Entangled singularity patterns of photons in Ince-Gauss modes

Krenn, Mario; Fickler, Robert; Huber, Marcus; Łapkiewicz, Radek; Plick, William N.; Ramelow, Sven; Zeilinger, Anton

doi:10.1103/physreva.87.012326

Cited by 80 publications

(51 citation statements)

References 39 publications

(37 reference statements)

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“…In a second experiment we take advantage of all three implemented slits and test for OAM qutrit entanglement. Similar to earlier results 12,22 , the entanglement witness enables us to draw conclusions about the global dimensionality of the entanglement while restricting ourselves to qubit-subspace measurements. In our experiment this approach corresponds to the measurements of all visibilities in all two-dimensional subspaces that is for l-values of 0/ À 3, 0/ þ 3 and À 3/ þ 3.…”

Section: Generation Of Oam Modes With a Ms In Reversesupporting

confidence: 54%

“…The fact that beams encoded with orbital angular momentum (OAM) can co-propagate along the same optical axes makes their use, especially over long distances, advantageous [5][6][7][8][9] . Various modes, such as OAM-carrying Laguerre-Gauss (LG) 10,11 , Ince-Gauss 12 and Bessel-Gauss 13 , have been used to demonstrate experimentally high-dimensionally entangled states and to implement quantum informational tasks. In a wide quantum network 14 , both degrees of freedom, local on-chip path encoding and long-distance bridging spatial modes, will have to be matched to each other.…”

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confidence: 99%

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Interface between path and orbital angular momentum entanglement for high-dimensional photonic quantum information

et al. 2014

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Photonics has become a mature field of quantum information science, where integrated optical circuits offer a way to scale the complexity of the set-up as well as the dimensionality of the quantum state. On photonic chips, paths are the natural way to encode information. To distribute those high-dimensional quantum states over large distances, transverse spatial modes, like orbital angular momentum possessing Laguerre Gauss modes, are favourable as flying information carriers. Here we demonstrate a quantum interface between these two vibrant photonic fields. We create three-dimensional path entanglement between two photons in a nonlinear crystal and use a mode sorter as the quantum interface to transfer the entanglement to the orbital angular momentum degree of freedom. Thus our results show a flexible way to create high-dimensional spatial mode entanglement. Moreover, they pave the way to implement broad complex quantum networks where high-dimensionally entangled states could be distributed over distant photonic chips.

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Section: Generation Of Oam Modes With a Ms In Reversesupporting

confidence: 54%

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confidence: 99%

Interface between path and orbital angular momentum entanglement for high-dimensional photonic quantum information

et al. 2014

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“…As such, the LG modes were first used to demonstrate OAM entanglement 5 . However, a variety of bases may also be used to demonstrate OAM entanglement, including Ince-Gaussian 6 , Bessel-Gaussian (BG) 7,8 as well as mutually unbiased bases derived from these sets 9,10 . The OAM modal basis defines an infinite-dimensional Hilbert space, allowing access to highdimensional entanglement 11 .…”

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confidence: 99%

Self-healing of quantum entanglement after an obstruction

et al. 2014

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Quantum entanglement between photon pairs is fragile and can easily be masked by losses in transmission path and noise in the detection system. When observing the quantum entanglement between the spatial states of photon pairs produced by parametric downconversion, the presence of an obstruction introduces losses that can mask the correlations associated with the entanglement. Here we show that we can overcome these losses by measuring in the Bessel basis, thus once again revealing the entanglement after propagation beyond the obstruction. We confirm that, for the entanglement of orbital angular momentum, measurement in the Bessel basis is more robust to these losses than measuring in the usually employed Laguerre-Gaussian basis. Our results show that appropriate choice of measurement basis can overcome some limitations of the transmission path, perhaps offering advantages in free-space quantum communication or quantum processing systems.

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“…For continuous variable systems it is of great practical importance to find operational discretizations for processing quantum information [19,20]. Notably, HW observables can be systematically extended to the continuous limit of infinite dimensional systems, holding analogous properties and with this also all corresponding results can be extended in this limit, thus providing a natural path towards a discretization of continuous variable systems.…”

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confidence: 99%

“…First, HW observables in contrast with GGM generically have full-rank, making them more efficient in sparsely characterizing states with a lot of coherence. Secondly, for a suitable parametrization, strict pairwise (anti-)commutativity relations can be obtained which can be applied to entanglement detection and will be demonstrated later .For continuous variable systems it is of great practical importance to find operational discretizations for processing quantum information [19,20]. Notably, HW observables can be systematically extended to the continuous limit of infinite dimensional systems, holding analogous properties and with this also all corresponding results can be extended in this limit, thus providing a natural path towards a discretization of continuous variable systems.…”

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confidence: 99%

Heisenberg-Weyl Observables: Bloch vectors in phase space

et al. 2016

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We introduce a Hermitian generalization of Pauli matrices to higher dimensions which is based on Heisenberg-Weyl operators. The complete set of Heisenberg-Weyl observables allows us to identify a real-valued Bloch vector for an arbitrary density operator in discrete phase space, with a smooth transition to infinite dimensions. Furthermore, we derive bounds on the sum of expectation values of any set of anti-commuting observables. Such bounds can be used in entanglement detection and we show that Heisenberg-Weyl observables provide a first non-trivial example beyond the dichotomic case.PACS numbers: 07.10. Cm, 03.65.Ta, 03.65.Ud Introduction. The Bloch representation is a cornerstone of analyzing the characteristics of quantum systems. It was first introduced for two-level systems by Bloch [1] and has since been used in a wide variety of settings (for comprehensive reviews consult [2][3][4]). It is usually defined via a decomposition of the density matrix into a complete operator basis. Defining quantum states via the expectation values of a complete set of measurements gives a very practical account of their properties. Apart from being intuitive this approach gives convenient solutions for Hamiltonian evolutions (see, e.g., [5]) and has found many applications in entanglement theory [6][7][8][9][10][11][12].However, there is not a unique Bloch decomposition of a given quantum state; this fact may favor a particular representation over another for certain tasks. The canonical choice for a complete basis of observables is usually given by the so-called generalized Gell-Mann matrices, generators of the special unitary group [SU(d)]. Being a natural choice for higher-dimensional spin representations they have been extensively used in parametrizations of corresponding density matrices [4,13] and in entanglement detection. Other choices, such as the HeisenbergWeyl (HW) operators, and the non-Hermitian generalization of the 1/2-spin Pauli operators, have also been explored [3,[14][15][16][17][18]. While having some convenient properties, they are unitary, but not Hermitian matrices. Thus the associated Bloch vector itself has imaginary entries that do not correspond to expectation values of physical observables. This makes both the theoretical description and experimental realization more cumbersome and therefore requires more effort to identify the relevant parameters.In this article we introduce a Hermitian Bloch-basis derived from HW-operators. It conveniently combines multiple desirable properties of Bloch vector parametrizations, allowing a smooth transition to the infinite dimensional limit. We first explore properties such as (anti-) commutativity. We then proceed with the derivation of an inequality which bounds sums of anti-commuting observables with which we show in exemplary cases how one can construct powerful criteria for entanglement detection in this new basis. Finally we present a scheme for practical experimental acquisition through a Ramseytype measurement.Phase-space displacements. We start our a...

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Entangled singularity patterns of photons in Ince-Gauss modes

Cited by 80 publications

References 39 publications

Interface between path and orbital angular momentum entanglement for high-dimensional photonic quantum information

Interface between path and orbital angular momentum entanglement for high-dimensional photonic quantum information

Self-healing of quantum entanglement after an obstruction

Heisenberg-Weyl Observables: Bloch vectors in phase space

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