Recovering the full dimensionality of hyperentanglement in collinear photon pairs

Abstract

Exploiting hyperentanglement of photon pairs, that is, simultaneous entanglement in multiple degrees of freedom(DOFs), increases the dimensionality of Hilbert spaces for quantum information processing. However, generation of hyperentangled photon pairs collinearlly, while produces high brightness, results in a smaller Hilbert space due to the two photons being in the same spatial mode. In this letter, we point out that one can recover the full dimensionality of such hyperentanglement through a simple interference set up, similar to the time-reversed Hong-Ou-Mandel (TR-HOM) process. Different from the standard TR-HOM, we point out a critical phase condition has to be satisfied in order to recover the hyperentanglement. We theoretically analyze the realization of this approach and discuss the feasibility of generating truly hyperentangled photon pairs. Our proposed approach does not require post-selection and hence enables efficient hyper-entangled photon pairs generation for high-dimensional quantum applications.Entangled photons play a critical role in many applications of quantum opticshorodecki2009quantum. Photons that are simultaneously entangled in more than one degree of freedom(DOF), the so-called 'hyperentangled' states, have attracted much recent interest [1][2][3]. Hyperentanglement expands the dimensionality of the Hilbert space of biphotons, enables complete Bell state analysis [4,5], increases the information capacity per pair photons [6,7] and therefore lays the fundation of superdense-coding quantum communication [8][9][10]. It has also become the key technology for certain tests of fundamental physics [11,12].The generation of entangled photons is most conveniently done in a nonlinear medium. When the phase matching can be satisfied over a bandwidth much greater than the pump bandwidth, the photons are frequency entangled as a result of energy conservation. Entanglement in another DOF can be arranged through various means, such as type II phase matching for polarizationentanglement[13], delayed interferometer for time-bin entanglement [14], or simultaneous phase matching for various orbital angular momentum modes [15]. Here, we consider hyper-entanglement in frequency and polarization DOFs, as frequency and polarization of photons are robust over large transmission distances in optical fibre. Entanglement in these two DOFs can also be generated relatively straightforwardly in fibre [16] and nonlinear waveguides [17]. While collinear photon pair generation in a fibre or a nonlinear waveguide is most efficient due to large nonlinear interaction length and no spatial filtering required (as opposed to non-collinear generation [18]), we will show that that collinear entangled photon pairs have a reduced dimensionality in Hilbert space.By "hyperentanglement", we mean not only the photons are entangled in both DOFs, but also that they are accessible individually, e.g. the hyperentangled photons are spatially separated. In collinear parametric processes such as type-II spontaneous parametric downconversion...

Telecom-band hyperentangled photon pairs from a fiber-based source

“…Entanglement in these two DOFs can be generated straightforwardly in fiber [10] and nonlinear waveguides [11] via nonlinear processes such as spontaneous parametric downconversion (SPDC) and spontaneous four-wave-mixing (SFWM). While these waveguide-based sources benefit from greater mode confinement (compared to their bulk crystal counterparts) and single spatial-mode emission, this latter property also limits the accessible dimensionality of the hyperentangled photon pairs generated, due to the fact that the two entangled photons are in the spatial mode [12]. Beamsplitter-based techniques have been used for the probabilistic separation of the biphotons to achieve polarization-frequency (PF) hyperentanglement * changjia.chen@mail.utoronto.ca [13], but the hyperentanglement is achieved only after post-selection of coincidence detection, with only 50% probability, limiting its potential for applications such as dense coding.…”

“…In order to deterministically separate the PF hyperentangled biphotons generated from collinearly propagating biphotons without destroying the entanglement in either DOF, one can make use of biphoton interference, specifically, the anti-bunching effect on a beamsplitter or a polarizing beamsplitter [14,15]. Based on the proposed design in our recent work [12], here we present an experimental demonstration of a PF hyperentangled photon-pair source. The photons are generated via a broadband type-II spontaneous parametric down conversion in a periodically-poled silica fiber (PPSF) [16], bidirectionally-pumped inside a Sagnac loop.…”

Hyperentanglement-enhanced quantum illumination

“…While the enhancement effected by hyperentanglement in a continuous parameter estimation problem has been analysed in an earlier work [12], this Letter shines light on the enhancement in what is essentially a hypothesis testing task. In this Letter, we propose object-detection using a probe state hyperentangled in polarization as well as frequency degrees of freedom [13]. We show that the QCB for object-detection using hyperentangled photons gives a remarkable 12dB improvement in the exponent of the error probability over QI in the "bad regime".…”

“…Hyperentanglement-enhanced sensitivity in the low noise regime: Ever since the first experimental demonstration of generation of hyperentangled photon pairs [17], different procedures to generate hyperentanglement in different degree of freedom of photons have been successfully demonstrated. Here we will briefly outline one such procedure [13] to generate states hyperentangled in polarization and frequency degrees of freedom. Using two identical type-II non-collinear SPDC generators driven by identical pumps, derived from a common pump, |Φ 1 and |Φ 2 , that are entangled in polarization degree of freedom [18] are produced.…”

“…A first order approximation in squeezing parameter of the resulting hyperentangled state yields a hyperentangled biphoton state. For the low noise regime, the time-bandwith product is adjusted such that the transmitter pulse spans over M temporal modes to give the following output state [13].…”