LTu1E.3.pdf
Frontiers in Optics/Laser Science 2016 © OSA 2016
Quantum Information with Structured Light 2 , M N O’Sullivan2 , B Rodenburg2 , Z ˜ Mohammad Mirhosseini∗,1,2 , O S Magana-Loaiza Shi3 , M Malik2,4 , M P J Lavery5 , M J Padgett6 , D J Gauthier 7 , Robert W Boyd2,8 1 California 2 The 3 4
Institute of Technology, Pasadena, CA 91125
Institute of Optics, University of Rochester, Rochester, New York 14627
Department of Physics, University of South Florida, Tampa, FL 33620, USA
Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria 5 6
School of Engineering, University of Glasgow, Glasgow, G12 8QQ, UK
School of Physics and Astronomy, University of Glasgow, Glasgow, G12 8QQ, UK 7 8
Department of Physics, Duke University, Durham, NC 27708 USA
Department of Physics, University of Ottawa, Ottawa ON K1N 6N5, Canada ∗
[email protected]
Abstract: We investigate structured photons as carriers of quantum information. We describe our implementation of quantum cryptography with orbital angular momentum, and present our results on efficient implementation of quantum state tomography for structured light fields. OCIS codes: 270.5565, 270.5568, 270.5585.
Quantum information processing promises dramatic improvement in a variety of applications such as cryptography, computation, and metrology. Although proof-of-concept experiments can be realized with only a few quantum bits (“qubits”), the implementation of any realistic quantum protocol requires operation in a large Hilbert space. The transverse structure of the light field is an unbounded space that, in principle, can be used for encoding information. The ease of control and the large dimensionality of the spatial degree of freedom provides an attractive platform for realizing multilevel quantum bits (“qudits”). Further, the weak interaction of optical photons with the environment makes them prominent candidates for long-range quantum applications such as quantum key distribution. We utilize the orbital angular momentum (OAM) of photons as a resource for encoding quantum information [1, 2]. The recent progress in the technology of reconfigurable spatial light modulators has enabled precise control of the transverse mode of the optical field. We show that the utilization of OAM modes in free-space link reduces the diffraction-induced loss and cross talk and hence it is suitable for applications that involve line-of-sight laser communication. Moreover, the inherently discrete nature of orbital angular momentum lends itself to a straightforward implementation of a qudit [1]. We describe the implementation of a quantum key distribution system that is based on a 7-dimensional alphabet encoded in OAM and in the mutually unbiased basis of angular (ANG) modes. In our experimental implementation (see figure), we have achieved mutual information of 2.05 bits per sifted photon, which is more than twice the maximum allowable capacity of a two-dimensional QKD system [3]. In our experiment, the precise measurement of OAM is realized by a mode-sorting device that can achieve a mode discrimination of greater than 92%. The symbol error rate of our scheme is measured as 10.5%, which is sufficient for proving security against coherent and individual eavesdropping attacks for an infinite key. While our experiment demonstrates the feasibility of using OAM modes for QKD, several challenges need to be addressed before such a protocol can be employed for practical applications. We analyze these limitations and lay out a clear path for enhancing our system for realizing practical, high-dimensional QKD using the currently existing technology. The quantum state of a superposition of OAM states can be found through the method of quantum state tomography [4]. However, quantum state tomography becomes increasingly challenging for larger dimensions. Here, we discuss a recently developed alternative for characterizing the transverse structure of photons. Direct Measurement, originally developed by Lundeen et al, provides a simple means of characterizing large-dimensional states with the aid of complex weak values [5]. We have applied this method to characterization of OAM modes and their superpositions.
LTu1E.3.pdf
Frontiers in Optics/Laser Science 2016 © OSA 2016
Fig. 1. a) The experimental setup for realization of QKD with orbital angular momentum of photons. b) The alphabet. CCD images of the intensity profiles in two complementary spatial bases of OAM and ANG (d = 7). Through the use of this method, we have been able to measure the probability amplitudes and the relative phase of the OAM components of an arbitrary light field in a 27-dimensional state space [6]. In addition, we have improved direct measurement by combining it with a computational technique known as compressive sensing. We have found that compressive direct measurement, can be used to drastically reduce the number of experiments required for the characterization of a wave function. Our experimental results demonstrate accurate determination of a 192-dimensional state with a fidelity of 90% using only 25 percent of measurements that are needed for the standard direct measurement approach. Taking this method to the extremes, we have shown a 350-fold speed up in the process of characterization a 19200-dimensional state [7]. References 1. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001). 2. G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, “Freespace information transfer using light beams carrying orbital angular momentum,” Opt. Express 12, 5448–5456 (2004). 3. M. Mirhosseini, O. S. Maga˜na-Loaiza, M. N. O’Sullivan, B. Rodenburg, M. Malik, M. P. J. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New J. Phys. 17, 033,033 (2015). 4. M. Mirhosseini, O. S. Maga˜na-Loaiza, C. Chen, S. M. H. Rafsanjani, and R. W. Boyd, “Wigner Distribution of Twisted Photons,” Phys. Rev. Lett. 116, 130,402 (2016). 5. J. S. Lundeen, B. Sutherland, A. Patel, C. Stewart, and C. Bamber, “Direct measurement of the quantum wavefunction.” Nature 474, 188–191 (2011). 6. M. Malik, M. Mirhosseini, M. P. J. Lavery, J. Leach, M. J. Padgett, and R. W. Boyd, “Direct measurement of a 27-dimensional orbital-angular-momentum state vector,” Nat. Commun. 5, 3115 (2014). 7. M. Mirhosseini, O. S. Maga˜na-Loaiza, S. M. Hashemi Rafsanjani, and R. W. Boyd, “Compressive Direct Measurement of the Quantum Wave Function,” Phys. Rev. Lett. 113, 090,402 (2014).
