Experimental Realization of Quantum Tomography of Photonic Qudits via Symmetric Informationally Complete Positive Operator-Valued Measures

Bent, Nicolas; Qassim, Hammam; Tahir, Afaq; Sych, Denis; Leuchs, Gerd; Sánchez-Soto, Luis L.; Karimi, Ebrahim; Boyd, Robert W.

doi:10.1103/physrevx.5.041006

Cited by 132 publications

(114 citation statements)

References 40 publications

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“…To experimentally verify shape of heralded photon the method can be accompanied with one of tomographic techniques, provided informationally complete measurements performed on the photon [39][40][41][42][43].…”

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confidence: 99%

Temporal shaping of single photons enabled by entanglement

et al. 2017

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We propose a method to produce pure single photons with an arbitrary designed temporal shape in a heralded, lossless and scalable way. As the indispensable resource, the method uses pairs of time-energy entangled photons. To accomplish the shaping, one photon of a pair undergoes temporal modulation according to the desired shape. Subsequent frequency-resolving detection of the photon heralds its entangled counterpart in a pure quantum state with a temporal shape non-locally affected by the modulation. We found conditions for the shape of the heralded photon to reproduce the modulation function. The method can be implemented with various sources of time-energy entangled photons. In particular, using entangled photons from the parametric down-conversion the method enables generation of pure photons with tunable shape within unprecedentedly broad range of temporal durations -from tenths of femtoseconds to microseconds. Proposed shaping of single photons will push forward implementation of scalable multidimensional quantum information protocols, efficient photon-matter coupling and quantum control at the level of single quanta.Single photons are indispensable tool in quantum information, quantum communication and quantum metrology [1]. Depending on specific application, photons must be tuned in wavelength, bandwidth, polarization, and other degrees of freedom. For example, to transmit information over optical fibers one uses photons at telecom wavelengths, while photonatom coupling requires wavelength and bandwidth of photons matched to the corresponding atomic transition.It has been realized in the last decade that full control over the spatio-temporal shape of a single photon light [2, 3] is required in a number of applications. For example, photons, having identical Lorentzian spectral shapes, can exhibit opposite temporal shapes -exponential decaying or rising -depending on spectral distribution of the phase. As a result, photons with exponential decaying shape excite a two-level atom in free space only with 50% efficiency, while exponentially rising photons with 100% efficiency [4][5][6]. There are other situations where the temporal photon shape is important: symmetric shape is optimal for cavity QED quantum communication [7]; Gaussian shape is superior for experiments relying on single-photon interference [8]. Furthermore, development of sources of shaped photons will push forward photonic implementation of high-dimensional quantum information protocols, e.g. quantum key distribution [9][10][11][12][13][14].Present-day methods for producing temporally shaped photons can be divided in two groups: single photons are shaped either during the generation process or photon shaping is performed after the generation. Methods of the first group are typically based on control of quantum emitters (single atom [15,16], ion [17], atomic ensemble [18], quantum dot [19]). Development of these methods is promising for deterministic production of shaped photons, however the methods often require sophisticated and costly setup...

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Section: −1 Cmentioning

confidence: 99%

Temporal shaping of single photons enabled by entanglement

et al. 2017

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“…[87] can in principle be used to store OAM qudits for d > 2. Hence, given that only experimental constraints limit the dimensionality of the qudits which may be encoded into OAM, and a range of high-quality measurements have been demonstrated on OAM-encoded qudits [15], OAM qudits may be particularly well suited to mediating gates on a register of atomic-ensemble-based qudits, with very high values of d possible in principle.…”

