Set of 4d–3 observables to determine any pure qudit state

Abstract

We present a tomographic method which requires only 4d − 3 measurement outcomes to reconstruct any pure quantum state of arbitrary dimension d. Using the proposed scheme we have experimentally reconstructed a large number of pure states of dimension d = 7, obtaining a mean fidelity of 0.94. Moreover, we performed numerical simulations of the reconstruction process, verifying the feasibility of the method for higher dimensions. In addition, the a priori assumption of purity can be certified within the same set of measurements, what represents an improvement with respect to other similar methods and contributes to answer the question of how many observables are needed to uniquely determine any pure state. 20020170100564BA).

Performance of the quantum MaxEnt estimation in the presence of physical symmetries

“…Then, for each observable A i , the expectation value in the target state, a ρ i = Tr(ρA i ), is approximated by the relative frequency f i = n i /N , experimentally obtained, where n i is the number of trials that resulted in a click of the detectors. In agreement with typical experimental setups based on optical platforms [38,39], we have assumed a source consisting of a pulsed attenuated laser, that emits weak coherent states at the single-photon level. In this context, it is reasonable to assume that the statistics of the photon emission process and the dark counts, caused by self triggering effects in the photon detectors, are Poissonian.…”

Determination of spatial quantum states by using point diffraction interferometry

“…For example, if some information about the state is known a priori, a reduction in the number of measurements is feasible. In fact, several works have demonstrated that pure quantum states can be accurately reconstructed from a number of measurements that scales as ∼ d [17][18][19]. Although, in general, an arbitrary quantum system will be in a mixed state, the reconstruction of pure states is especially important since most current applications of quantum information are based on pure states.…”

Ptychographic reconstruction of pure quantum states

“…In the face of increasing complexity of tomography with the state-space dimension [3], recent effort has been directed to simplify the process using prior information [4,5]. In particular, for a quantum state known to be pure, a number of tomographic techniques has been developed showing that up to five measurement bases will determine it in any finite dimension [6][7][8][9][10]. Although, in practice, purity is just an approximation, in many scenarios it is good enough.…”

“…Comparing with other tomographic approaches for pure states, which require projective measurements in a fixed number of bases [6][7][8][9][10], the ptychographic technique [11] resorts to a flexible number (n) of projective measurements in a single basis. It also uses simpler settings in the experimental setup, since the rank-r projectors are usually easy to implement.…”

“…HWP: half-wave plate; BS: beam splitter; SLM: spatial light modulator. other experiments, e.g., [7,9,10,19,20]. CMOS cameras (Thorlabs DCC1545M) at the transmitted and reflected arms record the far-field and near-field intensity distributions, respectively.…”