11 pages, LateX, no figures. Published in "Quantum Communication,Computing, and Measurement", Edited by O. Hirota, A. S. Holevo, and C. M. Caves, Plenum Publishing (New York and London 1997), p. 253
Homodyne tomography - i. e. homodyning while scanning the local oscillator phase - is now a well assessed method for ``measuring'' the quantum state. In this paper I will show how it can be used as a kind of universal detection, for measuring generic field operators, however at expense of some additional noise. The general class of field operators that can be measured in this way is presented, and includes also operators that are inaccessible to heterodyne detection. The noise from tomographical homodyning is compared to that from heterodyning, for those operators that can be measured in both ways. It turns out that for some operators homodyning is better than heterodyning when the mean photon number is sufficiently small. Finally, the robustness of the method to additive phase-insensitive noise is analyzed. It is shown that just half photon of thermal noise would spoil the measurement completely.
Direct photon detection is experimentally implemented to measure the squeezing and purity of a single-mode squeezed vacuum state without an interferometric homodyne detection. Following a recent theoretical proposal [arXiv quant-ph/0311119], the setup only requires a tunable beamsplitter and a single-photon detector to fully characterize the generated Gaussian states. The experimental implementation of this procedure is discussed and compared with other reference methods.
We propose a scheme for measuring the squeezing, purity, and entanglement of Gaussian states of light that does not require homodyne detection. The suggested setup only needs beam splitters and single-photon detectors. Two-mode entanglement can be detected from coincidences between photodetectors placed on the two beams.
We present a number of rapid-purification feedback protocols for optical homodyne detection of a single optical qubit. We derive first a protocol that speeds up the rate of increase of the average purity of the system, and find that like the equivalent protocol for a non-disspative measurement, this generates a deterministic evolution for the purity in the limit of strong feedback. We also consider two analogues of the Wiseman-Ralph rapid-purification protocol in this setting, and show that like that protocol they speed up the average time taken to reach a fixed level of purity. We also examin…
Conventional incoherent imaging based on measuring the spatial intensity distribution in the image plane faces the resolution hurdle described by the Rayleigh diffraction criterion. Here, we demonstrate theoretically using the concept of the Fisher information that quadrature statistics measured by means of array homodyne detection enables estimation of the distance between two incoherent point sources well below the Rayleigh limit for sufficiently high signal-to-noise ratio. This capability is attributed to the availability of spatial coherence information between individual detector pixels a…
Recently, in several theoretical investigations, amplitude nth-power squeezing has been studied with $n = 2,~3,~4,~5$. In the present paper, we give a proposal for experimental detection of amplitude $n$th-power squeezing using ordinary homodyning with coherent light for arbitrary power $n$ and discuss in detail its theory. The proposed scheme requires only repeated measurements of the factorial moments of number of photons in the light obtained after homodyning, with various shifts of phase of coherent light, and involves no approximations, whatsoever. This has advantage over the method propo…
Phase-sensitive properties of light play a crucial role in a variety of quantum optical phenomena, which have been mostly discussed in the framework of photoelectric detection theory. However, modern detection schemes, such as arrays of on-off detectors, are not based on photoelectric counting. We demonstrate that the theory of homodyning with such click counting detectors can be established by using a proper detection model. For practical applications, a variety of typically occurring imperfections are rigorously analyzed and directly observable nonclassicality criteria are studied. Fundament…
We consider the problem of measurement of optical transverse profile parameters and their conjugate variable. Using multi-mode analysis, we introduce the concept of detection noise-modes. For Gaussian beams, displacement and tilt are a pair of transverse profile conjugate variables. We experimentally demonstrate their optimal encoding and detection with a spatial homodyning scheme. Using higher order spatial mode squeezing, we show the sub-shot noise measurements for the displacement and tilt of a Gaussian beam.
We derive the quantum noise limit for the optical beam displacement of a TEM00 mode. Using a multimodal analysis, we show that the conventional split detection scheme for measuring beam displacement is non-optimal with 80% efficiency. We propose a new displacement measurement scheme that is optimal for small beam displacement. This scheme utilises a homodyne detection setup that has a TEM10 mode local oscillator. We show that although the quantum noise limit to displacement measurement can be surpassed using squeezed light in appropriate spatial modes for both schemes, the TEM10 homodyning sch…
In all practical communication channels, the code word consist of Gaussian states and the measurement strategy is often a Gaussian detector such as homodyning or heterodyning. In this paper we investigate the communication performance using a phase-conjugated alphabet and joint Gaussian detection in an phase-insensitive amplifying channel. We find that a communication scheme consisting of a phase-conjugated alphabet of coherent states and a joint detection strategy significantly outperforms a standard coherent-state strategy based in individual detection. Moreover, we show that the performance…
We address binary phase-shift-keyed communication channels based on Gaussian states and prove that squeezing improves state discrimination at fixed energy of the channel, also in the presence of phase diffusion. We then assess performances of homodyne detection against the ultimate quantum limits to discrimination, and show that homodyning achieves optimality in large noise regime. Finally, we consider noise in the preparation of the seed signal (before phase encoding) and show that also in this case squeezing may improve state discrimination in realistic conditions.
