Binary projective measurement via linear optics and photon counting

We investigate the implementation of binary projective measurements with linear optics. This problem can be viewed as a single-shot discrimination of two orthogonal pure quantum states. We show that any two orthogonal states can be perfectly discriminated using only linear optics, photon counting, coherent ancillary states, and feedforward. The statement holds in the asymptotic limit of a large number of these physical resources.     

Measuring a photonic qubit without destroying it

Measuring the polarization of a single photon typically results in its destruction. We propose, demonstrate, and completely characterize a quantum nondemolition (QND) scheme for realizing such a measurement nondestructively. This scheme uses only linear optics and photodetection of ancillary modes to induce a strong nonlinearity at the single-photon level, nondeterministically. We vary this QND measurement continuously into the weak regime and use it to perform a nondestructive test of complementarity in quantum mechanics. Our scheme realizes the most advanced general measurement of a qubit to date: it is nondestructive, can be made in any basis, and with arbitrary strength.     

Repeat-until-success linear optics distributed quantum computing

We demonstrate the possibility to perform distributed quantum computing using only single-photon sources (atom-cavity-like systems), linear optics, and photon detectors. The qubits are encoded in stable ground states of the sources. To implement a universal two-qubit gate, two photons should be generated simultaneously and pass through a linear optics network, where a measurement is performed on them. Gate operations can be repeated until a success is heralded without destroying the qubits at any stage of the operation. In contrast with other schemes, this does not require explicit qubit-qubit interactions, a priori entangled ancillas, nor the feeding of photons into photon sources.     

Quantum geometric phase between orthogonal states

We show that the geometric phase between any two states, including orthogonal states, can be extracted and measured using the notion of projective measurement, and we show that a topological number can be extracted in the geometric phase change in an infinitesimal loop near an orthogonal state. Also, the Pancharatnam phase change during the passage through an orthogonal state is shown to be either pi or zero (mod 2pi). All the off-diagonal geometric phases can be obtained from the projective geometric phase calculated with our generalized connection.     

Quantum teleportation of optical quantum gates

We show that a universal set of gates for quantum computation with optics can be quantum teleported through the use of EPR entangled states, homodyne detection, and linear optics and squeezing operations conditioned on measurement outcomes. This scheme may be used for fault-tolerant quantum computation in any optical scheme (qubit or continuous-variable). The teleportation of nondeterministic nonlinear gates employed in linear optics quantum computation is discussed.     

Stochastic Dynamics of Reduced Wave Functions and Continuous Measurement in Quantum Optics

The stochastic dynamics of open quantum systems interacting with a zero temperature environment is investigated by employing a formulation of quantum statistical ensembles in terms of probability distributions on projective Hilbert space. It is demonstrated that the open system dynamics can consistently be described by a stochastic process on the reduced state space. The physical meaning of reduced probability distributions on projective Hilbert space is derived from a complete, orthogonal measurement of the environment. The elimination of the variables of the environment is shown to lead to a piecewise deterministic process in Hilbert space defined by a differential Chapman-Kolmogorov equation. A Hilbert space path integral representation of the stochastic process is constructed. The general theory is illustrated by means of three examples from quantum optics. For these examples the microscopic derivation of the stochastic process is given and the general solution of the differential Chapman-Kolmogorov equation is constructed by means of the path integral representation.     

Filtering out photonic Fock states

Unprecedented optical nonlinearities can be generated probabilistically in simple linear-optical networks conditioned on specific measurement outcomes. We describe a highly controllable quantum filter for photon number states, which takes advantage of such a measurement-induced amplitude nonlinearity. The basis for this filter is multiphoton nonclassical interference which we demonstrate for one- and two-photon states over a wide range of beam splitter reflectivities. Specifically, we show that the transmission probability, conditional on a specific measurement outcome, can be larger for a two-photon state than a one-photon state; this is not possible with linear optics alone.     

