The eight-port homodyne detection apparatus is analyzed in the framework of the operational theory of quantum measurement. For an arbitrary quantum noise leaking through the unused port of the beam splitter, the positive operator valued measure and the corresponding operational homodyne observables are derived. It is shown that such an eight-port homodyne device can be used to construct the operational quantum trigonometry of an optical field. The quantum trigonometry and the corresponding phase space Wigner functions are derived for a signal field probed by a classical local oscillator and a squeezed vacuum in the unused port.
It is well known that the Husimi Q-function of the signal field can actually be measured by the eight-port homodyne detection technique, provided that the reference beam (used for homodyne detection) is a very strong coherent field so that it can be treated classically. Using recent rigorous results on the quantum theory of homodyne detection observables, we show that any phase space observable, and not only the Q-function, can be obtained as a high amplitude limit of the signal observable actually measured by an eight-port homodyne detector. The proof of this fact does not involve any classic…
We consider the quantum optical eight-port homodyne detection scheme in the case that each of the associated photon detectors is assigned with a different quantum efficiency. We give a mathematically rigorous and strictly quantum mechanical proof of the fact that the measured observable (positive operator measure) in the high-amplitude limit is a smearing of the covariant phase space observable related to the ideal measurement. The result is proved for an arbitary parameter field. Furthermore, we investigate some properties of the measured observable. In particular, we show that the state dist…
We experimentally generate arbitrary time-bin qubits using continuous-wave light. The advantage unique to our qubit is its compatibility with deterministic continuous-variable quantum information processing. This compatibility comes from its optical coherence with continuous waves, well-defined spatio-temporal mode, and frequency spectrum within the operational bandwidth of the current continuous-variable technology. We also demonstrate an efficient scheme to characterize time-bin qubits via eight-port homodyne measurement. This enables the complete characterization of the qubits as two-mode s…
We address measurements of covariant phase observables (CPOs) by means of realistic eight-port homodyne detectors. We do not assume equal quantum efficiencies for the four photodetectors and investigate the conditions under which the measurement of a CPO may be achieved. We show that balancing the efficiencies using an additional beam splitter allows us to achieve a CPO at the price of reducing the overall effective efficiency, and prove that it is never a smearing of the ideal CPO achievable with unit quantum efficiency. An alternative strategy based on employing a squeezed vacuum as a parame…
Heisenberg-scaling characterization of a two-channel optical network via two-port homodyne detection
School of Mathematics and Physics, University of Portsmouth（朴茨茅斯大学数学与物理学院）；Quantum Science and Technology Hub, University of Portsmouth（朴茨茅斯大学量子科学与技术中心）；Dipartimento di Fisica, Università di Bari & Politecnico di Bari（巴里大学与巴里理工大学物理系）；INFN, Sezione di Bari（意大利国家核物理研究所巴里分部）；Institute of Cosmology and Gravitation, University of Portsmouth（朴茨茅斯大学宇宙学与引力研究所）
Heterodyne, eight-port homodyne and six-port homodyne detectors belong to the class of two-photocurrent devices. Their full equivalence in probing radiation field has been proved both for ideal and not fully efficient photodetectors. The output probability distribution has been also evaluated for a generic probe mode.
