We present the experimental results of measurements of the overlap of both pure and mixed polarization states of photons. The fidelity and purity of mixed states were also measured. The experimental apparatus exploits the fact that a beam splitter can distinguish the singlet Bell state from the other Bell states, i.e., it realizes projections into the symmetric and antisymmetric subspaces of photons' Hilbert space.
For two symmetric quantum states one may be interested in maximizing the overlap under local operations applied to one of them. The question arises whether the maximal overlap can be obtained by applying the same local operation to each party. We show that for two symmetric multiqubit states and local unitary transformations this is the case; the maximal overlap can be reached by applying the same unitary matrix everywhere. For local invertible operations (stochastic local operations assisted by classical communication equivalence), however, we present counterexamples, demonstrating that consi…
Fidelity approach to quantum phase transitions uses the overlap between ground states of the system to gain some information about its quantum phases. Such an overlap is called fidelity. We illustrate how this approach works in the one dimensional quantum Ising model in the transverse field. Several closed-form analytical expressions for fidelity are discussed. An example of what insights fidelity provides into the dynamics of quantum phase transitions is carefully described. The role of fidelity in central spin systems is pointed out.
We use the semiclassical method proposed in \cite{Adelcio2003} to study scalar products such as the overlap, Husimi functions and fidelity decay. Scars of classical periodic orbits arise naturally in this pertubative expansion. We also derive analytically a well known numerical result that fidelity has a quadratic decay for short times. We study the overlap in the chaotic regime and integrable for some simple systems.
This paper presents a unified semiclassical framework for five regimes of quantum fidelity decay and conjectures a new universal regime. The theory is based solely on the statistics of actions in the dephasing representation. Counterintuitively, in this representation, all of the decay is due to interference and none due to the decay of classical overlaps. Both rigorous and numerical support of the theory is provided.
The fidelity of postselecting devices based on direct photon number detection can be significantly improved by insertion of a phase-insensitive optical amplifier in front of the detector. The scheme is simple, and the cost to the probability of obtaining the appropriate detector outcome is low.
Using a continuous-wave type-II optical parametric oscillator below threshold, we have demonstrated a novel source of heralded single-photons with high-fidelity. The generated state is characterized by homodyne detection and exhibits a 79% fidelity with a single-photon Fock state (91% after correction of detection loss). The low admixture of vacuum and the well-defined spatiotemporal mode are critical requirements for their subsequent use in quantum information processing.
We propose a detection scheme for measuring the overlap of the quantum state of a weakly excited traveling-field mode with a desired reference quantum state, by successive mixing the signal mode with modes prepared in coherent states and performing photon-number measurements in an array of beam splitters. To illustrate the scheme, we discuss the measurement of the quantum phase and the detection of Schrodinger-cat-like states.
We derive composite pulse sequences that achieve high-fidelity excitation of two-state systems in an optically dense, inhomogeneously broadened ensemble. The composite pulses are resistant to distortions due to the back-action of the medium they propagate in and are able to create high-fidelity inversion to optical depths $αz>10$. They function well with smooth pulse shapes used for coherent control of optical atomic transitions in quantum computation and communication. They are an intermediary solution between single $π$-pulse excitation schemes and adiabatic passage schemes, being far more e…
We experimentally generate and characterize a six-photon polarization entangled state, which is usually called "Psi 6 +". This is realized with a filtering procedure of triple emissions of entangled photon pairs from a single source, which does not use any interferometric overlaps. The setup is very stable and we observe the six-photon state with high fidelity. The observed state can be used for demonstrations of telecloning and secret sharing protocols.
We present a perturbative result for the temporal evolution of the fidelity of the quantum kicked rotor, i.e. the overlap of the same initial state evolved with two slightly different kicking strengths, for kicking periods close to a principal quantum resonance. Based on a pendulum approximation we describe the fidelity for rotational orbits in the pseudo-classical phase space of a corresponding classical map. Our results are compared to numerical simulations indicating the range of applicability of our analytical approximation.
A generic model of measurement device which is able to directly measure commonly used quantum-state characteristics such as fidelity, overlap, purity and Hilbert-Schmidt distance for two general uncorrelated mixed states is proposed. In addition, for two correlated mixed states, the measurement realizes an entanglement witness for Werner's separability criterion. To determine these observables, the estimation only one parameter - the visibility of interference, is needed. The implementations in cavity QED, trapped ion and electromagnetically induced transparency experiments are discussed.
