Parity Measurements Research Articles

Nearly optimal measurement schemes in a noisy Mach-Zehnder interferometer with coherent and squeezed vacuum

The use of an interferometer to perform an ultra-precise parameter estimation under noisy conditions is a challenging task. Here we discuss nearly optimal measurement schemes for a well known, sensitive input state, squeezed vacuum and coherent light. We find that a single mode intensity measurement, while the simplest and able to beat the shot-noise limit, is outperformed by other measurement schemes in the low-power regime. However, at high powers, intensity measurement is only outperformed by a small factor. Specifically, we confirm, that an optimal measurement choice under lossless conditions is the parity measurement. In addition, we also discuss the performance of several other common measurement schemes when considering photon loss, detector efficiency, phase drift, and thermal photon noise. We conclude that, with noise considerations, homodyne remains near optimal in both the low and high power regimes. Surprisingly, some of the remaining investigated measurement schemes, including the previous optimal parity measurement, do not remain even near optimal when noise is introduced.

Loss-tolerant parity measurement for distant quantum bits

We propose a scheme to measure the parity of two distant qubits, while ensuring that losses on the quantum channel between them does not destroy coherences within the parity subspaces. This capability enables deterministic preparation of highly entangled qubit states whose fidelity is not limited by the transmission loss. The key observation is that for a probe electromagnetic field in a particular quantum state, namely a superposition of two coherent states of opposite phases, the transmission loss stochastically applies a near-unitary back-action on the probe state. This leads to a parity measurement protocol where the main effect of the transmission losses is a decrease in the measurement strength. By repeating the non-destructive (weak) parity measurement, one achieves a high-fidelity entanglement in spite of a significant transmission loss.

Generation and characterization of discrete spatial entanglement in multimode nonlinear waveguides

We analyze theoretically spontaneous parametric down-conversion in a multimode nonlinear waveguide as a source of entangled pairs of spatial qubits, realized as superpositions of a photon in two orthogonal transverse modes of the waveguide. It is shown that by exploiting intermodal dispersion, down-conversion into the relevant pairs of spatial modes can be selected by spectral filtering, which also provides means to fine-tune the properties of the generated entangled state. We also discuss an inverting interferometer detecting the spatial parity of the input beam as a versatile tool to characterize properties of the generated state. A single-photon Wigner function obtained by a scan of the displaced parity can be used to identify the basis modes of spatial qubit, whereas correlations between displaced parity measurements on two photons can directly verify quantum entanglement through a violation of Bell's inequalities.

Heisenberg-limited Sagnac interferometer with multiparticle states

The Sagnac interferometry has been widely used to measure rotation frequency. Beyond the conventional single-particle Sagnac interferometry, we propose an atomic Sagnac interferometry via multi-particle entangled states. In our scheme, an ensemble of entangled two-state Bose atoms are moved in a ring by a state-dependent rotating potential and then are recombined for interference via Ramsey pulses after a specific time determined by the state-dependent rotating potential. The ultimate rotation sensitivity can be improved to the Heisenberg limit if the initial internal degrees of freedom are entangled. By implementing parity measurement, the ultimate measurement precision can be saturated and the achieved measurement precisions approach to the Heisenberg limit. Our results provide a promising way to exploit many-body quantum entanglement in precision metrology of rotation sensing.

Genuine multipartite nonlocality of permutationally invariant Gaussian states

We investigate genuine multipartite nonlocality of pure permutationally invariant multimode Gaussian states of continuous variable systems, as detected by the violation of Svetlichny inequality. We identify the phase space settings leading to the largest violation of the inequality when using displaced parity measurements, distinguishing our results between the cases of even and odd total number of modes. We further consider pseudospin measurements and show that, for three-mode states with asymptotically large squeezing degree, particular settings of these measurements allow one to approach the maximum violation of Svetlichny inequality allowed by quantum mechanics. This indicates that the strongest manifestation of genuine multipartite quantum nonlocality is in principle verifiable on Gaussian states.

Participatory parity and epistemological access in the extended curriculum programmes

The article examines students’ engagement in university classrooms in South Africa. Of interest is the extent to which students experience some measure of parity of participation in these engagements. Such “participatory parity” broadly refers to students being able to act on a more or less equal footing with their peers and lecturers. Though much has been written about student engagement and its educational value, such engagement is not typically examined through Fraser’s parity lens. Such parity matters because students are able to experience themselves as valued participants in the social world of the university. However, as what is being discussed is the university classroom, parity of participation in itself is not the only outcome, it is also gaining access to disciplinary knowledge through such participation, or what is referred to here as epistemological access. In order to examine the nexus between participatory parity and epistemological access a methodology for examining participation drawn from activity theory is mobilised. The paper then concludes with reflecting on the usefulness of using this theory and also the usefulness of promoting participatory parity in classroom engagement.