Systems of on-off detectors are well established for measuring radiation fields in the regime of small photon numbers. We propose to combine these detector systems with unbalanced homodyning with a weak local oscillator. This approach yields phase-space functions, which represent the click counterpart of the s parametrized quasiprobabilities of standard photoelectric detection theory. This introduced class of distributions can be directly sampled from the measured click counting statistics. Therefore, our technique visualizes nonclassical effects without further data processing. Surprisingly, …
The extraordinary sensitivity of the output field of an optical cavity to small quantum-scale displacements has led to breakthroughs such as the first detection of gravitational waves \cite{LIGO,LIGODC} and of the motions of quantum ground-state cooled mechanical oscillators \cite{Teufel2011,Chan2011}. While heterodyne detection of the cavity field preserves asymmetries which provide a key signature that mechanical oscillators has attained the quantum regime, detection of a rotating quadrature of the light averages out important quantum correlations, yielding a weaker signal and lower sensitiv…
We demonstrate accurate phase measurement from low photon level interference data using a constrained optimization method that takes into account the expected redundancy in the unknown phase function. This approach is shown to have significant noise advantage over traditional methods such as balanced homodyning or phase shifting that treat individual pixels in the interference data as independent of each other. Our interference experiments comparing the optimization method with the traditional phase shifting method show that when the same photon resources are used, the optimization method prov…
Entanglement, one of the central mysteries of quantum mechanics, plays an essential role in numerous applications of quantum information theory. A natural question of both theoretical and experimental importance is whether universal entanglement detection is possible without full state tomography. In this work, we prove a no-go theorem that rules out this possibility for any non-adaptive schemes that employ single-copy measurements only. We also examine in detail a previously implemented experiment, which claimed to detect entanglement of two-qubit states via adaptive single-copy measurements …
Detecting and quantifying quantum entanglement of a given unknown state poses problems that are fundamentally important for quantum information processing. Surprisingly, no direct (i.e., without quantum tomography) universal experimental implementation of a necessary and sufficient test of entanglement has been designed even for a general two-qubit state. Here we propose an experimental method for detecting a collective universal witness, which is a necessary and sufficient test of two-photon polarization entanglement. It allows us to detect entanglement for any two-qubit mixed state and to es…
We revisit the problem of detection of entanglement of an unknown two-qubit state using minimal resources. Using weak values and just two copies of an arbitrary two-qubit state, we present a protocol where a post selection measurement in the computational basis provides enough information to identify if the state is entangled or not. Our protocol enables complete state identification with a single-setting post selection measurement on two copies of the state. It follows that by restricting to pure states, the global interaction required for determining the weak values can be realized by local …
In this paper, we study how a displacement of a quantum system appears under a change of relativistic reference frame. We introduce a generic method in which a displacement operator in one reference frame can be transformed into another reference frame. It is found that, when moving between non-inertial reference frames there can be distortions of phase information, modal structure and amplitude. We analyse how these effects affect traditional homodyne detection techniques. We then develop an in principle homodyne detection scheme which is robust to these effect, called the ideal homodyne dete…
Universal entanglement detection with geometrically optimal witnesses
Southern University of Science and Technology（南方科技大学）；The Hong Kong University of Science and Technology（香港科技大学）；Quantum Science Center of Guangdong-HongKong-Macao Greater Bay Area（粤港澳大湾区量子科学中心）；The University of Hong Kong（香港大学）
We describe a generalization of the cluster-state model of quantum computation to continuous-variable systems, along with a proposal for an optical implementation using squeezed-light sources, linear optics, and homodyne detection. For universal quantum computation, a nonlinear element is required. This can be satisfied by adding to the toolbox any single-mode non-Gaussian measurement, while the initial cluster state itself remains Gaussian. Homodyne detection alone suffices to perform an arbitrary multi-mode Gaussian transformation via the cluster state. We also propose an experiment to demon…
A universal characterization of non-Markovianity for any open hybrid quantum systems is presented. This formulation is based on the negativity volume of the generalized Wigner function, which serves as an indicator of the quantum correlations in any composite quantum systems. It is shown, that the proposed measure can be utilized for any single or multi-partite quantum system, containing any discrete or continuous variables. To demonstrate its power in revealing non-Markovianity in such quantum systems, we additionally consider a few illustrative examples.
Using detector tomography, we investigate the detection mechanism in NbN-based superconducting single photon detectors (SSPDs). We demonstrate that the detection probability uniquely depends on a particular linear combination of bias current and energy, for a large variation of bias currents, input energies and detection probabilities, producing a universal detection curve. We obtain this result by studying multiphoton excitations in a nanodetector with a sparsity-based tomographic method that allows factoring out of the optical absorption. We discuss the implication of our model system for th…
Controlling the quadrature measured by a homodyne detector is a universal task in continuous-variable quantum optics. However, deriving an error signal that is linear across theentire range of quadrature angles remains an open experimental problem. Here we propose a scheme to produce such an error signal through the use of a universally tunable modulator.
We construct nonlinear multiparty entanglement measures for distinguishable particles, bosons and fermions. In each case properties of an entanglement measures are related to the decomposition of the suitably chosen representation of the relevant symmetry group onto irreducible components. In the case of distinguishable particles considered entanglement measure reduces to the well-known many particle concurrence. We prove that our entanglement criterion is sufficient and necessary for pure states living in both finite and infinite dimensional spaces. We generalize our entanglement measures to …
