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Quantum informationflow, concretely, abstractly
 PROC. QPL 2004
, 2004
"... These ‘lecture notes ’ are based on joint work with Samson Abramsky. I will survey and informally discuss the results of [3, 4, 5, 12, 13] in a pedestrian not too technical way. These include: • ‘The logic of entanglement’, that is, the identification and abstract axiomatization of the ‘quantum info ..."
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Cited by 10 (4 self)
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These ‘lecture notes ’ are based on joint work with Samson Abramsky. I will survey and informally discuss the results of [3, 4, 5, 12, 13] in a pedestrian not too technical way. These include: • ‘The logic of entanglement’, that is, the identification and abstract axiomatization of the ‘quantum informationflow ’ which enables protocols such as quantum teleportation. 1 To this means we defined strongly compact closed categories which abstractly capture the behavioral properties of quantum entanglement. • ‘Postulates for an abstract quantum formalism ’ in which classical informationflow (e.g. token exchange) is part of the formalism. As an example, we provided a purely formal description of quantum teleportation and proved correctness in abstract generality. 2 In this formalism types reflect kinds, contra the essentially typeless von Neumann formalism [25]. Hence even concretely this formalism manifestly improves on the usual one. • ‘A highlevel approach to quantum informatics’. 3 Indeed, the above discussed work can be conceived as aiming to solve: von Neumann quantum formalism � highlevel language lowlevel language. I also provide a brief discussion on how classical and quantum uncertainty can be mixed in the above formalism (cf. density matrices). 4
The data compression theorem for ergodic quantum information sources
, 2003
"... We extend the data compression theorem to the case of ergodic quantum information sources. Moreover, we provide an asymptotically optimal compression scheme which is based on the concept of high probability subspaces. The rate of this compression scheme is equal to the von Neumann entropy rate. 1 ..."
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Cited by 6 (1 self)
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We extend the data compression theorem to the case of ergodic quantum information sources. Moreover, we provide an asymptotically optimal compression scheme which is based on the concept of high probability subspaces. The rate of this compression scheme is equal to the von Neumann entropy rate. 1
Influencefree states on compound quantum systems
, 2005
"... Consider two spatially separated agents, Alice and Bob, each of whom is able to make local quantum measurements, and who can communicate with each other over a purely classical channel. As has been pointed out by a number of authors, the set of mathematically consistent joint probability assignments ..."
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Cited by 3 (2 self)
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Consider two spatially separated agents, Alice and Bob, each of whom is able to make local quantum measurements, and who can communicate with each other over a purely classical channel. As has been pointed out by a number of authors, the set of mathematically consistent joint probability assignments (“states”) for such a system is properly larger than the set of quantummechanical mixed states for the joint AliceBob system. Indeed, it is canonically isomorphic to the set of positive (but not necessarily completely positive) linear maps L(HA) → L(HB) from the bounded linear operators on Alice’s Hilbert space to those on Bob’s, satisfying Tr (φ(1)) = 1. The present paper explores the properties of these states. We review what is known, including the fact that allowing classical communication between parties is equivalent to enforcing “noinstantaneoussignalling” (“no–influence”) in the direction opposite the communication. We establish that in the subclass of “decomposable”
PerronFrobenius Theory For Positive Maps On Trace Ideals
"... . This article provides sufficient conditions for positive maps on the Schatten classes Jp ; 1 p < 1 of bounded operators on a separable Hilbert space such that a corresponding PerronFrobenius theorem holds. With applications in quantum information theory in mind sufficient conditions are given f ..."
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Cited by 2 (0 self)
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. This article provides sufficient conditions for positive maps on the Schatten classes Jp ; 1 p < 1 of bounded operators on a separable Hilbert space such that a corresponding PerronFrobenius theorem holds. With applications in quantum information theory in mind sufficient conditions are given for a trace preserving, positive map on J1 , the space of trace class operators, to have a unique, strictly positive density matrix which is left invariant under the map. Conversely to any given strictly positive density matrix there are trace preserving, positive maps for which the density matrix is the unique PerronFrobenius vector. Dedicated to S. Doplicher and J.E. Roberts on the occasion of their 60th birthday 1. INTRODUCTION In the theory of quantum information the transmission through noisy channels plays an important role. Usually it is described by what physicists either call a quantum operation (see e.g. [25]) or a stochastic map ([1], see also [19]) or a superoperator (see e.g. ...