We present a systematic comparison of different methods of fidelity estimation of a linear optical quantum controlled-Z gate implemented by two-photon interference on a partially polarizing beam splitter. We have utilized a linear fidelity estimator based on the Monte Carlo sampling technique as well as a non-linear estimator based on maximum likelihood reconstruction of a full quantum process matrix. In addition, we have also evaluated lower bound on quantum gate fidelity determined by average quantum state fidelities for two mutually unbiased bases. In order to probe various regimes of opera…
We have modelled the Zeno effect Control-Sign gate of Franson et al (PRA 70, 062302, 2004) and shown that high two-photon to one-photon absorption ratios, $κ$, are needed for high fidelity free standing operation. Hence we instead employ this gate for cluster state fusion, where the requirement for $κ$ is less restrictive. With the help of partially offline one-photon and two-photon distillations, we can achieve a fusion gate with unity fidelity but non-unit probability of success. We conclude that for $κ> 2200$, the Zeno fusion gate will out perform the equivalent linear optics gate.
Silicon-vacancy and tin-vacancy defects in diamond are of interest as alternative qubits to the NV center due to their superior optical properties. While the availability of optical transitions in these defects is one of their assets, high-fidelity optical coherent control has not been demonstrated. Here, we design novel optical control schemes tailored to these defects. We evaluate the performance of arbitrary single-qubit rotations of the electron spin qubit both in the absence and presence of an external magnetic field, by taking into account both coherent and incoherent errors. We find tha…
Arrays of neutral-atom qubits in optical tweezers are a promising platform for quantum computation. Despite experimental progress, a major roadblock for realizing neutral atom quantum computation is the qubit initialization. Here we propose that supersymmetry -- a theoretical framework developed in particle physics -- can be used for ultra-high fidelity initialization of neutral-atom qubits. We show that a single atom can be deterministically prepared in the vibrational ground state of an optical tweezer by adiabatically extracting all excited atoms to a supersymmetric auxiliary tweezer. The s…
We propose an efficiently measurable lower bound on quantum process fidelity of N-qubit controlled-Z gates. This bound is determined by average output state fidelities for N partially conjugate product bases. A distinct advantage of our approach is that only fidelities with product states need to be measured while keeping the total number of measurements much smaller than what is necessary for full quantum process tomography. As an application, we use this method to experimentally estimate quantum process fidelity F of a three-qubit linear optical quantum Toffoli gate and we find that F>=0.83.…
We propose a linear-optical setup for heralded qubit amplification with tunable output qubit fidelity. We study its success probability as a function of output qubit fidelity showing that at the expense of lower fidelity, the setup can considerably increase probability of successful operation. These results are subsequently applied in a proposal for state dependent qubit amplification. Similarly to state-dependent quantum cloning, the a priori information about the input state allows to optimize the qubit amplification procedure to obtain better fidelity versus success probability trade-off.
We show that the KLM scheme [Knill, Laflamme and Milburn, Nature {\bf 409}, 46] can be implemented using polarization encoding, thus reducing the number of path modes required by half. One of the main advantages of this new implementation is that it naturally incorporates a loss detection mechanism that makes the probability of a gate introducing a non-detected error, when non-ideal detectors are considered, dependent only on the detector dark-count rate and independent of its efficiency. Since very low dark-count rate detectors are currently available, a high-fidelity gate (probability of err…
We investigate the effect of variations in beam splitter transmissions and path length differences in the nonlinear sign gate that is used for linear optical quantum computing. We identify two implementations of the gate, and show that the sensitivity to variations in their components differs significantly between them. Therefore, circuits that require a precision implementation may benefit from additional circuit analysis of component variations to identify the most practical implementation. We suggest possible routes to efficient circuit analysis in terms of quantum parameter estimation.
Confined electron spins are preferred candidates for embodying quantum information in the solid state. A popular idea is the use of optical excitation to achieve the ``best of both worlds'', i.e. marrying the long spin decoherence times with rapid gating. Here we study an all-optical adiabatic approach to generating single qubit phase gates. We find that such a gate can be extremely robust against the combined effect of all principal sources of decoherence, with an achievable fidelity of 0.999 even at finite temperature. Crucially this performance can be obtained with only a small time cost: t…
In our previous paper [Phys. Rev. A 84, 042303 (2011)], we proposed an efficient scheme to purify dynamically a bipartite entangled state using short chains of atoms coupled to high-finesse optical cavities. In contrast to conventional entanglement purification protocols, we avoid controlled-NOT gates and thus reduce complicated pulse sequences and superfluous qubit operations. In this paper, we significantly improve the output fidelity of remotely entangled atoms by introducing one additional entanglement protocol in each of the repeater nodes and by optimizing the laser beams required to con…
Knill, Laflamme, and Milburn [Nature 409, 46 (2001)] have shown that quantum logic operations can be performed using linear optical elements and additional ancilla photons. Their approach is probabilistic in the sense that the logic devices fail to produce an output with a failure rate that scales as 1/n, where n is the number of ancilla. Here we present an alternative approach in which the logic devices always produce an output with an intrinsic error rate that scales as 1/n^2,which may have several advantages in quantum computing applications.
