Detection devices in entanglement-based optical state preparation

Abstract

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...

Linear optics and projective measurements alone suffice to create large-photon-number path entanglement

“…Due to interference of the two paths, one obtains an intensity pattern at the lithographic surface which is proportional to 1 + cos N ϕ, where ϕ parametrizes the position on the surface. A superposition of these states with varying N and suitable phase shifts then yields a Fourier series of the desired pattern, up to a constant [5].In view of these potential applications, finding methods for generating path-entangled states has been a longstanding endeavor in quantum optics. Unfortunately, with the notable exception of N = 2, the optical generation of these states seemed to require single-photon quantum logic gates that involve a large nonlinear interaction, namely, a Kerr element with χ (3) on the order of unity.…”

“…Due to interference of the two paths, one obtains an intensity pattern at the lithographic surface which is proportional to 1 + cos N ϕ, where ϕ parametrizes the position on the surface. A superposition of these states with varying N and suitable phase shifts then yields a Fourier series of the desired pattern, up to a constant [5].…”

“…For a realistic, singlephoton resolution, photo-detector with efficiency η 2 = 0.88 [19], the fidelity of the outgoing state with respect to the envisioned state |Ψ = |4, 0 + |0, 4 is F = Ψ|ρ|Ψ = 0.64, conditioned on a single-photon detector coincidence. Even though these imperfect detections lead to a degraded fidelity, this might be exploited in order to create incoherent superpositions of pathentangled states, which may be useful for the pseudoFourier method in quantum lithography [5].…”

“…4). Such input states as |N, 0 can be produced by manipulating states of the form |N, N , or from N -photon sources, now under development [18,19]. 00000 00000 11111 11111 00000 00000 11111 11111…”

“…States of this form are typically produced in optical parametric oscillators and down-converters [17,18]. We have also devised schemes, which start from the state |5, 0 instead, and from which we generate states of the form |N, 0 + |0, N , for N ∈ {2, 3, 4} (see Fig.…”