Multiparticle entanglement via resonant interaction between light and atomic ensembles

Multiparticle entangled states generated via interaction between narrowband light and an ensemble of identical two-level atoms are considered. Depending on the initial photon statistics, correlation between atoms and photons can give rise to entangled states of these systems. It is found that the state of any pair of atoms interacting with weak single-mode squeezed light is inseparable and robust against decay. Optical schemes for preparing entangled states of atomic ensembles by projective measurement are described.     

基于线性光学的多通道混合纠缠态

本文提出了一种基于线性光学的多通道混合纠缠态方案。最初的混合纠缠态是在连续变量猫态和分离变量单光子量子比特之间产生。该方案基于线性光学元件,利用分束器在初始混合纠缠态基础上产生多通道混合纠缠态(M组)。在此基础上,对每对混合纠缠态相对初始混合纠缠态的保真度进行了计算,并分析了保真度随所分份数多少及猫态大小的变化关系。这种多通道混合纠缠态将会为涉及分离变量与连续变量的多通道量子信息传输及存储、量子网络节点信息分布等提供重要的资源。     

Polarization-momentum hyper-entangled two photon states

We present a parametric source which allows the engineering of polarization-momentum hyperentangled two photon states based on linear optics and a single type-I nonlinear crystal. The nonlocal character of these states has been verified by various tests, including the “All Versus Nothing” test of local realism [A. Cabello, Phys. Rev. Lett. 87, 010403 (2001)], which represents a generalization of the GHZ to the case of two entangled particles and two observers. We have also created a complete and deterministic Bell-state measurement by a novel experimental scheme which adopts polarization-momentum hyper-entanglement and requires linear optics and single photon detectors. The text was submitted by the authors in English.     

No-Cloning Theorem,Kochen-Specker Theorem,and Quantum Measurement Theories

The usual no-cloning theorem implies that two quantum states are identical or orthogonal if we allow a cloning to be on the two quantum states. Here, we investigate a relation between the no-cloning theorem and the projective measurement theory that the results of measurements are either + 1 or − 1. We introduce the Kochen-Specker (KS) theorem with the projective measurement theory. We result in the fact that the two quantum states under consideration cannot be orthogonal if we avoid the KS contradiction. Thus the no-cloning theorem implies that the two quantum states under consideration are identical in that case. It turns out that the KS theorem with the projective measurement theory says a new version of the no-cloning theorem. Next, we investigate a relation between the no-cloning theorem and the measurement theory based on the truth values that the results of measurements are either + 1 or 0. We return to the usual no-cloning theorem that the two quantum states are identical or orthogonal in the case.

     

Scheme for remotely preparing a four-particle entangled cluster-type state

A protocol for remotely preparing a four-particle entangled cluster-type state by a set of new four-particle orthogonal basis projective measurement. It is secure that the entangled four-particle cluster-type state can be successfully realized at Bob place. Moreover we have also investigated that quantum channel shared by Alice and Bob is composed of four non-maximally entangled states. It is shown that Bob can also reestablish the original state (to be prepared remotely) with certain probability by means of appropriate unitary transformation.     

Scalable generation of graph-state entanglement through realistic linear optics

We propose a scheme for efficient construction of graph states using realistic linear optics, imperfect photon source, and single-photon detectors. For any many-body entanglement represented by tree-graph states, we prove that the overall preparation and detection efficiency scales nearly polynomially with the size of the graph, no matter how small the efficiencies for the photon source and the detectors.     

High‐resolution spectral characterization of two photon states via classical measurements

Quantum optics plays a central role in the study of fundamental concepts in quantum mechanics, and in the development of new technological applications. Typical experiments employ sources of photon pairs generated by parametric processes such as spontaneous parametric down‐conversion and spontaneous four‐wave‐mixing. The standard characterization of these sources relies on detecting the pairs themselves and thus requires single photon detectors, which limit both measurement speed and accuracy. Here it is shown that the two‐photon quantum state that would be generated by parametric fluorescence can be characterised with unprecedented spectral resolution by performing a classical experiment. This streamlined technique gives access to hitherto unexplored features of two‐photon states and has the potential to speed up design and testing of massively parallel integrated nonlinear sources by providing a fast and reliable quality control procedure. Additionally, it allows for the engineering of quantum light states at a significantly higher level of spectral detail, powering future quantum optical applications based on time‐energy photon correlations.     