Quantum Networks with Chiral-Light-Matter Interaction in Waveguides.

We propose a scalable architecture for a quantum network based on a simple on-chip photonic circuit that performs loss-tolerant two-qubit measurements. The circuit consists of two quantum emitters positioned in the arms of an on-chip Mach-Zehnder interferometer composed of waveguides with chiral-light-matter interfaces. The efficient chiral-light-matter interaction allows the emitters to perform high-fidelity intranode two-qubit parity measurements within a single chip and to emit photons to generate internode entanglement, without any need for reconfiguration. We show that, by connecting multiple circuits of this kind into a quantum network, it is possible to perform universal quantum computation with heralded two-qubit gate fidelities F∼0.998 achievable in state-of-the-art quantum dot systems.

Demonstration of Weight-Four Parity Measurements in the Surface Code Architecture.

We present parity measurements on a five-qubit lattice with connectivity amenable to the surface code quantum error correction architecture. Using all-microwave controls of superconducting qubits coupled via resonators, we encode the parities of four data qubit states in either the X or the Z basis. Given the connectivity of the lattice, we perform a full characterization of the static Z interactions within the set of five qubits, as well as dynamical Z interactions brought along by single- and two-qubit microwave drives. The parity measurements are significantly improved by modifying the microwave two-qubit gates to dynamically remove nonideal Z errors.

Potential for optimizing the Higgs boson CP measurement in H→ττ decays at the LHC including machine learning techniques

We investigate potential for measuring CP state of the Higgs boson in the H to tau tau$ decay with consecutive tau-lepton decays in channels: tau^+- to rho^+- nu_tau and tau^+- to a1^+- nu_tau combined. Subsequent decays rho^+- to pi^+- pi^0, a1^+- to rho^0 pi^+- and rho^0 to pi^+ pi^- are taken into account. We will explore extensions of the method, where acoplanarity angle for the planes build on the visible decay products, pi^+- pi^0 of tau^+- to pi^pm pi^0 nu_tau, was used. The angle is sensitive to transverse spin correlations, thus to parity. We show, that in the case of the cascade decays of tau to a1 nu, information on the CP state of Higgs can be extracted from the acoplanarity angles as well. Because in the cascade decay a1^+- to rho^0 pi^pm,rho^0 to pi^+ pi^- up to four planes can be defined, up to 16 distinct acoplanarity angles are available for H \to tau tau to a1^+ a1^- nu nu decays. These acoplanarities carry in part supplementary but also correlated information. It is thus cumbersome to evaluate an overall sensitivity. We investigate sensitivity potential of such analysis, by developing and implementing model in the Machine Learning (ML) techniques. We quantify possible improvements when multi-dimensional phase-space of outgoing decay products directions is used, instead of 1-dimensional projections i.e. the acoplanarity angles. We do not take into account ambiguities resulting from detector uncertainties or background contamination, we concentrate on usefulness of ML methods and tau to 3pi nu decays for Higgs boson parity measurement.

Readout of Majorana parity states using a quantum dot

We theoretically examine a scheme for projectively reading out the parity state of a pair of Majorana bound states (MBS) using a tunnel coupled quantum dot. The dot is coupled to one end of the topological wire but isolated from any reservoir, and is capacitively coupled to a charge sensor for measurement. The combined parity of the MBS-dot system is conserved and charge transfer between the MBS and dot only occurs through resonant tunnelling. Resonance is controlled by the dot potential through a local gate and by the MBS energy splitting due to the overlap of the MBS pair wavefunctions. The latter splitting can be tuned from zero (topologically protected regime) to a finite value by gate-driven shortening of the topological wire. Simulations show that the oscillatory nature of the MBS splitting is not a fundamental obstacle to readout, but requires precise gate control of the MBS spatial position and dot potential. With experimentally realistic parameters, we find that high-fidelity parity readout is achievable given nanometer-scale spatial control of the MBS, and that there is a tradeoff between required precisions of temporal and spatial control. Use of the scheme to measure the MBS splitting versus separation would present a clear signature of topological order, and could be used to test the robustness of this order to spatial motion, a key requirement in certain schemes for scalable topological qubits. We show how the scheme can be extended to distinguish valid parity measurements from invalid ones due to gate calibration errors.

The value of ultrasound measurement of cervical length and parity in prediction of cesarean section risk in term premature rupture of membranes and unfavorable cervix.

