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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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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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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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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”
Measures and dynamics of entangled states
, 2005
"... We develop an original approach for the quantitative characterisation of the entanglement properties of, possibly mixed, bi and multipartite quantum states of arbitrary finite dimension. Particular emphasis is given to the derivation of reliable estimates which allow for an efficient evaluation of ..."
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We develop an original approach for the quantitative characterisation of the entanglement properties of, possibly mixed, bi and multipartite quantum states of arbitrary finite dimension. Particular emphasis is given to the derivation of reliable estimates which allow for an efficient evaluation of a specific entanglement measure, concurrence, for further implementation in the monitoring of the time evolution of multipartite entanglement under incoherent environment coupling. The flexibility of the technical machinery established here is illustrated by its implementation for
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 give ..."
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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
Quantum/classical correspondence in the light of Bell’s inequalities
, 1990
"... Instead of the usual asymptotic passage from quantum mechanics to classical mechanics when a parameter tended to infinity, a sharp boundary is obtained for the domain of existence of classical reality. The last is treated as separable empirical reality following d’Espagnat, described by a mathemati ..."
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Instead of the usual asymptotic passage from quantum mechanics to classical mechanics when a parameter tended to infinity, a sharp boundary is obtained for the domain of existence of classical reality. The last is treated as separable empirical reality following d’Espagnat, described by a mathematical superstructure over quantum dynamics for the universal wave function. Being empirical, this reality is constructed in terms of both fundamental notions and characteristics of observers. It is presupposed that considered observers perceive the world as a system of collective degrees of freedom that are inherently dissipative because of interaction with thermal degrees of freedom. Relevant problems of foundation of statistical physics are considered. A feasible example is given of a macroscopic system not admitting such classical reality. The article contains a concise survey of some relevant domains: quantum and classical Belltype inequalities; universal wave function; approaches to quantum description of macroscopic world, with emphasis on dissipation; spontaneous reduction models; experimental tests of the universal validity of the quantum the
Computational Distinguishability of Quantum Channels
, 2009
"... 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 h ..."
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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.