Spectral Entanglement in Parametric Down-Conversion with Nondegenerate Frequencies

Volkov, P. A.; Mikhailova, Yu. M.; Федоров, М. В.

doi:10.1166/asl.2009.1057

Cited by 9 publications

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“…The TPSA fully characterizes the spectral properties of a biphoton state and its physical meaning is the joint spectral probability am-plitude of the down-converted photons in signal and idler modes with frequencies ω s and ω i respectively. TPSA is used to determine the degree of frequency entanglement [1,4,[16][17][18] and plays a central role in the heralded generation of pure single-photon states [19].…”

Section: Introductionmentioning

confidence: 99%

Separable Schmidt modes of an entangled state

et al. 2014

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Section: Introductionmentioning

confidence: 99%

Separable Schmidt modes of an entangled state

et al. 2014

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“…Of course, in order to evaluate the entanglement of a quantum state one may resort to full quantum state tomography [8] that, however, becomes impractical in higher dimensions and may be affected by large uncertainty [9,10]. Other methods, requiring a reduced number of observables, are based on visibility measurements [11], Bell tests [12,13], entanglement witnesses [14][15][16][17][18], or are related to Schmidt number [19][20][21]. Many of them have been implemented experimentally [22][23][24][25][26][27], also in the presence of decoherence effects [28,29].…”

Section: Introductionmentioning

confidence: 99%

Optimal estimation of entanglement in optical qubit systems

et al. 2011

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We address the experimental determination of entanglement for systems made of a pair of polarization qubits. We exploit quantum estimation theory to derive optimal estimators, which are then implemented to achieve ultimate bound to precision. In particular, we present a set of experiments aimed at measuring the amount of entanglement for states belonging to different families of pure and mixed two-qubit two-photon states. Our scheme is based on visibility measurements of quantum correlations and achieves the ultimate precision allowed by quantum mechanics in the limit of Poissonian distribution of coincidence counts. Although optimal estimation of entanglement does not require the full tomography of the states we have also performed state reconstruction using two different sets of tomographic projectors and explicitly shown that they provide a less precise determination of entanglement. The use of optimal estimators also allows us to compare and statistically assess the different noise models used to describe decoherence effects occurring in the generation of entanglement

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“…The TPSA fully characterizes the spectral properties of a biphoton state and its physical meaning is the joint spectral probability amplitude of the down-converted photons in signal and idler modes with frequencies ω s and ω i respectively. TPSA is used to determine the degree of frequency entanglement [1,4,[16][17][18] and plays a central role in the heralded generation of pure single-photon states [19].…”

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confidence: 99%

Separable Schmidt modes of a nonseparable state

et al. 2014

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Two-photon states entangled in continuous variables such as wavevector or frequency represent a powerful resource for quantum information protocols in higher-dimensional Hilbert spaces. At the same time, there is a problem of addressing separately the corresponding Schmidt modes. We propose a method of engineering two-photon spectral amplitude in such a way that it contains several non-overlapping Schmidt modes, each of which can be filtered losslessly. The method is based on spontaneous parametric down-conversion (SPDC) pumped by radiation with a comb-like spectrum. There are many ways of producing such a spectrum; here we consider the simplest one, namely passing the pump beam through a Fabry-Perot interferometer. For the two-photon spectral amplitude (TPSA) to consist of non-overlapping Schmidt modes, the crystal dispersion dependence, the length of the crystal, the Fabry-Perot free spectral range and its finesse should satisfy certain conditions. We experimentally demonstrate the control of TPSA through these parameters. We also discuss a possibility to realize a similar situation using cavity-based SPDC.PACS numbers: 42.50. Dv, 42.50.Ar, 03.65.Ta, 85.60.Gz Introduction.Entanglement of two-photon states (biphotons) in continuous variables such as frequency or wavevector suggests the use of biphotons as a quantum-information resource in higher-dimensional Hilbert spaces [1,2]. The dimensionality of the Hilbert space is determined in this case by the Schmidt number, the effective number of Schmidt modes, which can reach several hundred [2][3][4]. But in order to realize any protocols with multimode states, it is necessary to address single Schmidt modes separately. For wavevector variables, any single Schmidt mode can be filtered out using a single-mode fibre and a spatial light modulator [6]. This filtering, in principle, can be lossless, which is crucial for experiments with twin-beam squeezing [7][8][9][10][11][12]. For frequency variables, it is far more difficult to losslessly select a single Schmidt mode. Attempts are being made in homodyne detection [13]; in direct detection experiments the procedure is more difficult. For instance, methods based on nonlinear frequency conversion are proposed, technically complicated to realize with high efficiency [14]. Here we propose and demonstrate a method of engineering a two-photon state in such a way that it contains non-overlapping Schmidt modes, each of which can be filtered losslessly using a spectral device.Frequency entanglement of biphotons. A two-photon state generated via SPDC can be written in the formwhereâ † s ,â † i are the creation operators of the signal and idler photons, and F (ω s , ω i ) represents the two-photon spectral amplitude (TPSA) [15]. The TPSA fully characterizes the spectral properties of a biphoton state and its physical meaning is the joint spectral probability amplitude of the down-converted photons in signal and idler modes with frequencies ω s and ω i respectively. TPSA is used to determine the degree of frequency entanglemen...

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Spectral Entanglement in Parametric Down-Conversion with Nondegenerate Frequencies

Cited by 9 publications

References 0 publications

Separable Schmidt modes of an entangled state

Separable Schmidt modes of an entangled state

Optimal estimation of entanglement in optical qubit systems

Separable Schmidt modes of a nonseparable state

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