Erik Woodhead

Implementing two-photon interference in the frequency domain with electro-optic phase modulators

Frequency-entangled photons can be readily produced using parametric down-conversion. We have recently shown how such entanglement could be manipulated and measured using electro-optic phase modulators and narrow-band frequency filters, thereby leading to two-photon interference patterns in the frequency domain. Here we introduce new theoretical and experimental developments showing that this method is potentially a competitive platform for the realization of quantum communication protocols in standard telecommunication fibres. We derive a simple theoretical expression for the coincidence probabilities and use it to optimize a Bell inequality. Furthermore, we establish an equivalence between the entangled-photon scheme and a classical interference scheme. Our measurements of two-photon interference in the frequency domain yield raw visibilities in excess of 99%. We use our high-quality setup to experimentally validate the theoretical predictions, and in particular we report a violation of the CH74 inequality by more than 18 standard deviations.

Effects of preparation and measurement misalignments on the security of the Bennett-Brassard 1984 quantum-key-distribution protocol

The ideal Bennett-Brassard 1984 (BB84) quantum-key-distribution protocol is based on the preparation and measurement of qubits in two alternative bases differing by an angle of π/2. Any real implementation of the protocol, though, will inevitably introduce misalignments in the preparation of the states and in the alignment of the measurement bases with respect to this ideal situation. Various security proofs take into account (at least partially) such errors, i.e., show how Alice and Bob can still distill a secure key in the presence of these imperfections. Here, we consider the complementary problem: How can Eve exploit misalignments to obtain more information about the key than would be possible in an ideal implementation? Specifically, we investigate the effects of misalignment errors on the security of the BB84 protocol in the case of individual attacks, where necessary and sufficient conditions for security are known. Though the effects of these errors are small for expected deviations from the perfect situation, our results nevertheless show that Alice and Bob can incorrectly conclude that they have established a secure key if the inevitable experimental errors in the state preparation and in the alignment of the measurements are not taken into account. This gives further weight to the idea that the formulation and security analysis of any quantum cryptography protocol should be based on realistic assumptions about the properties of the apparatus used. Additionally, we note that BB84 seems more robust against alignment imperfections if both the x and z bases are used to generate the key.

Semi-device-independent QKD Based on BB84 and a CHSH-Type Estimation

Device-independent quantum key distribution (QKD) aims to certify the security of a cryptographic key generated between two parties based only on the violation of a Bell inequality. This strongest possible form of QKD requires the manipulation of entanglement, and is thus impossible to implement in a one-way (“prepare and measure”) scheme. Here, we introduce a semi-device-independent QKD scheme in the prepare-and-measure configuration where the only assumption is a bound on the dimension of the Hilbert space, and prove its security against collective attacks. Our scheme can be understood as a modification of the original BB84 protocol where an extra CHSH-type estimation is carried out by Bob on the qubits sent by Alice.

Two-photon experiments in the frequency domain

We report on the study of two-photon interference in the frequency domain. Bell and Hong-Ou-Mandel experiments are investigated. These experiments involve the manipulation of photons in the frequency domain, using off-the-shelf telecommunication components such as electro-optic phase modulators and narrow-band frequency filters. In the first experiment, photon pairs entangled in frequency are created and separated. Each photon is then directed through an independent electro-optic phase modulator. Variation of the radio-frequency parameters of the modulation gives rise to a well-controlled Bessel-shape two-photon interference pattern in the frequency domain. This is efficiently measured with narrow-band frequency filters and superconducting single photon detectors. Experimental measurements exhibit high visibilities (over 99 percent both for net and raw visibilities) and allow the (theoretically proven) optimal violation of a Bell inequality for our setup (by more than 18 standard deviations). The second experiment is a Hong-Ou-Mandel experiment in the frequency domain. We show that a grating (spatial domain) or a phase modulator (temporal domain) can be seen as a frequency beam splitter. A broadband spectrum of photon pairs is divided into two interleaved frequency combs, each one used as an independent input to this acting beam splitter. A theoretical calculation shows clear photon anti-bunching behavior.

Bell inequality violation in frequency domain using 25 GHz frequency sideband modulation architecture

Since the pioneering work of A. Ekert, it has been known that entangled quantum states could be used for quantum key distribution (QKD). Using entangled photons could potentially allows the realization of key distribution protocols over distances greater than a few hundred kilometres, and allows security certification without a priori trust of the devices [1]. Although practical QKD methods based on time-bin entanglement have seen significant development, it is only recently that frequency-bin entanglement has been investigated [2]. In what follows, we report the performance of a new automated architecture based on 25 GHz frequency sideband modulation designed specifically for manipulation of frequency-bins, with potential applications such as QKD.