Abstract:We introduce a novel time-frequency quantum key distribution (TFQKD) scheme based on photon pairs entangled in these two conjugate degrees of freedom. The scheme uses spectral detection and phase modulation to enable measurements in the temporal basis by means of time-to-frequency conversion. This allows large-alphabet encoding to be implemented with realistic components. A general security analysis for TFQKD with binned measurements reveals a close connection with finite-dimensional QKD protocols and enables analysis of the effects of dark counts on the secure key size. References and links1. JG Rarity, PR Tapster, JG Walker, and S Seward. Experimental demonstration of single photon rangefinding using parametric downconversion.

* These authors contributed equally to this work.The ability to manipulate the spectral-temporal waveform of optical pulses has enabled a wide range of applications from ultrafast spectroscopy 1 to high-speed communications. 2 Extending these concepts to quantum light has the potential to enable breakthroughs in optical quantum science and technology. [3][4][5] However, filtering and amplifying often employed in classical pulse shaping techniques are incompatible with non-classical light. Controlling the pulsed mode structure of quantum light requires efficient means to achieve deterministic, unitary manipulation that preserves fragile quantum coherences. Here we demonstrate an electro-optic method for modifying the spectrum of non-classical light by employing a time lens. [6][7][8] In particular we show highlyefficient wavelength-preserving six-fold compression of single-photon spectral intensity bandwidth, enabling over a two-fold increase of singlephoton flux into a spectrally narrowband absorber.These results pave the way towards spectral-temporal photonic quantum information processing and facilitate interfacing of different physical platforms 9,10,12 where quantum information can be stored 12 or manipulated. 13 The time-frequency (TF) degree of freedom of nonclassical light has come to the fore as a promising candidate for multidimensional quantum information science, 3-5 due in part to its compatibility with integrated photonic platforms and fibre networks. 14 Recent research efforts have diversified from generation of singlephoton wavepackets with controlled TF properties 15 and their characterization 15 to active modification of the TF state of quantum light. Tremendous progress has been made in techniques to shift the central frequency of quantum light, using nonlinear optical methods. [2][3][4]10,12,17,18 Going beyond frequency conversion towards pulse shaping, for example bandwidth or general spectral-amplitude manipulation, has proven challenging for nonlinear optical methods to realize with low-noise, deterministic, broad spectral range operation required for non-classical light.Essential to nearly all optical experiments is the concept of mode matching, whether to achieve high-visibility interference or strong absorption. In the TF domain, spectral mode matching must be achieved for efficient interfacing between physical systems whose optical emission varies both in central wavelength and characteristic bandwidths, such as quantum dots and atomic vapours. Spectral bandwidth manipulation is an essential capability for interfacing different systems with characteristic bandwidths ranging from MHz to THz. 23,24 Here we experimentally demonstrate TF manipulation of heralded single-photon wavepackets in a low-loss, all-fibre electro-optic platform, which is intrinsically free from optical noise and does not spectrally shift the central wavelength of the pulse. We apply an electro-optic time lens 6,8 to single-photon pulses, achieving wavelength-preserving six-fold bandwidth compression of single-photon ...

We experimentally demonstrate the generation of multi-photon Fock states with up to three photons in well-defined spatial-temporal modes synchronized with a classical clock. The states are characterized using quantum optical homodyne tomography to ensure mode selectivity. The three-photon Fock states are probabilistically generated by pulsed spontaneous parametric down conversion at a rate of one per second, enabling complete characterization in 12 hours.

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 wavepacket 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.The frequency of a single light quantum, or photon, is a key physical property of individual excitations of the quantized electromagnetic field [1], which were introduced to describe the photoelectric effect [2]. Frequency is a mode characteristic, just as polarization, transverse-spatial amplitude, and direction of propagation define the modes of electromagnetic radiation. Thus frequency can be transformed using linear-optical elements in much the same way lenses transform transverse-spatial modes and wave plates manipulate polarization modes. Frequency is not an immutable property of photons-it can be coherently and deterministically modified. For example, retroreflection from a moving mirror results in a frequency shift due to the Doppler effect [3,4]. The various independent degrees of freedom that comprise the modes of light can be used to encode information in the electromagnetic field, namely position-momentum, time-frequency, and polarization. Information-technology applications require precise means for manipulation and measurement of light in the encoding degree of freedom. Many preliminary demonstrations of quantum optical technologies have utilized polarization, path or transverse-spatial mode encoding. These degrees of freedom are limited to relatively few quantum bits that can be practically addressed per photon within an integrated-optics platform, in which high-stability, low-loss multiphoton interference, necessary for optical quantum technologies, can occur. Recently, the time-frequency (TF) mode structure of light has come to the fore in quantum photonics as an ideal means of quantum information encoding for integrated optical quantum technologies [5][6][7][8][9][10][11].Essential to both quantum and classical technologies based upon TF mode encoding is the ability to control the pulsemode structure of light-where the central frequency and arrival time play prominent roles. In the classical domain the primary methods to control an optical pulse are based upon direct modification of the wave packet by amplifying and filtering different frequency and time components [12,13]. This approach to pulse shaping is incompatible with quantum states of light owing to noise and signal degradation arising from amplification and loss, resulting in destruction of the fragile quantum coherences between di...

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