Polarization optics of biphotons

We discuss a procedure of measurement followed by the reproduction of the quantum state of a three-level optical system -a frequency-and spatially degenerate two-photon field. The method of statistical estimation of the quantum state based on solving the likelihood equation and analyzing the statistical properties of the obtained estimates is developed. Using the root approach of estimating quantum states, the initial two-photon state vector is reproduced from the measured fourth moments in the field . The developed approach applied to quantum states reconstruction is based on the amplitudes of mutually complementary processes. Classical algorithm of statistical estimation based on the Fisher information matrix is generalized to the case of quantum systems obeying Bohr's complementarity principle. It has been experimentally proved that biphoton-qutrit states can be reconstructed with the fidelity of 0.995-0.999 and higher.

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Section: B Representation Of Qutrits Using the Poincaré Spherementioning

confidence: 99%

Statistical reconstruction of qutrits

et al. 2004

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“…The use of the polarization states of single-mode biphotons for data recording was proposed in [5], and the polarization characteristics of these fields were discussed in [6,7]. A pure polarization state of a biphoton in the collinear frequency-degenerate regime can be written as [5] (3)…”

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Operationalistic orthogonality condition for single-mode biphotons (qutrits)

2002

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In recent years, considerable interest has been shown in multilevel systems with dimensionality higher than two, because they provide a way for more dense data recording, as compared to the traditional two-level systems. This is particularly important for quantum cryptography, because it enables one to increase the data-exchange rate [1] and enhance security against eavesdropping attacks of a certain class [2]. However, the transition to higher-dimensionality systems inevitably gives rise to experimental difficulties associated with the implementation and the adequate measurement of parameters. The solution of these problems requires the design of a data output device, error-correction protocols, repeaters, and other quantum communication devices. After the two-level system, the three-level system is the simplest. Its state in quantum information is called "qutrit" by analogy with qubit. The wave function of an arbitrary three-level system can be written as Biphoton fields have been used in many experiments of quantum optics practically since its inception. These fields are fluxes of photon pairs strongly correlated in coordinate and time of their creation. In the great majority of experiments, spontaneous parametric down-conversion (SPDC) is used as a source of biphoton field. It will be shown below that, in the case where a photon pair is emitted into the same spatial and frequency mode, the state polarization characteristics of the biphoton allow it to be considered as a qutrit [5]. The use of single-mode biphotons as qutrits in quantum communication protocols, e.g., in quantum cryptography poses the problem of separating a certain biphoton from the subset of biphotons with polarizations orthogonal to the polarization of the former. In this work, the operationalistic biphoton orthogonality condition is formulated for an arbitrary degree of polarization, and the experimental scheme is proposed that allows unambiguous separation of a certain biphoton polarization state from a set of states orthogonal to it. This is a fundamental problem, and its solution can be used, e.g., in the practical implementation of quantum cryptography protocol for the three-level systems.Biphotons and qutrits. The use of the polarization states of single-mode biphotons for data recording was proposed in [5], and the polarization characteristics of these fields were discussed in [6,7]. A pure polarization state of a biphoton in the collinear frequency-degenerate regime can be written as [5] (3)Here, | n , m 〉 denote the state with n photons in the horizontal ( H ) polarization mode and m photons in the vertical ( V ) mode ( n + m = 2) and An arbitrary polarization state of a single-mode biphoton is considered. The operationalistic criterion is formulated for the orthogonality of these states. It can be used to separate a biphoton with an arbitrary degree of polarization from a set of biphotons orthogonal to it. This is necessary for the implementation of quantum cryptography protocol based on the three-level systems. The experimental t...

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“…where ρ (3) pol is the qutrit's coherence matrix [15][16][17], [5]. By comparing with the full ququart's density matrix of Eq.…”

Section: Full Density Matrix: Eigenvalues Entropy and Von Neumanmentioning

confidence: 99%

Single biphoton ququarts as either pure or mixed states

2011

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We analyze features of mixed biphoton polarization states, which arise from pure states of polarizationfrequency biphoton ququarts after averaging over frequencies of photons. For mixed states, we find their concurrence C, Schmidt parameter K, degree of polarization P , as well as the von Neumann mutual information I . In some simple cases, we also find the relative entropy S rel and the degree of classical correlations C cl . In mixed states, the Schmidt parameter does not characterize the degree of entanglement anymore, as it does in pure states. Nevertheless, the Schmidt parameter remains useful even in the case of mixed states because it remains directly related to the degree of polarization. We compare results occurring in the cases of full pure polarization-frequency states of ququarts and mixed states (averaged over frequencies). Differences between these results can be seen in experiments with and without frequency filters in front of a detector.

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Polarization optics of biphotons

Cited by 34 publications

References 7 publications

Statistical reconstruction of qutrits

Statistical reconstruction of qutrits

Operationalistic orthogonality condition for single-mode biphotons (qutrits)

Single biphoton ququarts as either pure or mixed states

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