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Generalized concurrence Cg (3.4),von Neumann entropy of the twice reduced density matrix Srr (3.5) and the Schmidt parameter K (3.6) as functions of the parameter λ − (3.3)
Source publication
We consider polarization states of three photons, each in the same given
spectral-angular mode. A general form of such states is a superposition of four
basic three-photon polarization modes, to be referred to as three-photon
polarization ququarts. All such states can be considered as consisting of one-
and two-photon parts, which can be entangled...
Contexts in source publication
Context 1
... Fig. 1 the functions S rr (λ − ) and C g (λ − ) are plotted together. Both of them show that, as mentioned above, the degree of entanglement of three-photon states varies from 0 to 1. An example of maximally entangled state ...
Context 2
... opposite case of a disentangled state is the state with C 1 = 1, C 2,3,4 = 0, |Ψ = |3 H , λ + = 1, λ − = 0, and S rr = C g = 0. The third curve shown in Fig. 1 is the Schmidt entanglement ...
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Citations
... Note that for biphoton states the method of density matri ces of the described type was suggested by D N Klyshko in 1997 [5] and somewhat later used in the works [6,7]. More recently there was a series of works on some aspects of entan glement in multipohoton states [8][9][10][11][12]. However, as far as we know, there were no works where the Klyshko method of den sity matrices would be generalized for multiphoton states with numbers of photons higher than 3. ...
... In the cases of states with large numbers of photons, n 4, there is more than one way of imagining how the original nphoton state can be divided into two parts. E.g. for n = 4 there are are two ways of the gedanken splitting this state into two parts: 4 = 2 + 2 and 4 = 3 + 1 [12]. Thus, in these cases one can discuss different degrees of entanglement corre sponding to different ways of splitting the original state into two parts. ...
... For other relations between n H and n V the Schmidt parameter K is smaller than The simplest example of the basic Fock state with odd n is that of threephoton states |1 H , 2 V and |2 H , 1 V . In both cases equation (11) gives K = 9/5 in agreement with the results of the work [12]. The main conclusion from this brief analysis concerns the achievable entanglement of nphoton basic Fock states with respect to division into subsystems of a singlepho ton and an (n − 1)photon state: entanglement of such states with respect to such division for subsystems does not exceed that occurring in the case of biphoton states, and the maximal entanglement with K = 2 or close to 2 is achieved in the states with maximally close numbers of horizontally and vertically polarized photons, n H and n V . ...
... Thus the development an effective three-photon source can become the next big step in this progress. Generation of GHZ-states [37], study the features of three-photon polarization states [11], heralded generation of entangled biphotons are possible applications of such three-photon source. ...
We analyze the origins of the luminescence in germania–silica fibers with high germanium concentration (about 30 mol.% GeO 2 ) in the region of 1–2 μm with a laser pump at the wavelength 532 nm. We show that such fibers demonstrate the high level of luminescence which unlikely allows the observation of photon triplets, generated in a third-order spontaneous parametric downconversion process in such fibers. The only efficient approach to the luminescence reduction is the hydrogen saturation of fiber samples; however, even in this case, the level of residual luminescence is still too high for three-photon registration.
... It acts as a measure of information about parameters of a quantum state contained in the measurements determined by the tomography protocol. Above we have described complete tomographic protocols, i.e., protocols that provide arbitrarily accurate recovery of any mixed state as the sample size grows 28 ...
... All possible superpositions of states (9) span a state space of a three-photon polarization ququart 28 (15) The solution to the initial state reconstruction in a reduced basis is similar to the one in the original basis, but lets us take into account the smaller number of parameters. In Fig.5a the distribution of the number of nines in numerical representation of fidelity for four dimensional state is shown. ...
Reliable generation and measurement of triphoton states has yet to be achieved in laboratory. We give an overview of the problems in generating and measuring triphoton quantum states and analyze several protocols of quantum measurements, which allow for high precision of reconstruction when sizes of available statistical data samples are limited. The tomography procedure under investigation is based on root approach to state estimation. In particular, we use the generalized Fisher information matrix to assess the accuracy of the quantum state parameters measurement. We use tomographic protocols, based on the symmetry of the Platonic solids. We demonstrate the capability to reconstruct triphoton quantum states with precision close to the maximum achievable value allowed by quantum mechanics
The interaction of a three-level atom with two quantum field modes has been studied analytically. Strong quantum entanglement between individual parts of the considered multipartite system has been revealed and the possibility of its controlled variation has been demonstrated. Methods of the transmission and exchange of phase information between field modes, as well as of direct measurement of the phase characteristics of an unknown state of the input field, have been developed on the basis of quantum entanglement between initially independent quantum fields interacting with an atom.
