The density matrix of the canonically transformed multidimensional Hamiltonian in the Fock basis

Dodonov, V. V.; Man’ko, Vladimir I.; Semjonov, V. V.

doi:10.1007/bf02721587

Cited by 37 publications

(31 citation statements)

References 19 publications

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“…It leads to the choice δ = 1 in Eq. (29) in the previous section. Suppose the outgoing state conditioned on a 'one-photon' indication in the detection device is ρ.…”

Section: Comparing Detection Devicesmentioning

confidence: 92%

Detection devices in entanglement-based optical state preparation

2001

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We study the use of detection devices in entanglement-based state preparation. In particular we consider optical detection devices such as single-photon sensitivity detectors, single-photon resolution detectors and detector cascades (with an emphasis on the performance of realistic detectors). We develop an extensive theory for the use of these devices. In entanglement-based state preparation we perform measurements on subsystems, and we therefore need precise bounds on the distinguishability of these measurements (this is fundamentally different from, e.g., tomography, where an ensemble of identical states is used to determine probability distributions, etc.). To this end, we introduce the confidence of preparation, which may also be used to quantify the performance of detection devices in entanglement-based preparation. We give a general expression for detector cascades of arbitrary size for the detection up to two photons. We show that, contrary to the general belief, cascading does not give a practical advantage over detectors with single-photon resolution in entanglement-based state preparation. PACS number(s): 42.50.ArThe accurate creation of quantum states is important to many applications in, for example, quantum computation and information [1,2]. One method of state preparation is to entangle two systems and subsequently perform a so-called conditional measurement on one subsystem: depending on the measurement outcome the undetected subsystem is 'prepared' (collapsed) into a particular predetermined state (see also Rubin [3]). Considerable progress has been made using this method in the creation of optical quantum states [4][5][6][7][8] and in the creation of three-photon polarisation entanglement [9]. Optical entanglement sources include, for example, crossKerr media [7] or the mixing of states at beam-splitters [8]. In general, the quality of this entanglement-based state preparation strongly depends on the details of the conditional measurement.In this paper we study the effect of realistic (photo-) detectors on the state preparation process. To this end we introduce the concept of the confidence of preparation in Sec. I. This measure does not only quantify the 'quality' of the state preparation process, but it also allows us to compare different types of detection devices. In Sec. II we discuss the distinction between single-photon sensitivity and single-photon resolution detectors. The statistics of detector cascading with single-photon sensitivity detectors is studied in Sec. III and Sec. IV makes a numerical comparison between such detector cascades and single-photon resolution detectors.Let's consider entanglement-based state preparation [3] (not necessarily restricted to quantum optics). We want to prepare a single (pure) state |φ by means of some entanglement-based process, and we want the resulting state ρ to be as 'close' to |φ as possible. A measure of resemblance between states is given by the fidelity F [10]:The quality of a state preparation process can therefore be measured by the fidel...

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“…It leads to the choice δ = 1 in Eq. (29) in the previous section. Suppose the outgoing state conditioned on a 'one-photon' indication in the detection device is ρ.…”

Section: Comparing Detection Devicesmentioning

confidence: 92%

Detection devices in entanglement-based optical state preparation

2001

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“…Therefore, it seems reasonable to consider only the term Tr(ρρ c ), searching for its maximum with respect to the enlarged family of "classical" states, consisting of all displaced thermal states [40][41][42] …”

Section: Classicality Measurementioning

confidence: 99%

“…This probability was calculated by many authors, e.g., in [40][41][42]51]. Using the results of [51] and taking into account the expression for purity of the thermal state (it does not depend on the shift parameter α),…”

Section: Classicality Of the Fock Statesmentioning

confidence: 99%

Classicality and anticlassicality measures of pure and mixed quantum states

Dodonov

Renó

2003

Physics Letters A

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We introduce a simple measure of "classicality" of pure and mixed quantum states as a maximum value of the Hilbert-Schmidt "scalar products" between the renormalized statistical operators of the state concerned and all displaced thermal states. Choosing Fock states as the reference set, we introduce the measure of "anticlassicality". Both measures are illustrated for the Fock, coherent phase, and generic mixed Gaussian states. Gaussian states are shown to be the closest to thermal states possessing the same degree of quantum purity. On the contrary, Fock states appear to be more close to mixed thermal states than to pure coherent states. 42.50.Dv PACS:

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“…An early paper by Vourdas [4] discusses the superposition of squeezed states with thermal photons; a more recent paper [5] considers only the case of thermal coherent states. An early study of canonically transformed thermal states similar to the approach of the present work was made in [6], and also in [7,8]. Two further papers adopt essentially the same definition as the present note s [9,10] using a slightly different approach.…”

Section: Introductionmentioning

confidence: 81%