Interconvertibility of single-rail optical qubits

We show how to convert between partially coherent superpositions of a single photon with the vacuum by using linear optics and postselection based on homodyne measurements. We introduce a generalized quantum efficiency for such states and show that any conversion that decreases this quantity is possible. We also prove that our scheme is optimal by showing that no linear optical scheme with generalized conditional measurements, and with one single-rail qubit input, can improve the generalized efficiency.     

Generation of macroscopic entangled states by means of x(2) nonlinearity without photon number resolving detection

We generalize the scheme of conditional preparation of x⁽²⁾ macroscopic entangled states [S.A. Podoshvedov, JETP 129 (2006)]. The studied system consists of a system of coupled down converters with type-I phase matching pumped simultaneously by powerful optical fields in coherent states with one auxiliary photon in the superposition state of two input modes and a projective measurement system. The projective measurement system involves two Hadamard gates introduced to generated output modes followed by photodetectors. Identification of macroscopic entangled states is produced by registration of one photon. No photon number resolving detection is required for the studied scheme. The text was submitted by the author in English.     

Characterizing the dynamics of quantum discord under phase damping with POVM measurements

In the analysis of quantum discord, the minimization of average entropy traditionally involved over orthogonal projective measurements may be attained at more optimal decompositions by using the positive-operator-valued measure(POVM)measurements. Taking advantage of the quantum steering ellipsoid in combination with three-element POVM optimization,we show that, for a family of two-qubit X states locally interacting with Markovian non-dissipative environments, the decay rates of quantum discord show smooth dynamical evolutions without any sudden change. This is in contrast to two-element orthogonal projective measurements, in which case the sudden change of the decay rates of quantum and classical decoherences may be a common phenomenon. Notwithstanding this, we find that a subset of X states(including the Bell diagonal states) involving POVM optimization can still preserve the sudden change character as usual.     

Nearly deterministic linear optical controlled-NOT gate

We show how to construct a near deterministic CNOT gate using several single photons sources, linear optics, photon number resolving quantum nondemolition detectors, and feed forward. This gate does not require the use of massively entangled states common to other implementations and is very efficient on resources with only one ancilla photon required. The key element of this gate is nondemolition detectors that use a weak cross-Kerr nonlinearity effect to conditionally generate a phase shift on a coherent probe if a photon is present in the signal mode. These potential phase shifts can then be measured using highly efficient homodyne detection.     

How quantum correlations enhance prediction of complementary measurements

If there are correlations between two qubits, then the results of the measurement on one of them can help to predict measurement results on the other one. It is an interesting question as to what can be predicted about the results of two complementary projective measurements on the first qubit. To quantify these predictions the complementary knowledge excesses are used. A nontrivial constraint restricting them is derived. For any mixed state and for arbitrary measurements the knowledge excesses are bounded by a factor depending only on the maximal violation of Bell's inequalities. This result is experimentally verified on two-photon Werner states prepared by means of spontaneous parametric down-conversion.     

Optical hybrid approaches to quantum information

This article reviews recent hybrid approaches to optical quantum information processing, in which both discrete and continuous degrees of freedom are exploited. There are well‐known limitations to optical single‐photon‐based qubit and multi‐photon‐based qumode implementations of quantum communication and quantum computation, when the toolbox is restricted to the most practical set of linear operations and resources such as linear optics and Gaussian operations and states. The recent hybrid approaches aim at pushing the feasibility, the efficiencies, and the fidelities of the linear schemes to the limits, potentially adding weak or measurement‐induced nonlinearities to the toolbox.