The eight-port homodyne detector is an optical circuit designed to perform the monitoring of two quadratures of an optical field, the signal. By using quantum Bose fields and quantum stochastic calculus, we give a complete quantum description of this apparatus, when used as quadrature detector in continuous time. We can treat either the travelling waves in the optical circuit, either the observables involved in the detection part: two couples of photodiodes, postprocessing of the output currents. The analysis includes imperfections, such as not perfectly balanced beam splitters, detector effic…
Performing homodyne detection at one port of squeezed-state light interferometer and then binarzing measurement data are important to achieve super-resolving and super-sensitive phase measurements. Here we propose a new data-processing technique by dividing the measurement quadrature into three bins (equivalent to a multi-outcome measurement), which leads to a higher improvement in the phase resolution and the phase sensitivity under realistic experimental condition. Furthermore, we develop a new phase-estimation protocol based on a combination of the inversion estimators of each outcome and s…
Variable measurement operators enable the optimization of strategies for testing quantum properties and the preparation of a range of quantum states. Here, we experimentally implement a weak-field homodyne detector that can continuously tune between measuring photon numbers and field quadratures. We combine a quantum signal with a coherent state on a balanced beam splitter and detect light at both output ports using photon-number-resolving transition edge sensors. We observe that the discrete difference statistics converge to the quadrature distribution of the signal as we increase the coheren…
Cavity-assisted homodyne detection with a single photodiode
Institute for Applied Physics, Friedrich Schiller University Jena（耶拿弗里德里希·席勒大学应用物理研究所）；Abbe Center of Photonics, Friedrich Schiller University Jena（耶拿弗里德里希·席勒大学阿贝光子学中心）
Using a recent result of Albini et al. to represent quantum homodyne tomography in terms of a single observable (as a normalized positive operator measure) we construct a generalized Markov kernel which transforms (the measurement outcome statistics of) this observable into (the measurement outcome statistics of) a covariant phase space observable. We also consider the inverse question. Finally, we add some remarks on the quantum theoretical justification of the experimental implementations of these observables in terms of balanced homodyne and 8-port detection techniques, respectively.
We propose an efficient strategy to attack a continuous-variable quantum key distribution (CV-QKD) system, that we call homodyne detector blinding. This attack strategy takes advantage of a generic vulnerability of homodyne receivers: a bright light pulse sent on the signal port can lead to a saturation of the detector electronics. While detector saturation has already been proposed to attack CV-QKD, the attack we study in this paper has the additional advantage of not requiring an eavesdropper to be phase locked with the homodyne receiver. We show that under certain conditions, an attacker ca…
Quantum scissors device of Pegg et al. (1998 Phys. Rev. Lett. 81, 1604) enables truncation of the Fock-state expansion of an input optical field to qubit and qutrit (three-dimensional) states only. Here, a generalized scissors device is proposed using an eight-port optical interferometer. Upon post-selection based on photon counting results, the interferometer implements generation and teleportation of qudit (d-dimensional) states by truncation of an input field at the (d-1)th term of its Fock-state expansion up to d=6. Examples of selective truncations, which can be interpreted as a Fock-stat…
In the context of the readout scheme for gravitational-wave detectors, the "double balanced homodyne detection" proposed in [K.~Nakamura and M.-K.~Fujimoto, arXiv:1709.01697.] is discussed in detail. This double balanced homodyne detection enables us to measure the expectation values of the photon creation and annihilation operators. Although it has been said that the operator $\hat{b}_θ:=\cosθ\hat{b}_{1}+\sinθ\hat{b}_{2}$ can be measured through the homodyne detection in literature, we first show that the expectation value of the operator $\hat{b}_θ$ cannot be measured as the linear combinati…
The distributed absorption of photons in photodiodes induces an excess noise in continuous-wave photodetection above the transit-time roll-off frequency. We show that it can be treated as a frequency-dependent excess optical loss in homodyne detection. This places a limit on the bandwidth of high-accuracy homodyne detection, even if an ideal photodetector circuit is available. We experimentally verify the excess loss in two ways; a comparison of signal gain and shot-noise gain of one-port homodyne detection, and a balanced homodyne detection of squeezed light at 500 MHz sideband. These results…
