and then entanglement verification procedures such as Bell inequalitie ..."
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Cited by 14 (0 self)
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How can one prove that a given state is entangled? In this paper we review different methods that have been proposed for entanglement detection. We first explain the basic elements of entanglement theory for two or more particles and then entanglement verification procedures such as Bell inequalities, entanglement witnesses, the determination of nonlinear properties of a quantum state via measurements on several copies, and spin squeezing inequalities. An emphasis is given to the theory and application of entanglement witnesses. We also discuss several experiments, where some of the presented methods have been implemented.
Implementation of Grover’s quantum search algorithm in a scalable system
 Phys. Rev. A
, 2005
"... For my mom and dad ii ACKNOWLEDGEMENTS My graduate school experience here at Michigan has been amazing and that is due, in large part, to the people that I have met and the friends that I have made along the way. First and foremost I need to thank Chris for letting me work in his lab, Chris, thank y ..."
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Cited by 13 (2 self)
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For my mom and dad ii ACKNOWLEDGEMENTS My graduate school experience here at Michigan has been amazing and that is due, in large part, to the people that I have met and the friends that I have made along the way. First and foremost I need to thank Chris for letting me work in his lab, Chris, thank you so much. In my six years here I have learned more than I could have possibly imagined. When I look back to when I first joined the lab, compared to where I am now the difference, in my mind at least, is unreal. In your lab I had the opportunity to learn about so many different aspects of experimental physics, from microwave sources, to optics and lasers, to atomic physics. Thank you for all of the opportunities you have given me and for supporting me along the way. I feel well prepared for whatever my physics future holds and I am truly grateful. Next I need to thank all my collegues especially Louis, Patty, and Paul with whom I worked and from whom I learned the most. Louis and Patty, thank you for showing
Szegő limit theorem for operators with discontinuous symbols and applications to entanglement entropy
, 2006
"... Abstract. The main result in this paper is a one term Szegö type asymptotic formula with a sharp remainder estimate for a class of integral operators of the pseudodifferential type with symbols which are allowed to be nonsmooth or discontinuous in both position and momentum. The simplest example of ..."
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Cited by 8 (1 self)
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Abstract. The main result in this paper is a one term Szegö type asymptotic formula with a sharp remainder estimate for a class of integral operators of the pseudodifferential type with symbols which are allowed to be nonsmooth or discontinuous in both position and momentum. The simplest example of such symbol is the product of the characteristic functions of two compact sets, one in real space and the other in momentum space. The results of this paper are used in a study of the violation of the area entropy law for free fermions in [18]. This work also provides evidence towards a conjecture due to Harold Widom. 1.
Symmetries, group actions, and entanglement
 Open Sys. Information Dyn
"... Abstract. We address several problems concerning the geometry of the space of Hermitian operators on a finitedimensional Hilbert space, in particular the geometry of the space of density states and canonical group actions on it. For quantum composite systems we discuss and give examples of measures ..."
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Cited by 7 (4 self)
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Abstract. We address several problems concerning the geometry of the space of Hermitian operators on a finitedimensional Hilbert space, in particular the geometry of the space of density states and canonical group actions on it. For quantum composite systems we discuss and give examples of measures of entanglement. 1.