Sparsity-based recovery of three-photon quantum states from two-fold correlations

Abstract

The field of quantum information has been growing fast over the past decade. In particular, optical quantum computation, based on the concepts of KLM 1 and cluster states 2 , has witnessed experimental realizations of larger and more complex systems in terms of photon number 3 . Quantum optical systems, which offer long coherence times and easy manipulation of single qubits and photons, allow us to probe quantum properties of the light itself 4 and of the physical systems around it 5 . Recently, a linear scheme for quantum computing, relying on the bosonic nature of particles, has been proposed 6 and realized experimentally with photons 4,7,8 . The ability to efficiently measure superpositions of quantum states consisting of several photons is essential to the characterization of such systems and computation units.In fact, the entire field of quantum information completely relies on the ability to recover quantum states from measurements. However, the characterization of quantum states requires many measurements, and often necessitates complicated measurements schemes; for example, characterizing m qubits requires 2 2 m measurements. Here, we utilize structure, inherent to physically interesting quantum states of light, in order to reduce the complexity in the recovery of a

Scalable on-chip quantum state tomography

“…Some approaches seek to avoid unnecessary measurements by assuming that the system is in particular low rank states, such as sparse states [14,15] measurements have increased error robustness relative to using only local qubit measurements, and thus can be completed in less time [19]. The computational burden of inverting large data sets to find the density matrix is reduced with simple real-time optimization algorithms in self guided tomography, or can be completely avoided with systems for direct projection of density matrix parameters [20][21][22].…”

Quantum optical feedback control for creating strong correlations in many-body systems

“…However, the effects we described can be generalized to other physical systems where the measurement backaction can compete with the usual unitary dynamics. For example, the phenomena we presented could be observed in purely photonic systems with multiple path interferometers known as photonic chips or photonic circuits [41,45,65,66]. In these systems, single photons can propagate across multiple paths, generating dynamics which is analogous to the tunneling of atoms in an optical lattices.…”

“…The effects presented in this work can be generalized to other many-body (or simply multimode) physical systems such as optomechanical arrays [35,36], superconducting qubits as used in circuit cavity QED [37][38][39][40], and even purely photonic systems (i.e. photonic chips or circuits) with multiple path interference, where, similarly to optical lattices, the quantum walks and boson sampling have been already discussed [41][42][43][44][45]. Recently it has been achieved ultra-strong light matter coupling in a 2D electron gas in THz metamaterials [46], while developments have been made with respect to light induced high-Tc superconductivity in real materials [47][48][49].…”

Sparsity-Based Super Resolution for SEM Images

“…The mathematical framework provided by CS assures that a sparse signal can be exactly recovered from just a small set of linear measurements [7], given a known dictionary and a known measurement (sensing) system. Relying on these principles, the concepts of sparsity and CS have been used for a variety of applications, ranging from sub-Nyquist sampling [11,12] with applications in radar [13,14] and ultrasound [15][16][17], to super-resolution imaging [18,19], phase retrieval [20][21][22], ankylography [23], mapping the coherence function of light [24], holography [25], single pixel camera [26], ghost imaging [27], and even quantum state tomography [28][29][30][31]. These sparsity-based ideas inspired our current work.…”