Precise readout of spin states is crucial for any approach towards physical realization of a spin-based quantum computer and for magnetometry with single spins. Here, we report a new method to strongly improve the optical readout fidelity of electron spin states associated with single nitrogen-vacancy (NV) centers in diamond. The signal-to-noise ratio is enhanced significantly by performing conditional flip-flop processes between the electron spin and the nuclear spin of the NV center's nitrogen atom. The enhanced readout procedure is triggered by a short preparatory pulse sequence. As the nit…
We demonstrate a quantum error correction scheme that protects against accidental measurement, using an encoding where the logical state of a single qubit is encoded into two physical qubits using a non-deterministic photonic CNOT gate. For the single qubit input states |0>, |1>, |0>+|1>, |0>-|1>, |0>+i|1>, and |0>-i|1> our encoder produces the appropriate 2-qubit encoded state with an average fidelity of 0.88(3) and the single qubit decoded states have an average fidelity of 0.93(5) with the original state. We are able to decode the 2-qubit state (up to a bit flip) by performing a measurement…
Noise is the price to pay when trying to clone or amplify arbitrary quantum states. The quantum noise associated to linear phase-insensitive amplifiers can only be avoided by relaxing the requirement of a deterministic operation. Here we present the experimental realization of a probabilistic noiseless linear amplifier that is able to amplify coherent states at the highest level of effective gain and final state fidelity ever reached. Based on a sequence of photon addition and subtraction, and characterized by a significant amplification and low distortions, this high-fidelity amplification sc…
We investigated the preservation of information encoded into the relative phase and amplitudes of optical pulses during storage and retrieval in an optical memory based on stimulated photon echo. By interfering photon echoes produced in a Ti-indiffused single-mode Er-doped LiNbO$_{3}$ waveguiding structure at telecom wavelength, we found that decoherence in the atomic medium translates only as losses (and not as degradation) of information, as long as the data pulse series is short compared to the atomic decoherence time. The experimentally measured value of the visibility for interfering echo…
We demonstrate single-shot qubit readout with fidelity sufficient for fault-tolerant quantum computation, for two types of qubit stored in single trapped calcium ions. For an optical qubit stored in the (4S_1/2, 3D_5/2) levels of 40Ca+ we achieve 99.991(1)% average readout fidelity in one million trials, using time-resolved photon counting. An adaptive measurement technique allows 99.99% fidelity to be reached in 145us average detection time. For a hyperfine qubit stored in the long-lived 4S_1/2 (F=3, F=4) sub-levels of 43Ca+ we propose and implement a simple and robust optical pumping scheme …
We demonstrate high fidelity single-qubit gate operation in a trapped single neutral atom. The atom is trapped in the recently invented magic-intensity optical dipole trap (MI-ODT) with more stable magnetic field. The MI-ODT efficiently mitigates the detrimental effects of light shifts thus sufficiently improves the performance of single qubit-gates. The gates are driven with microwave, and the fidelity of gate operation is characterized by using the randomized benchmarking method. We obtain an average error per Clifford gate of $3.0(7)\times10^{-5}$ which is much below the error threshold ($1…
We analyze the possibility of modifying the original Farhi-Gutmann Hamiltonian algorithm in order to speed up the procedure for producing a suitably distributed unknown normalized quantum mechanical state. Such a modification is feasible provided only a nearly optimal fidelity is sought. We propose to select the lower bounds of the nearly optimal fidelity values such that their deviations from unit fidelity are less than the minimum error probability characterizing the optimum ambiguous discrimination scheme between the two nonorthogonal quantum states yielding the chosen nearly optimal fideli…
Linear optics quantum computing (LOQC) is a leading candidate for the implementation of large scale quantum computers. Here quantum information is encoded into the quantum states of light and computation proceeds via a linear optics network. It is well known that in such schemes there are stringent requirements on the spatio-temporal structure of photons -- they must be completely indistinguishable and of very high purity. We show that in the Boson-sampling model for LOQC these conditions may be significantly relaxed. We present evidence that by increasing the size of the system we can impleme…
We report the first experimental demonstration of an optical controlled-NOT gate constructed entirely in fibre. We operate the gate using two heralded optical fibre single photon sources and find an average logical fidelity of 90% and an average process fidelity of 0.83<F<0.91. On the basis of a simple model we are able to conclude that imperfections are primarily due to the photon sources, meaning that the gate itself works with very high fidelity.
