Large-Alphabet Quantum Key Distribution Using Energy-Time Entangled Bipartite States

Ali-Khan, I.; Broadbent, Curtis J.; Howell, John C.

doi:10.1103/physrevlett.98.060503

Cited by 232 publications

(197 citation statements)

References 19 publications

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“…We measured the joint spectral intensity, describing the twophoton state's frequency distribution, see Methods. Specifically, we routed different frequency 4 modes of the signal and idler photons to two single photon detectors and counted photon coincidences for all sets of mode combinations. As shown in Fig.…”

Section: Methodsmentioning

confidence: 99%

On-chip generation of high-dimensional entangled quantum states and their coherent control

Kues

Reimer

Roztocki

et al. 2017

Nature

840

656

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[8][9][10][11] . Here, we demonstrate on- as schematized in Fig. 1. In particular, we used a spectrally-filtered mode-locked laser to excite a single resonance of the microring at ~1550 nm wavelength, in turn producing pairs of correlated signal and idler photons spectrally-symmetric to the excitation field and which cover multiple resonances, see Fig. 1. The individual photons were intrinsically generated in a superposition of multiple frequency modes and owing the energy conservation of SFWM, this approach leads to the realization of a two-photon high-dimensional frequency-entangled state.We performed two experiments to characterize the dimensionality of the generated state. The large free spectral range (FSR) of the ring cavity (~200 GHz), i.e. the spectral separation between adjacent resonance modes, enabled us to use a commercially available telecommunications programmable filter (see Methods) for individually selecting and manipulating the states in these modes (given the filter's operational bandwidth of 1527.4 to 1567.5 nm, we were able to access 10 signal and 10 idler resonances). We measured the joint spectral intensity, describing the twophoton state's frequency distribution, see Methods. Specifically, we routed different frequency 4 modes of the signal and idler photons to two single photon detectors and counted photon coincidences for all sets of mode combinations. As shown in Fig. 2a, photon coincidences were measured only for mode combinations spectrally-symmetric to the excitation, a characteristic of frequency-entangled states. In addition, we evaluate the Schmidt number of our source. This parameter describes the lowest number of significant orthogonal modes in a bipartite system, and therefore describes its effective dimension. Through a Schmidt mode decomposition of the correlation matrix (see Methods), we extracted the lower bound for the Schmidt number to be 9.4, see Fig. 2b.Due to the narrow spectral linewidth of the photons (~800 MHz) and the related long coherence time (~0.6 ns), the effective time resolution of our full detection system (~100 ps) was sufficient to perform time-domain measurements and extract the maximal dimensionality of the state, seeMethods. Specifically, we measured the second-order coherence of the signal and idler fields using These measurements confirmed that one photon pair simultaneously spans multiple frequency modes, forming a high-dimensional entangled state of the form, with ∑| | 2 = 1 (Eq. 1).Here | ⟩ s and | ⟩ i are pure, single-frequency quantum states of the signal (s) and idler (i) photons, and k=1,2,…,D is the mode number, as indicated in Fig. 3 In general, the exploitation of quDit states for quantum information processing motivates the need for high-dimensional operations that enable access to multiple modes with a minimum number of components. While the individual elements (phase shifters and beam splitters) employed in the framework of spatial-mode quantum information processing usually operate on only one or two modes at a time 1 , the frequency...

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Section: Methodsmentioning

confidence: 99%

On-chip generation of high-dimensional entangled quantum states and their coherent control

Kues

Reimer

Roztocki

et al. 2017

Nature

840

656

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“…Sect. 17.1 of this chapter we noted that the process of spontaneous parametric downconversion can lead to entanglement in several different degrees of freedom, including position-momentum [26], time-energy [9,10], polarization [3,4], and superpositions of OAM modes [27] or explicitly angle-OAM [28]. In this section we provide a brief account of work aimed at studying these various types of entanglement.…”

Section: Fundamental Quantum Studies Of Structured Light Beamsmentioning

confidence: 99%

“…It seems that the product of uncertainty in tightness in the correlation of energies multiplied the uncertainty in the correlation of times can be arbitrarily small and certainly smaller than the value 1 2 ℏ that one might have envisaged from the naive application of uncertainty relations [9,10]. The situation is the essence of entanglement: the resolution of this seeming paradox is that a measurement that one performs on the signal photon results in a restriction of our ability to predict the properties of the idler photon, even if that idler photon is arbitrarily distant from…”

Section: Introductionmentioning

confidence: 99%

Quantum Mechanical Properties of Light Fields Carrying Orbital Angular Momentum

Boyd

Padgett

2016

Optics in Our Time

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“…Note that a long pump coherence time corresponds to a large alphabet (the dimensionality is essentially given by the ratio between the pump coherence time and the photon pair bandwidth, in turn determined by the cavity lifetime), i.e., high number of bits of information per photon [37]. When using an amplifier with a long gain medium (e.g., a standard erbium-doped fiber amplifier, EDFA), the external cavity length is typically of the order of tens of meters, leading to a FSR well below the ring resonance linewidth.…”

Section: Figmentioning

confidence: 99%

“…The higher dimensionality allows one, e.g., to increase the quantity of information carried by a single photon. Different high dimensional variables, either discrete such as orbital angular momentum [34,35], or continuous such as time (or its conjugate, frequency) [36,37] and space (or its conjugate, the transverse wave vector) [38] have been considered and investigated in the framework of bulk optics, yet mainly with χ (2) media.…”

Section: Introductionmentioning

confidence: 99%

Multifrequency sources of quantum correlated photon pairs on-chip: a path toward integrated Quantum Frequency Combs

et al. 2016

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Recent developments in quantum photonics have initiated the process of bringing photonic-quantumbased systems out-of-the-lab and into real-world applications. As an example, devices to enable the exchange of a cryptographic key secured by the laws of quantum mechanics are already commercially available. In order to further boost this process, the next step is to transfer the results achieved by means of bulky and expensive setups into miniaturized and affordable devices. Integrated quantum photonics is exactly addressing this issue. In this paper, we briefly review the most recent advancements in the generation of quantum states of light on-chip. In particular, we focus on optical microcavities, as they can offer a solution to the problem of low efficiency that is characteristic of the materials typically used in integrated platforms. In addition, we show that specifically designed microcavities can also offer further advantages, such as compatibility with telecom standards (for exploiting existing fibre networks) and quantum memories (necessary to extend the communication distance), as well as giving a longitudinal multimode character for larger information transfer and processing. This last property (i.e., the increased dimensionality of the photon quantum state) is achieved through the ability to generate multiple photon pairs on a frequency comb, corresponding to the microcavity resonances. Further achievements include the possibility of fully exploiting the polarization degree of freedom, even for integrated devices. These results pave the way for the generation of integrated quantum frequency combs that, in turn, may find important applications toward the realization of a compact quantum-computing platform.

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Large-Alphabet Quantum Key Distribution Using Energy-Time Entangled Bipartite States

Cited by 232 publications

References 19 publications

On-chip generation of high-dimensional entangled quantum states and their coherent control

On-chip generation of high-dimensional entangled quantum states and their coherent control

Quantum Mechanical Properties of Light Fields Carrying Orbital Angular Momentum

Multifrequency sources of quantum correlated photon pairs on-chip: a path toward integrated Quantum Frequency Combs

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