Path Integral for Quantum Operations
, 706
"... In this paper we consider a phase space path integral for general timedependent quantum operations, not necessarily unitary. We obtain the path integral for a completely positive quantum operation satisfied Lindblad equation (quantum Markovian master equation). We consider the path integral for qua ..."
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In this paper we consider a phase space path integral for general timedependent quantum operations, not necessarily unitary. We obtain the path integral for a completely positive quantum operation satisfied Lindblad equation (quantum Markovian master equation). We consider the path integral for quantum operation with a simple infinitesimal generator. PACS 03.67.Lx, 03.067a, 03.65.w 1
The incompatibility relation between visibility of interference and distinguishability of paths
, 2007
"... A model of the Young doubleslit experiment is formulated in a fully quantum theoretical setting. The state and dynamics of a wall which has the double slits in it, as well as the state of a particle incoming to the double slits, are described in quantum theoretical terms. Incompatibility between pr ..."
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A model of the Young doubleslit experiment is formulated in a fully quantum theoretical setting. The state and dynamics of a wall which has the double slits in it, as well as the state of a particle incoming to the double slits, are described in quantum theoretical terms. Incompatibility between producing the interference pattern and distinguishing the particle path is studied and their quantitative relation is established. It is argued that the uncertainty relation involved in the doubleslit experiment is not the Ozawatype uncertainty relation but the Kennardtype uncertainty relation of the position and the momentum of the doubleslit wall. A possible experiment to test the incompatibility relation is suggested. It is also argued that various phenomena which occur at the interface of a quantum system and a classical system, including measurement, decoherence, interference and distinguishability, can be understood as different aspects of entanglement. Keywords: doubleslit experiment, uncertainty relation, KennardRobertson inequalities, Ozawa inequality, entanglement 1 1
Computational Distinguishability of Quantum Channels
, 909
"... c ○ William Rosgen 2009I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. The computational problem of disti ..."
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c ○ William Rosgen 2009I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. The computational problem of distinguishing two quantum channels is central to quantum computing. It is a generalization of the wellknown satisfiability problem from classical to quantum computation. This problem is shown to be surprisingly hard: it is complete for the class QIP of problems that have quantum interactive proof systems, which implies that it is hard for the class PSPACE of problems solvable by a classical computation in polynomial space. Several restrictions of distinguishability are also shown to be hard. It is no easier when restricted to quantum computations of logarithmic depth, to mixedunitary channels, to degradable channels, or to antidegradable channels. These hardness results are demonstrated by finding reductions between these classes of quantum channels. These techniques have applications outside the distinguishability problem, as the construction for mixedunitary channels is used to prove that the additivity problem for the classical capacity of quantum channels can be equivalently restricted to the mixed unitary channels. iii Acknowledgements I would like to thank my supervisor John Watrous for years of guidance, support, and insight. Without his help this would not have been possible. I would also like to thank the rest of my committee, Richard Cleve, Stephen Fenner, Achim Kempf, and Ben Reichardt, for providing helpful comments on an earlier draft of this thesis. I would also like to thank Lana for putting up with me during the writing of this thesis and supporting me throughout the process. v 4 The Close Images Problem 77 4.1 Logdepth mixedstate quantum circuits................... 78 4.2 QIP completeness of close images...................... 79
Open nQubit System as a Quantum Computer with FourValued Logic
, 2001
"... In this paper we generalize the usual model of quantum computer to a model in which the state is an operator of density matrix and the gates are general superoperators (quantum operations), not necessarily unitary. A mixed state (operator of density matrix) of n twolevel quantum system (open or clos ..."
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In this paper we generalize the usual model of quantum computer to a model in which the state is an operator of density matrix and the gates are general superoperators (quantum operations), not necessarily unitary. A mixed state (operator of density matrix) of n twolevel quantum system (open or closed nqubit system) is considered as an element of 4 ndimensional operator Hilbert space (Liouville space). It allows to use quantum computer (circuit) model with 4valued logic. The gates of this model are general superoperators which act on nququats state. Ququat is quantum state in a 4dimensional (operator) Hilbert space. Unitary twovalued logic gates and quantum operations for nqubit open system are considered as fourvalued logic gates acting on nququats. We discuss properties of quantum 4valued logic gates. In the paper we study universality for quantum fourvalued logic gates. PACS 3.67.Lx; 03.65w; 3.65.Bz