Section: Physical Implementationmentioning

confidence: 99%

Ancilla-driven quantum computation for qudits and continuous variables

et al. 2017

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(2017) 'Ancilla-driven quantum computation for qudits and continuous variables. ', Physical review A., 95 (5). 052317.Further information on publisher's website:https://doi.org/10.1103/PhysRevA.95.052317Publisher's copyright statement:Reprinted with permission from the American Physical Society: Physical Review A 95, 052317 c (2017) by the American Physical Society. Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modied, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society.Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. Although qubits are the leading candidate for the basic elements in a quantum computer, there are also a range of reasons to consider using higher-dimensional qudits or quantum continuous variables (QCVs). In this paper, we use a general "quantum variable" formalism to propose a method of quantum computation in which ancillas are used to mediate gates on a well-isolated "quantum memory" register and which may be applied to the setting of qubits, qudits (for d > 2), or QCVs. More specifically, we present a model in which universal quantum computation may be implemented on a register using only repeated applications of a single fixed two-body ancilla-register interaction gate, ancillas prepared in a single state, and local measurements of these ancillas. In order to maintain determinism in the computation, adaptive measurements via a classical feed forward of measurement outcomes are used, with the method similar to that in measurement-based quantum computation (MBQC). We show that our model has the same hybrid quantum-classical processing advantages as MBQC, including the power to implement any Clifford circuit in essentially one layer of quantum computation. In some physical settings, high-quality measurements of the ancillas may be highly challenging or not possible, and hence we also present a globally unitary model which replaces the need for measurements of the ancillas with the requirement for ancillas to be prepared in states from a fixed orthonormal basis. Finally, we discuss settings in which these models may be of practical interest.

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“…The most general description of a quantum state requires knowledge of its density matrix, which can be found through use of standard quantum state tomography [19,20]. However, quantum state tomography in the OAM basis requires the capability to perform projective measurements on arbitrary superpositions of two or more OAM eigenstates [21], a task that remains challenging due to technical limitations such as variations in the efficiency of measuring different OAM modes and the cross-talk between neighboring modes [22].In this article, we propose and demonstrate a method for obtaining the Wigner distribution for the azimuthal structure of light as an alternative to conventional quantum state tomography. We achieve this task by experimentally finding the projections of the density matrix in the basis of azimuthal angle and subsequently calculating the Wigner function via a linear transformation.…”

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Wigner Distribution of Twisted Photons

et al. 2016

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We present the first experimental characterization of the azimuthal Wigner distribution of a photon. Our protocol fully characterizes the transverse structure of a photon in conjugate bases of orbital angular momentum (OAM) and azimuthal angle (ANG). We provide a test of our protocol by characterizing pure superpositions and incoherent mixtures of OAM modes in a seven-dimensional space. The time required for performing measurements in our scheme scales only linearly with the dimension size of the state under investigation. This time scaling makes our technique suitable for quantum information applications involving a large number of OAM states.Ever since its introduction in 1932 [1], the Wigner distribution has been widely applied in different fields of study ranging from statistical mechanics, and optics [2] in physics to more applied fields such as electrical engineering and even seismology [3]. In physics, the Wigner distribution has been utilized to bring the machinery of phase-space statistical mechanics into study of quantum physics [4]. Wigner distribution provides a comprehensive characterization of the system, and as a quasiprobability distribution the negativity of the Wigner distribution signals a wave-like behavior [5,6].The orbital angular momentum (OAM) of single photons has lately been identified as a valuable platform for realizing multilevel quantum systems [7,8]. The discrete nature of OAM makes it attractive for encoding quantum [9] and classical information [10]. The ongoing research suggests that there is no fundamental limit to the maximum value of OAM that a photon can carry. In a recent experiment, quantum entanglement was demonstrated between states differing by 600 in their value of OAM [11]. The full characterization of a quantum state in the Hilbert space of OAM poses a serious experimental challenge.A large body of previous research has enabled efficient and accurate projective measurements of light's OAM [8,[12][13][14][15][16]. Quantum mechanically, a pure state in the Hilbert space of OAM is described by a discrete state vector. Thus, the probability distribution provided by projective measurements along with the knowledge of relative phase between the different OAM components found by interferometry adequately described a pure state [17]. Nevertheless, pure states are only a restricted set of physical states, because the vast majority of conceivable states are mixed states [18]. The most general description of a quantum state requires knowledge of its density matrix, which can be found through use of standard quantum state tomography [19,20]. However, quantum state tomography in the OAM basis requires the capability to perform projective measurements on arbitrary superpositions of two or more OAM eigenstates [21], a task that remains challenging due to technical limitations such as variations in the efficiency of measuring different OAM modes and the cross-talk between neighboring modes [22].In this article, we propose and demonstrate a method for obtaining the Wigner distributio...

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Experimental Realization of Quantum Tomography of Photonic Qudits via Symmetric Informationally Complete Positive Operator-Valued Measures

Cited by 132 publications

References 40 publications

Temporal shaping of single photons enabled by entanglement

Temporal shaping of single photons enabled by entanglement

Ancilla-driven quantum computation for qudits and continuous variables

Wigner Distribution of Twisted Photons

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