To evaluate the influence of cervical length (CL) and parity as prediction factors for assessment of cesarean section (CS) risk in women with premature rupture of membranes (PROM) at term and unfavorable cervix, undergoing induction of labor (IOL) with dinoprostone intracervical gel. A prospective study involved 50 nulliparous and 51 multiparous women admitted for IOL. Pre-induction CL was measured and delivery outcomes were recorded. Nulliparous women were younger than the multiparous (26.6±5.2 vs. 30.5±4.9; P<0.001) and had longer pre-induction CL (35.6±5.5 vs. 31.5±4.8; P<0.001) and induction-delivery interval (582 vs. 420 min; P<0.001). There was no difference in the mode of delivery, CS indications, Apgar score, neonatal weight, the rate of neonatal intensive care unit admission and perinatal death in respect of parity. CL was significantly shorter in vaginal vs. cesarean deliveries regardless of parity (31.4 vs. 38.8 mm, P<0.001, respectively). Cut-off values of CL for predicting CS were 37.5 mm in nulliparae and 34.5 mm in multiparae. CLs of 37.5 mm in nulliparae and 34.5 mm in multiparae were determined as the cut-off values in predicting CS risk in women with PROM at term and unfavorable cervix.

Ultra-sensitive and super-resolving angular rotation measurement based on photon orbital angular momentum using parity measurement.

Photon orbital angular momentum has led to many novel insights and applications in quantum measurement. Photon orbital angular momentum can increase the resolution and sensitivity of angular rotation measurement. However, quantum measurement strategy can further surpass this limit and improve the resolution of angular rotation measurement. This Letter proposes and demonstrates a parity measurement method in angular rotation measurement scheme for the first time. Parity measurement can make the resolution superior to the limit of the existing method. The sensitivity can be improved with higher orbital angular momentum photons. Moreover, this Letter gives a detailed discussion of the change of resolution and sensitivity in the presence of photon loss.

Quantum phase estimation using path-symmetric entangled states.

We study the sensitivity of phase estimation using a generic class of path-symmetric entangled states |φ〉|0〉 + |0〉|φ〉, where an arbitrary state |φ〉 occupies one of two modes in quantum superposition. With this generalization, we identify the fundamental limit of phase estimation under energy constraint that is characterized by the photon statistics of the component state |φ〉. We show that quantum Cramer-Rao bound (QCRB) can be indefinitely lowered with super-Poissonianity of the state |φ〉. For possible measurement schemes, we demonstrate that a full photon-counting employing the path-symmetric entangled states achieves the QCRB over the entire range [0, 2π] of unknown phase shift ϕ whereas a parity measurement does so in a certain confined range of ϕ. By introducing a component state of the form , we particularly show that an arbitrarily small QCRB can be achieved even with a finite energy in an ideal situation. This component state also provides the most robust resource against photon loss among considered entangled states over the range of the average input energy Nav > 1. Finally we propose experimental schemes to generate these path-symmetric entangled states for phase estimation.

Quantum optical interferometry via the photon-added two-mode squeezed vacuum states

We investigate the sensitivity and resolution of phase estimation in a Mach–Zehnder interferometer with photon-added two-mode squeezed vacuum states (PA-TMSVS) with a photon-number parity measurement scheme. Our results indicate that, when the phase to be estimated is small, the PA-TMSVS offers an improved phase resolution over both the two-mode squeezed vacuum and the photon-subtracted two-mode squeezed vacuum for a given initial squeezing level. In addition, we study the behavior of the quantum Fisher information of the PA-TMSVS, and show that the optimum phase uncertainty predicted by the corresponding Cramer–Rao bound can be achieved with a parity measurement.

Heisenberg-scaled magnetometer with dipolar spin-1 condensates

We propose a scheme to realize a Heisenberg-scaled magnetometer using dipolar spin-1 condensates. The input state of magnetometer is prepared by slowly sweeping a transverse magnetic field to zero, which yields a highly entangled spin state of $N$ atoms. We show that this process is protected by a parity symmetry such that the state preparation time is within the reach of the current experiment. We also propose a parity measurement with a Stern-Gerlach apparatus which is shown to approach the optimal measurement in the large atom number limit. Finally, we show that the phase estimation sensitivity of the proposed scheme roughly follows the Heisenberg scaling.