In an experiment using the odd calcium isotope 43Ca+ we combine the merits of a high fidelity entangling operation on an optical transition (optical qubit) with the long coherence times of two 'clock' states in the hyperfine ground state (hyperfine qubit) by mapping between these two qubits. For state initialization, state detection, global qubit rotations and mapping operations, errors smaller than 1% are achieved whereas the entangling gate adds errors of 2.3%. Based on these operations, we create Bell states with a fidelity of 96.9(3)% in the optical qubit and a fidelity of 96.7(3)% when ma…
We demonstrate a sequence of two quantum teleportations of optical coherent states, combining two high-fidelity teleporters for continuous variables. In our experiment, the individual teleportation fidelities are evaluated as F_1 = 0.70 \pm 0.02 and F_2 = 0.75 \pm 0.02, while the fidelity between the input and the sequentially teleported states is determined as F^{(2)} = 0.57 \pm 0.02. This still exceeds the optimal fidelity of one half for classical teleportation of arbitrary coherent states and almost attains the value of the first (unsequential) quantum teleportation experiment with optical…
We put forth a hitherto unexplored control strategy that enables finite-speed, high-fidelity transport of a quantum wavepacket through a low-temperature dissipative medium. The control consists in confining the wavepacket within a shallow anharmonic trap (tweezer), whose nonuniform velocity is steered so as to maximize the transfer fidelity between two locations. A relevant scenario is a quantum impurity moving through an ultracold gas. Unlike shortcuts to adiabaticity, our approach can simultaneously cope with wavepacket leakage via non-adiabatic and phonon-mediated processes, provided both a…
A significant problem for optical quantum computing is inefficient, or inaccurate photo-detectors. It is possible to use CNOT gates to improve a detector by making a large cat state then measuring every qubit in that state. In this paper we develop a code that compares five different schemes for making multiple measurements, some of which are capable of detecting loss and some of which are not. We explore how each of these schemes performs in the presence of different errors, and derive a formula to find at what probability of qubit loss is it worth detecting loss, and at what probability does…
We study decoherence induced by stochastic squeezing control errors considering the particular implementation of Hadamard gate on optical and ion trap holonomic quantum computers. We analytically obtain both the purity of the final state and the fidelity for Hadamard gate when the control noise is modeled by Ornstein-Uhlenbeck stochastic process. We demonstrate the purity and the fidelity oscillations depending on the choice of the initial superimposed state. We derive a linear formulae connecting the gate fidelity and the purity of the final state.
The fidelity, defined as overlap of eigenstates of two slightly different Hamiltonians, is proposed as an efficient detector of avoided c rossings in the energy spectrum. This new application of fidelity is motivated for model systems, and its value for analyzing complex qua ntum spectra is underlined by applying it to a random matrix model and a tilted Bose-Hubbard system.
We study quantum fidelity, the overlap between two ground states of a many-body system, focusing on the thermodynamic regime. We show how drop of fidelity near a critical point encodes universal information about a quantum phase transition. Our general scaling results are illustrated in the quantum Ising chain for which a remarkably simple expression for fidelity is found.
