Tomography of the quantum state of photons entangled in high dimensions

Agnew, Megan; Leach, Jonathan; McLaren, Melanie; Roux, Filippus S.; Boyd, Robert W.

doi:10.1103/physreva.84.062101

Cited by 154 publications

(151 citation statements)

References 29 publications

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“…For reconstructing the full quantum state via state tomography, the number of required measurements is impractical even for relatively low dimensions because it scales quadratically with the quantum system dimension (24,27). Even if one had reconstructed the full quantum state, the quantification of the entangled dimensions is a daunting task analytically and even numerically (32).…”

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confidence: 99%

“…There, different multilevel degrees of freedom, such as spatial modes (13), time-energy (14), path (15,16), as well as continuous variables (17,18), have been used. Entanglement of spatial modes of photons has especially attracted much attention in recent years (19)(20)(21)(22)(23)(24)(25)(26)(27)(28), because it is readily available from optical nonlinear crystals and the number of involved modes of the entanglement can be very high (29).…”

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confidence: 99%

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Generation and confirmation of a (100 × 100)-dimensional entangled quantum system

Krenn

Huber

Fickler

et al. 2014

Proc. Natl. Acad. Sci. U.S.A.

311

254

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Entangled quantum systems have properties that have fundamentally overthrown the classical worldview. Increasing the complexity of entangled states by expanding their dimensionality allows the implementation of novel fundamental tests of nature, and moreover also enables genuinely new protocols for quantum information processing. Here we present the creation of a (100 × 100)-dimensional entangled quantum system, using spatial modes of photons. For its verification we develop a novel nonlinear criterion which infers entanglement dimensionality of a global state by using only information about its subspace correlations. This allows very practical experimental implementation as well as highly efficient extraction of entanglement dimensionality information. Applications in quantum cryptography and other protocols are very promising.photonic spatial modes | quantum optics | Schmidt rank | entanglement witness Q uantum entanglement of distant particles leads to correlations that cannot be explained in a local realistic way (1-3). To obtain a deeper understanding of entanglement itself, as well as its application in various quantum information tasks, increasing the complexity of entangled systems is important. Essentially, this can be done in two ways. The first method is to increase the number of particles involved in the entanglement (4). The alternative method is to increase the entanglement dimensionality of a system.Here we focus on the latter one, namely on the dimension of the entanglement. The text is structured as follows. After a short review of properties and previous experiments, we present a unique method to verify high-dimensional entanglement. Then we show how we experimentally create our high-dimensional two-photon entangled state. We analyze this state with our method and verify a 100 × 100-dimensional entangled quantum system. We conclude with a short outlook to potential future investigations.High-dimensional entanglement provides a higher information density than conventional two-dimensional (qubit) entangled states, which has important advantages in quantum communication. First, it can be used to increase the channel capacity via superdense coding (5). Second, high-dimensional entanglement enables the implementation of quantum communication tasks in regimes where mere qubit entanglement does not suffice. This involves situations with a high level of noise from the environment (6, 7), or quantum cryptographic systems where an eavesdropper has manipulated the random number generator involved (8). Moreover, the entangled dimensions of the whole Hilbert space also play a very interesting role in quantum computation: high-dimensional systems can be used to simplify the implementation of quantum logic (9). Furthermore, it has been found recently (10) that any continuous measure of entanglement (such as concurrence, entanglement of formation, or negativity) can be very small, while the quantum system still permits an exponential computation speedup over classical machines. This is not the case for the dim...

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confidence: 99%

mentioning

confidence: 99%

Generation and confirmation of a (100 × 100)-dimensional entangled quantum system

Krenn

Huber

Fickler

et al. 2014

Proc. Natl. Acad. Sci. U.S.A.

311

254

View full text Add to dashboard Cite

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“…QST was previously demonstrated with entangled qudits using OAM modes (up to d = 8) spatial modes (up to d = 3), and time-energy modes (up to d = 4) [16][17][18][19]. To the best of our knowledge, time-bin QST has been previously demonstrated for qubits only [20][21][22][23].…”

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confidence: 99%

Tomographic reconstruction of time-bin-entangled qudits

et al. 2016

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We describe an experimental implementation to generate and measure high-dimensional, time-bin entangled qudits. Two-photon time-bin entanglement is generated via spontaneous four-wave mixing in single-mode fiber. Unbalanced Mach-Zehnder interferometers transform selected time-bins to polarization entanglement, allowing standard polarization-projective measurements to be used for complete quantum state tomographic reconstruction. Here, we generate maximally entangled qubits (d = 2), qutrits (d = 3), and ququarts (d = 4), as well as other phase-modulated non-maximally entangled qubits and qutrits. We reconstruct and verify all generated states using maximum likelihood estimation tomography.

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“…For the full characterization of the density matrix in a Hilbert space of dimension d = 2N + 1, one needs to measure d 2 − 1 uknown quantities [20]. The quadratic scaling of the number of required measurement has posed a long-standing challenge for measuring states with large dimensions [42,43]. Through the use of a CCD/iCCD camera for post-selection, we are able to sequence individual images to find d elements of the density matrix simultaneously.…”

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confidence: 99%

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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Tomography of the quantum state of photons entangled in high dimensions

Cited by 154 publications

References 29 publications

Generation and confirmation of a (100 × 100)-dimensional entangled quantum system

Generation and confirmation of a (100 × 100)-dimensional entangled quantum system

Tomographic reconstruction of time-bin-entangled qudits

Wigner Distribution of Twisted Photons

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