It has been proposed and demonstrated that path-entangled Fock states (PEFSs) are robust against photon loss over NOON states [S. D. Huver \emph{et al.}, Phys. Rev. A \textbf{78}, 063828 (2008)]. However, the demonstration was based on a measurement scheme which was yet to be implemented in experiments. In this work, we quantitatively illustrate the advantage of PEFSs over NOON states in the presence of photon losses by analytically calculating the quantum Fisher information. To realize such an advantage in practice, we then investigate the achievable sensitivities by employing three types of …
Sagnac speed meter (SSM) topology is known as an alternative technique to reduce quantum back-action in gravitational-wave interferometers. However, any potential imbalance of the main beamsplitter was shown to reduce the quantum noise superiority of speed meter at low frequencies, caused due to increased laser noise coupling to the detection port. In this paper, we show that implementing balanced homodyne readout scheme and for a particular choice of the local oscillator (LO) delivery port, the excess laser noise contribution to quantum noise limited sensitivity (QNLS) is partly compensated a…
We show that the generation of entanglement of two heavily macroscopic mirrors with masses of up to several kilograms are feasible with state of the art techniques of high-precision laser interferometry. The basis of such a demonstration would be a Michelson interferometer with suspended mirrors and simultaneous homodyne detections at both interferometer output ports. We present the connection between the generation of entanglement and the Standard Quantum Limit (SQL) for a free mass. The SQL is a well-known reference limit in operating interferometers for gravitational-wave detection and prov…
With the recent discovery of Gravitational waves, marking the start of the new field of GW astronomy, the push for building more sensitive laser-interferometric gravitational wave detectors (GWD) has never been stronger. Balanced homodyne detection (BHD) allows for a quantum noise limited readout of arbitrary light field quadratures, and has therefore been suggested as a vital building block for upgrades to Advanced LIGO and third generation observatories. In terms of the practical implementation of BHD, we develop a full framework for analyzing the static optical high order modes (HOMs) occur…
Using multiport beam-splitter (BS) configurations eight input operators a(0),a(1),a(2) a(3),a(4) a(5),a(6), a(7) are mixed by 12 BS's to produce the output operators b(0), b(1), b(2), b(3), b(4), b(5), b(6), b(7). A single photon entering into, or exiting from, one port of a BS is considered as the |0> state while that in the second port of the BS is considered as the |1> state. Two single photons are inserted into two of the BS's simulating two input qubit-states by operators a(0), a(1),a(2), a(3) . In order to simulate the two-qubit gates we exclude by postselection all the cases in which on…
The concept of intrinsic and operational observables in quantum mechanics is introduced. It is argued that, in any realistic description of a quantum measurement that includes a detecting device, it is possible to construct from the statistics of the recorded raw data a set of operational quantities that correspond to the intrinsic quantum mechanical observable. Using the concept of the propensity and the associated operational positive operator valued measure (POVM) a general description of the operational algebra of quantum mechanical observables is derived for a wide class of realistic dete…
We consider an oscillating micromirror replacing one of the two fixed mirrors of a Mach-Zehnder interferometer. In this ideal optical set-up the quantum oscillator is subjected to the radiation pressure interaction of travelling light waves, no cavity is involved. This configuration shows that squeezed light can be generated by pure scattering on a quantum system, without involving a cavity. The squeezing can be detected at the output ports of the interferometer either by direct detection or by measuring the spectrum of the difference current. We use the Hudson-Parthasarathy equation to model …
The Michelson interferometer is a cornerstone of experimental physics. Its applications range from providing first impressions of wave interference in educational settings to probing spacetime at minuscule precision scales. Interferometer precision provides a unique view of the fundamental medium of matter and energy, enabling tests for new physics as well as searches for the gravitational wave signatures of distant astrophysical events. Optical interferometers are typically operated by continuously measuring the power at their output port. Signal perturbations then create sideband fields, for…
Increasing the complexity of quantum photonic devices is essential for many optical information processing applications to reach a regime beyond what can be classically simulated, and integrated photonics has emerged as a leading platform for achieving this. Here, we demonstrate three-photon quantum operation of an integrated device containing three coupled interferometers, eight spatial modes and many classical and nonclassical interferences. This represents a critical advance over previous complexities and the first on-chip nonclassical interference with more than two photonic inputs. We int…