By interpreting the well-known, qualitative criteria for the existence of quantum error correction (QEC) codes by Knill and Laflamme from a quantitative perspective, we propose a figure of merit for assessing a QEC scheme based on the average fidelity between codewords. This enables us to quantify the performance of a protocol as a whole, including errors beyond the correctable set. Various examples are calculated for photonic qubit codes dealing with the experimentally relevant case of photon loss, demonstrating the advantages of the new measure. In the context of continuous-variable QEC, our…
We propose an architecture for a high-fidelity deterministic controlled-phase gate between two photonic qubits using bulk optical nonlinearities in near-term feasible photonic integrated circuits. The gate is enabled by converting travelling continuous-mode photons into stationary cavity modes using strong classical control fields that dynamically change the cavity-waveguide coupling rate. This process limits the fidelity degrading noise pointed out by Shapiro [J. Shapiro, Phys. Rev. A, 73, 2006] and Gea-Banacloche [J. Gea-Banacloche, Phys. Rev. A, 81, 2010]. We show that high-fidelity gates c…
We describe a scheme for the teleportation of entanglements of zero- and one-photon running-wave field states. In addition to linear optical elements, Kerr nonlinearity is also employed so as to achieve a 100% probability of success in the ideal case. A comprehensive phenomenological treatment of errors in the domain of running-wave physics, for linear and nonlinear optical elements, is also given, making it possible to calculate the fidelity of the teleportation process. A strategy for carrying out the Bell-type measurement which is able to probe the absorption of photons in the optical eleme…
The implementation of polarization-based quantum communication is limited by signal loss and decoherence caused by the birefringence of a single-mode fiber. We investigate the Knill dynamical decoupling scheme, implemented using half-wave plates, to minimize decoherence and show that a fidelity greater than $99\%$ can be achieved in absence of rotation error and fidelity greater than $96\%$ can be achieved in presence of rotation error. Such a scheme can be used to preserve any quantum state with high fidelity and has potential application for constructing all optical quantum delay line, quant…
It is a fundamental principle of quantum theory that an unknown state cannot be copied or, as a consequence, an unknown optical signal cannot be amplified deterministically and perfectly. Here we describe a protocol that provides nondeterministic quantum optical amplification in the coherent state basis with high gain, high fidelity and which does not use quantum resources. The scheme is based on two mature quantum optical technologies, coherent state comparison and photon subtraction. The method compares favourably with all previous nondeterministic amplifiers in terms of fidelity and success…
We experimentally address the significance of fidelity as a figure of merit in quantum state reconstruction of discrete (DV) and continuous variable (CV) quantum optical systems. In particular, we analyze the use of fidelity in quantum homodyne tomography of CV states and maximum-likelihood polarization tomography of DV ones, focussing attention on nonclassicality, entanglement and quantum discord as a function of fidelity to a target state. Our findings show that high values of fidelity, despite well quantifying geometrical proximity in the Hilbert space, may be obtained for states displaying…
Cluster states are the essential resource used in the implementation of Fusion-based quantum computation (FBQC). We introduce a method to generate high-fidelity optical cluster states by utilising the concept of unitary averaging. This error averaging technique is entirely passive and can be readily incorporated into the proposed PsiQuantum's FBQC architecture. Using postselection and the redundant encoding of Fusion gates, we observe an enhancement in the average fidelity of the output cluster state. We also show an improvement in the linear optical Bell-state measurement (BSM) success probab…
We investigate the polarization state dynamics of single photon pulse for optical fiber quantum communication channels. On the basis of a birefringence vector model in which amplitude and direction are both stochastic variables, Jones vector is obtained by solving the frequency domain wave equation. The fidelity of output quantum state and degree of polarization of the pulse are also obtained from the density operators. It is shown that the fidelity of quantum state decreases quickly and tends to a stable value along optical fiber, and increases for larger mean fluctuation magnitude of the sto…
Quantum fidelity is a measure to quantify the closeness of two quantum states. In an operational sense, it is defined as the minimal overlap between the probability distributions of measurement outcomes and the minimum is taken over all possible positive-operator valued measures (POVMs). Quantum fidelity has been investigated in various scientific fields, but the identification of associated optimal measurements has often been overlooked despite its great importance for practical purposes. We find here the optimal POVMs for quantum fidelity between multi-mode Gaussian states in a closed analyt…
High fidelity preservation of photonic hyperentanglement in a free-space optical delay line
Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）；Department of Physics, National University of Singapore（新加坡国立大学物理系）；Thales Research and Technology（泰雷兹研究技术）
We have performed experimental quantum state tomography of NOON states with up to four photons. The measured states are generated by mixing a classical coherent state with spontaneous parametric down-conversion. We show that this method produces states which exhibit a high fidelity with ideal NOON states. The fidelity is limited by the overlap of the two-photon down-conversion state with any two photons originating from the coherent state, for which we introduce and measure a figure of merit. A second limitation on the fidelity set by the total setup transmission is discussed. We also apply th…
We present a theoretical treatment of conditional preparation of one-photon states from a continuous-wave non-degenerate optical parametric oscillator. We obtain an analytical expression for the output state Wigner function, and we maximize the one-photon state fidelity by varying the temporal mode function of the output state. We show that a higher production rate of high fidelity Fock states is obtained if we condition the outcome on dark intervals around trigger photo detection events.