Comparing and Combining Measurement-Based and Driven-Dissipative Entanglement Stabilization

We demonstrate and contrast two approaches to the stabilization of qubit entanglement by feedback. Our demonstration is built on a feedback platform consisting of two superconducting qubits coupled to a cavity which are measured by a nearly-quantum-limited measurement chain and controlled by high-speed classical logic circuits. This platform is used to stabilize entanglement by two nominally distinct schemes: a "passive" reservoir engineering method and an "active" correction based on conditional parity measurements. In view of the instrumental roles that these two feedback paradigms play in quantum error-correction and quantum control, we directly compare them on the same experimental setup. Further, we show that a second layer of feedback can be added to each of these schemes, which heralds the presence of a high-fidelity entangled state in realtime. This "nested" feedback brings about a marked entanglement fidelity improvement without sacrificing success probability.

About measurements of Higgs boson parity

Recently CMS and ATLAS announced that they had measured the Higgs boson parity. In this note we show that their approach can determine this parity only under the additional assumption that an extension of Standard Model of some special type is realized in Nature.We show that the used approach gives no information about the Higgs boson parity when assuming most other extensions of the Standard Model.

Infrared laser induced population transfer and parity selection in (14)NH3: A proof of principle experiment towards detecting parity violation in chiral molecules.

We have set up an experiment for the efficient population transfer by a sequential two photon-absorption and stimulated emission-process in a molecular beam to prepare quantum states of well defined parity and their subsequent sensitive detection. This provides a proof of principle for an experiment which would allow for parity selection and measurement of the time evolution of parity in chiral molecules, resulting in a measurement of the parity violating energy difference ΔpvE between enantiomers of chiral molecules. Here, we present first results on a simple achiral molecule demonstrating efficient population transfer (about 80% on the average for each step) and unperturbed persistence of a selected excited parity level over flight times of about 1.3 ms in the beam. In agreement with model calculations with and without including nuclear hyperfine structure, efficient population transfer can be achieved by a rather simple implementation of the rapid adiabatic passage method of Reuss and coworkers and considering also the stimulated Raman adiabatic passage technique of Bergmann and coworkers as an alternative. The preparation step uses two powerful single mode continuous wave optical parametric oscillators of high frequency stability and accuracy. The detection uses a sensitive resonantly enhanced multiphoton ionization method after free flight lengths of up to 0.8 m in the molecular beam. Using this technique, we were able to also resolve the nuclear hyperfine structure in the rovibrational levels of the ν1 and ν3 fundamentals as well as the 2ν4 overtone of (14)NH3, for which no previous data with hyperfine resolution were available. We present our new results on the quadrupole coupling constants for the ν1, ν3, and 2ν4 levels in the context of previously known data for ν2 and its overtone, as well as ν4, and the ground state. Thus, now, (14)N quadrupole coupling constants for all fundamentals and some overtones of (14)NH3 are known and can be used for further theoretical analysis.

Quantum metrology with spin cat states under dissipation.

Quantum metrology aims to yield higher measurement precisions via quantum techniques such as entanglement. It is of great importance for both fundamental sciences and practical technologies, from testing equivalence principle to designing high-precision atomic clocks. However, due to environment effects, highly entangled states become fragile and the achieved precisions may even be worse than the standard quantum limit (SQL). Here we present a high-precision measurement scheme via spin cat states (a kind of non-Gaussian entangled states in superposition of two quasi-orthogonal spin coherent states) under dissipation. In comparison to maximally entangled states, spin cat states with modest entanglement are more robust against losses and their achievable precisions may still beat the SQL. Even if the detector is imperfect, the achieved precisions of the parity measurement are higher than the ones of the population measurement. Our scheme provides a realizable way to achieve high-precision measurements via dissipative quantum systems of Bose atoms.

Precision tests of parity violation over cosmological distances

Recent measurements of the cosmic microwave background (CMB) B-mode polarization power spectrum by the Bicep2 and POLARBEAR experiments have demonstrated new precision tools for probing fundamental physics. Regardless of origin, the detection of sub-μK CMB polarization represents a technological tour de force. Yet more information may be latent in the CMB's polarization pattern. Because of its tensorial nature, CMB polarization may also reveal parity-violating physics via a detection of cosmic polarization rotation. Although current CMB polarimeters are sensitive enough to measure one degree-level polarization rotation with >5σ statistical significance, they lack the ability to differentiate this effect from a systematic instrumental polarization rotation. Here, we motivate the search for cosmic polarization rotation from current CMB data as well as independent radio galaxy and quasar polarization measurements. We argue that an improvement in calibration accuracy would allow the unambiguous measurement of parity- and Lorentz-violating effects. We describe the CalSat space-based polarization calibrator that will provide stringent control of systematic polarization angle calibration uncertainties to 0.05° – an order of magnitude improvement over current CMB polarization calibrators. CalSat-based calibration could be used with current CMB polarimeters searching for B-mode polarization, effectively turning them into probes of cosmic parity violation, ‘for free’ – i.e. without the need to build dedicated instruments.