Multidimensional quantum information based on single-photon temporal wavepackets

Time-frequency optical filtering: efficiency vs. temporal-mode discrimination in incoherent and coherent implementations

Time-frequency (TF) filtering of analog signals has played a crucial role in the development of radio-frequency communications and is currently being recognized as an essential capability for communications, both classical and quantum, in the optical frequency domain. How best to design optical time-frequency (TF) filters to pass a targeted temporal mode (TM), and to reject background (noise) photons in the TF detection window? The solution for 'coherent' TF filtering is known-the quantum pulse gate-whereas the conventional, more common method is implemented by a sequence of incoherent spectral filtering and temporal gating operations. To compare these two methods, we derive a general formalism for two-stage incoherent time-frequency filtering, finding expressions for signal pulse transmission efficiency, and for the ability to discriminate TMs, which allows the blocking of unwanted background light. We derive the tradeoff between efficiency and TM discrimination ability, and find a remarkably concise relation between these two quantities and the time-bandwidth product of the combined filters. We apply the formalism to two examples-rectangular filters or Gaussian filters-both of which have known orthogonal-function decompositions. The formalism can be applied to any state of light occupying the input temporal mode, e.g., 'classical' coherent-state signals or pulsed single-photon states of light. In contrast to the radio-frequency domain, where coherent detection is standard and one can use coherent matched filtering to reject noise, in the optical domain direct detection is optimal in a number of scenarios where the signal flux is extremely small. Our analysis shows how the insertion loss and SNR change when one uses incoherent optical filters to reject background noise, followed by direct detection, e.g. photon counting. We point out implications in classical and quantum optical communications. As an example, we study quantum key distribution, wherein strong rejection of background noise is necessary to maintain a high quality of entanglement, while high signal transmission is needed to ensure a useful key generation rate.

Photonic quantum information processing: a review

Photonic quantum technologies represent a promising platform for several applications, ranging from long-distance communications to the simulation of complex phenomena. Indeed, the advantages offered by single photons do make them the candidate of choice for carrying quantum information in a broad variety of areas with a versatile approach. Furthermore, recent technological advances are now enabling first concrete applications of photonic quantum information processing. The goal of this manuscript is to provide the reader with a comprehensive review of the state of the art in this active field, with a due balance between theoretical, experimental and technological results. When more convenient, we will present significant achievements in tables or in schematic figures, in order to convey a global perspective of the several horizons that fall under the name of photonic quantum information.

Experimental Demonstration of Four-Dimensional Photonic Spatial Entanglement between Multi-core Optical Fibres

Fibre transport of multi-dimensional photonic quantum states promises high information capacity per photon without space restriction. This work experimentally demonstrates transmission of spatial ququarts through multi-core optical fibres and measurement of the entanglement between two fibres with quantum state analyzers, each composed of a spatial light modulator and a single-mode fibre. Quantum state tomography reconstructs the four-dimension entangled state that verifies the nonlocality through concurrences in two-dimensional subspaces, a lower bound of four-dimensional concurrence and a Bell-type CGLMP inequality.

Spectral Shearing of Quantum Light Pulses by Electro-Optic Phase Modulation

Frequency conversion of nonclassical light enables robust encoding of quantum information based upon spectral multiplexing that is particularly well-suited to integrated-optics platforms. Here we present an intrinsically deterministic linear-optics approach to spectral shearing of quantum light pulses and show it preserves the wave-packet coherence and quantum nature of light. The technique is based upon an electro-optic Doppler shift to implement frequency shear of heralded single-photon wave packets by ±200  GHz, which can be scaled to an arbitrary shift. These results demonstrate a reconfigurable method to controlling the spectral-temporal mode structure of quantum light that could achieve unitary operation.

Experimental demonstration of a flexible time-domain quantum channel

We present an experimental realization of a flexible quantum channel where the Hilbert space dimensionality can be controlled electronically. Using electro-optical modulators (EOM) and narrow-band optical filters, quantum information is encoded and decoded in the temporal degrees of freedom of photons from a long-coherence-time single-photon source. Our results demonstrate the feasibility of a generic scheme for encoding and transmitting multidimensional quantum information over the existing fiber-optical telecommunications infrastructure.

Continuous-variable quantum computing in optical time-frequency modes using quantum memories

We develop a scheme for time-frequency encoded continuous-variable cluster-state quantum computing using quantum memories. In particular, we propose a method to produce, manipulate, and measure two-dimensional cluster states in a single spatial mode by exploiting the intrinsic time-frequency selectivity of Raman quantum memories. Time-frequency encoding enables the scheme to be extremely compact, requiring a number of memories that are a linear function of only the number of different frequencies in which the computational state is encoded, independent of its temporal duration. We therefore show that quantum memories can be a powerful component for scalable photonic quantum information processing architectures.

Efficient sorting of quantum-optical wave packets by temporal-mode interferometry

Long-distance quantum communication relies on storing and retrieving photonic qubits in orthogonal field modes. The available degrees of freedom for photons are polarization, spatial-mode profile, and temporal/spectral profile. To date, methods exist for decomposing, manipulating, and analyzing photons into orthogonal polarization modes and spatial modes. Here we propose and theoretically verify the first highly efficient method to carry out analogous operations for temporally and spectrally overlapping, but field-orthogonal, temporal modes. The method relies on cascaded nonlinear-optical quantum frequency conversion.

Linear optical quantum computing in a single spatial mode

We present a scheme for linear optical quantum computing using time-bin-encoded qubits in a single spatial mode. We show methods for single-qubit operations and heralded controlled-phase (cphase) gates, providing a sufficient set of operations for universal quantum computing with the Knill-Laflamme-Milburn [Nature (London) 409, 46 (2001)] scheme. Our protocol is suited to currently available photonic devices and ideally allows arbitrary numbers of qubits to be encoded in the same spatial mode, demonstrating the potential for time-frequency modes to dramatically increase the quantum information capacity of fixed spatial resources. As a test of our scheme, we demonstrate the first entirely single spatial mode implementation of a two-qubit quantum gate and show its operation with an average fidelity of 0.84±0.07.