Detector-Agnostic Phase-Space Distributions

Abstract

The representation of quantum states via phase-space functions constitutes an intuitive technique to characterize light. However, the reconstruction of such distributions is challenging as it demands specific types of detectors and detailed models thereof to account for their particular properties and imperfections. To overcome these obstacles, we derive and implement a measurement scheme that enables a reconstruction of phase-space distributions for arbitrary states whose functionality does not depend on the knowledge of the detectors, thus defining the notion of detector-agnostic phase-space distributions. Our theory presents a generalization of wellknown phase-space quasiprobability distributions, such as the Wigner function. We implement our measurement protocol, using state-of-the-art transition-edge sensors without performing a detector characterization. Based on our approach, we reveal the characteristic features of heralded single-and two-photon states in phase space and certify their nonclassicality with high statistical significance.

Blueprint for a Scalable Photonic Fault-Tolerant Quantum Computer

“…The numerous procedures for generating optical GKP states that have been proposed tend either to be non-deterministic, as they rely on post-selected measurements directly [25][26][27][28][29][30] or indirectly [31][32][33]; or require the experimentally challenging conditions of coherent interactions with matter [34,35] or extremely strong optical nonlinearity [35]. Recent advances in photon-number-resolving (PNR) detectors [36][37][38][39] have substantially improved the viability of the post-selection approach in the near term, with methods based on Gaussian boson sampling (GBS) [27][28][29][30] now within reach of state-of-the-art optical devices. Low-probability sources can be improved with the help of multiplexing at the cost of an increased overhead.…”

Quasiprobability distributions for quantum-optical coherence and beyond

“…where α represents the local oscillator that is mixed on a |t| 2 :|r| 2 beam splitter with the signal, before sending one of the output fields to the multiplexing stage, cf. [172]. It is rather interesting to observe that formula (11) resembles the convolution (2), when identifying G z and G (vac) z with P K and K, respectively.…”

“…One main issue one encounters when performing measurements for a quantum state reconstruction is that the inner operation of detectors is typically unknown, meaning that only outcomes from the detection process can be recorded. Surprisingly, one can overcome this challenge by devising a detector-agnostic approach [172], which consists of an unbalanced homodyne configuration and a multiplexed detection [173] that uniformly splits a signal into N = 2 d output signals, employing d iterations of 50:50 beam splitters. In such a scenario, it has been shown that the generating function G z of the measurement outcome statistics, parametrized throught z, is nonnegative for any classical state and even N.…”

Probing nonclassicality with matrices of phase-space distributions

“…Each of the resulting modes is measured with a detector or detection scheme based on photon absorption, thus being described by a positive operatorvalued measure (POVM) which is diagonal in the photon-number representation [79]. Consequently, one or a combination of detector outcomes (e.g., in a generating-function-type combination [80]) corresponds to a POVM element of the form Π(n) = :e −Γ(n) :.…”

“…We may emphasize that all experimental techniques and components that are used in the proposed setup are readily available; see, e.g., the related quantum state reconstruction experiments reported in Refs. [83,80].…”