Information and computation: Classical and quantum aspects

Galindo, Alberto; Martín-Delgado, M. A.

doi:10.1103/revmodphys.74.347

Cited by 505 publications

(448 citation statements)

References 241 publications

(321 reference statements)

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“…Since quantum theory is irreducibly probabilistic, it has thus a partly subjective nature -or rather "inter-subjective" since under similar conditions all observers, using the same knowledge, will describe a quantum system in the same way and will make the same probabilistic predictions about it. The recent developments about the use of quantum systems as information processors [42] enforce this information-based interpretation [88,316] (see the end of § 12.4.2).…”

Section: Interpretation Of Probabilities and Statistical Ensembles Ofmentioning

confidence: 99%

“…Not only Bell's inequalities [27,34,36] but also the Greenberger-Horne-Zeilinger (GHZ) logical paradox [37] have been tested experimentally [38]. Moreover, rather than considering cases where quantum interference terms (the infamous "Schrödinger cat problem" [8,13,39]) vanish owing to decoherence processes [40], experimentalists have become able to control these very interferences [41], which are essential to describe the physics of quantum superpositions of macroscopic states and to explore the new possibilities offered by quantum information [22,42]. Examples include left and right going currents in superconducting circuits [15,43,44,45], macroscopic atomic ensembles [41] and entangled mechanical oscillators [46].…”

Section: General Features Of Quantum Measurementsmentioning

confidence: 99%

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Understanding quantum measurement from the solution of dynamical models

Allahverdyan¹,

Balian²,

2013

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The quantum measurement problem, to wit, understanding why a unique outcome is obtained in each individual experiment, is currently tackled by solving models. After an introduction we review the many dynamical models proposed over the years for elucidating quantum measurements. The approaches range from standard quantum theory, relying for instance on quantum statistical mechanics or on decoherence, to quantum-classical methods, to consistent histories and to modifications of the theory. Next, a flexible and rather realistic quantum model is introduced, describing the measurement of the z-component of a spin through interaction with a magnetic memory simulated by a Curie-Weiss magnet, including N 1 spins weakly coupled to a phonon bath. Initially prepared in a metastable paramagnetic state, it may transit to its up or down ferromagnetic state, triggered by its coupling with the tested spin, so that its magnetization acts as a pointer. A detailed solution of the dynamical equations is worked out, exhibiting several time scales. Conditions on the parameters of the model are found, which ensure that the process satisfies all the features of ideal measurements. Various imperfections of the measurement are discussed, as well as attempts of incompatible measurements. The first steps consist in the solution of the Hamiltonian dynamics for the spin-apparatus density matrixD(t). Its off-diagonal blocks in a basis selected by the spin-pointer coupling, rapidly decay owing to the many degrees of freedom of the pointer. Recurrences are ruled out either by some randomness of that coupling, or by the interaction with the bath. On a longer time scale, the trend towards equilibrium of the magnet produces a final stateD(t f ) that involves correlations between the system and the indications of the pointer, thus ensuring registration. AlthoughD(t f ) has the form expected for ideal measurements, it only describes a large set of runs. Individual runs are approached by analyzing the final states associated with all possible subensembles of runs, within a specified version of the statistical interpretation. There the difficulty lies in a quantum ambiguity: There exist many incompatible decompositions of the density matrixD(t f ) into a sum of sub-matrices, so that one cannot infer from its sole determination the states that would describe small subsets of runs. This difficulty is overcome by dynamics due to suitable interactions within the apparatus, which produce a special combination of relaxation and decoherence associated with the broken invariance of the pointer. Any subset of runs thus reaches over a brief delay a stable state which satisfies the same hierarchic property as in classical probability theory; the reduction of the state for each individual run follows. Standard quantum statistical mechanics alone appears sufficient to explain the occurrence of a unique answer in each run and the emergence of classicality in a measurement process. Finally, pedagogical exercises are proposed and lessons for future works on m...

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Section: Interpretation Of Probabilities and Statistical Ensembles Ofmentioning

confidence: 99%

Section: General Features Of Quantum Measurementsmentioning

confidence: 99%

Understanding quantum measurement from the solution of dynamical models

Allahverdyan¹,

Balian²,

2013

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“…In general, this procedure leads to the formation of the "Zeno subspaces" [7], on whose boundaries the wave function must vanish (Dirichlet): this is the ultimate reason for the absence of amplitude (and probability) leakage between "adjacent" subspaces. Quantum computation [29] is one of the most promising fields of potential application of the QZE. Interactions with the environment deteriorate the purity of quantum states and represent a very serious obstacle against the preservation of quantum superpositions and entanglement over long periods of time.…”

Section: Concluding Remarks On Potential Applicationsmentioning

confidence: 99%

Zeno dynamics and constraints

Facchi

Marmo

Pascazio

et al. 2004

J. Opt. B: Quantum Semiclass. Opt.

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Abstract. We investigate some examples of quantum Zeno dynamics, when a system undergoes very frequent (projective) measurements that ascertain whether it is within a given spatial region. In agreement with previously obtained results, the evolution is found to be unitary and the generator of the Zeno dynamics is the Hamiltonian with hard-wall (Dirichlet) boundary conditions. By using a new approach to this problem, this result is found to be valid in an arbitrary N -dimensional compact domain. We then propose some preliminary ideas concerning the algebra of observables in the projected region and finally look at the case of a projection onto a lower dimensional space: in such a situation the Zeno ansatz turns out to be a procedure to impose constraints.

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“…It has been the subject of intense research activity in recent years [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. Quantum entanglement constitutes a physical resource that lies at the basis of important quantum information processes [4] such as quantum teleportation [5], superdense coding [6], and quantum computation [7].…”

Section: Introductionmentioning

confidence: 99%

Entanglement and the speed of evolution of multi-partite quantum systems

Zander¹,

Plastino²,

Casas³

2007

J. Phys. A: Math. Theor.

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There exists an interesting relationship between entanglement and the time evolution of composite quantum systems: quantum entanglement enhances the 'speed' of evolution of certain quantum states, as measured by the time needed to reach an orthogonal state. Previous research done on this subject has been focused upon comparing extreme cases (highly entangled states versus separable states) or upon bi-partite systems. In the present contribution we explore the aforementioned connection (between entanglement and time evolution) in the cases of two-qubits and N-qubits systems, taking into account states of intermediate entanglement. In particular, we investigate a family of energetically symmetric states of low entanglement that saturate the quantum speed bound. We show that, as the number of qubits increases, very little entanglement is needed to reach the quantum speed limit.

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Information and computation: Classical and quantum aspects

Cited by 505 publications

References 241 publications

Understanding quantum measurement from the solution of dynamical models

Understanding quantum measurement from the solution of dynamical models

Zeno dynamics and constraints

Entanglement and the speed of evolution of multi-partite quantum systems

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