Harnessing high-dimensional hyperentanglement through a biphoton frequency comb

Abstract

Increasing the dimensionality of quantum entanglement is a key enabler for high-capacity quantum communications and key distribution [1, 2], quantum computation [3] and information processing [4, 5], imaging [6], and enhanced quantum phase measurement [7,8]. A large Hilbert space can be achieved through entanglement in more than one degree of freedom (known as hyperentanglement [2,7,9]), where each degree of freedom can also be expanded to more than two dimensions (known as high-dimensional entanglement). The high-dimensional entanglement can be prepared in several physical attributes, for example, in orbital angular momentum [1,[10][11][12] and other spatial modes [13][14][15]. The drawback of these high-dimensional spatial states is complicated beam-shaping for entanglement generation and detection, which reduces the brightness of the sources as the dimension scales up, and complicates their use in optical-fiber-based communications systems. In contrast, the continuous-variable energy-time entanglement [16][17][18][19][20][21][22] is intrinsically suitable for high-dimensional coding and, if successful, can potentially be generated and be communicated in the telecommunication network. However, most studies focus on time-bin entanglement, which is discrete-variable entanglement with typical dimensionality of two [23][24][25]. Difficulties in pump-pulse shaping and phase control limit the dimensionality of the time-bin entanglement [26], and high-dimensional time-bin entanglement has not been fully characterized because of the overwhelmingly complicated analyzing interferometers. On the other hand, a biphoton state with a comb-like spectrum could potentially serve for high-dimensional entanglement generation and take full advantage of the continuous-variable energy-time subspace. Based on this state, promising applications have been proposed for quantum computing, secure wavelength-division multiplexing, and dense quantum key distribution [3,27,28]. A phase-coherent biphoton frequency comb (BFC) is also known for 3 its mode-locked behavior in its second-order correlation. Unlike classical frequency combs, where mode-locking directly relies on phase coherence over individual comb lines, the mode-locked behavior of a BFC is the representation of the phase coherence of a biphoton wavepacket over comb-line pairs, and results in periodic recurrent correlation at different time-bins [29, 30]. This time correlation feature can be characterized through quantum interference when passing the BFC through an unbalanced Hong-Ou-Mandel (HOM)-type interferometer [31]. A surprising revival of the correlation dips can be observed at time-bins with half the period of the BFC revival time.However, because of the limited type-I collinear spontaneous parametric downconversion (SPDC) configuration in the prior studies [29], post-selection was necessary for the BFC generation where the signal and idler photons are indistinguishable, limiting the maximum two-photon interference to 50 %.Here we achieve high-dimensional hyperentangle...

50-GHz-spaced comb of high-dimensional frequency-bin entangled photons from an on-chip silicon nitride microresonator

“…Typical QIP systems are based on two-level quantum states, also called qubits. To simplify the complexity of quantum circuits [10,11] and increase the practicality of quantum computation, high-dimensional entangled states (entangled qudits) are strong candidates as a result of their robustness and stronger immunity to noise, compared to two-dimensional systems [12][13][14][15].…”

Mutual Unbiasedness in Coarse-Grained Continuous Variables

“…A most common approach is the selection of a finite set of transverse spatial modes labeled by discrete mode indexes [26][27][28][29], for which MUB measurements are attainable by the use of phase holograms [6]. Free-space [30], multi-core fibers [31] or on-chip [32] path encoding as well as time-bin [33] are also interesting techniques with potencial for high-dimensionality. These methods, despite being useful, discard a fraction of available modes and do not straightforwardly extend to the complementary (Fourier) domain of CVs.…”

Narrowband Single Photons for Light-Matter Interfaces

“…The theoretical predictions follow the calculations for mode-locked biphoton states [69,71,72], where 2N is the number of cavity frequency modes within the phase matching bandwidth with spacing ω F SR = 2πν F SR and the FWHM of each mode is ∆ω = 2π∆ν SP . For a frequency comb, as emitted by a multimode OPO, the spectrum amplitude function has the form:…”

“…Spontaneous parametric down-conversion (SPDC) inside an optical cavity, also known as an optical parametric oscillator (OPO), is a good candidate for this purpose: SPDC is the current gold standard of producing high-purity heralded single photons at flexible wavelengths and the cavity enhances emission into certain spectral modes, tailoring the photon into the desired shape. In their groundbreaking work at the end of the last millennium, Ou and Lu expand the preliminary theoretical framework of SPDC inside an optical cavity from squeezing [69] to narrowband emission and demonstrated their predictions in an experiment [28,41]. The authors achieved single-mode operation from a semi-monolithic standing wave cavity combined with a mode-cleaning cavity (MCC).…”