Measurement Of Photon Number Research Articles

CHSH Bell tests for optical hybrid entanglement

Optical hybrid entanglement can be created between two qubits, one encoded in a single photon and another one in coherent states with opposite phases. It opens the path to a variety of quantum technologies, such as heterogeneous quantum networks, merging continuous- and discrete-variable encoding, and enabling the transport and interconversion of information. However, reliable characterization of the non-local nature of this quantum state is limited so far to full quantum state tomography. Here, we perform a thorough study of Clauser–Horne–Shimony–Holt Bell inequality tests, enabling practical verification of quantum nonlocality for optical hybrid entanglement. We show that a practical violation of this inequality is possible with simple photon number on/off measurements if detection efficiencies stay above 82%. Another approach, based on photon-number parity measurements, requires 94% efficiency but works well in the limit of higher photon populations. Both tests use no postselection of the measurement outcomes and they are free of the fair-sampling hypothesis. Our proposal paves the way to performing loophole-free tests using feasible experimental tasks such as coherent state interference and photon counting.

Witnessing edge modes in trimerized circuit quantum electrodynamic lattice

We propose a scheme to investigate and witness edge modes of general one-dimensional photonic trimers in a circuit quantum electrodynamic lattice. These in-gap edge modes are strictly and analytically solved and the criteria for their emergence are indicated respectively. Moreover, the energy spectrum of the system shows two different regimes characterized by a discrepancy in the number of edge modes. Specifically, while there are always a couple of edge modes only present at one single boundary in both the regimes, one of the regimes also shows another pair of edge modes localized on the opposite boundary. Furthermore, these edge modes are witnessed with the aid of continuous-time quantum walks and average photon number measurements. Our scheme provides a comprehensive method for studying the edge modes of matter.

Adaptive protocols for SU(1,1) interferometers to achieve ab initio phase estimation at the Heisenberg limit

The precision of phase estimation with interferometers can be greatly enhanced using non-classical quantum states, and the SU(1,1) interferometer is an elegant scheme, which generates two-mode squeezed state internally and also amplifies the signal. It has been shown in Anderson et al (2017 Phys. Rev. A 95 063843) that the photon-number measurement can achieve the Heisenberg limit, but only for estimating a small phase shift. We relax the constraint on the range of phase by considering two adaptive protocols: one also uses the photon-number measurement with a specially tuned sequence of feedback phase; the other implements the yet-to-be-realized optimal measurement but without fine tuning.

Nonlinear Interferometry for Quantum-Enhanced Measurements of Multiphoton Absorption.

Multiphoton absorption is of vital importance in many spectroscopic, microscopic, or lithographic applications. However, given that it is an inherently weak process, the detection of multiphoton absorption signals typically requires large field intensities, hindering its applicability in many practical situations. In this Letter, we show that placing a multiphoton absorbent inside an imbalanced nonlinear interferometer can enhance the precision of multiphoton cross section estimation with respect to strategies based on photon-number measurements using coherent or even squeezed light directly transmitted through the medium. In particular, the power scaling of the sensitivity with photon flux can be increased by 1 order compared with transmission measurements of the sample with coherent light, such that the measurement precision at any given intensity can be greatly enhanced. Furthermore, we show that this enhanced measurement precision is robust against experimental imperfections leading to photon losses, which usually tend to degrade the detection sensitivity. We trace the origin of this enhancement to an optimal degree of squeezing which has to be generated in a nonlinear SU(1,1) interferometer.

Quantification of Quantum Correlations in Two-Beam Gaussian States Using Photon-Number Measurements.

Identification, and subsequent quantification of quantum correlations, is critical for understanding, controlling, and engineering quantum devices and processes. We derive and implement a general method to quantify various forms of quantum correlations using solely the experimental intensity moments up to the fourth order. This is possible as these moments allow for an exact determination of the global and marginal impurities of two-beam Gaussian fields. This leads to the determination of steering, tight lower and upper bounds for the negativity, and the Kullback-Leibler divergence used as a quantifier of state nonseparability. The principal squeezing variances are determined as well using the intensity moments. The approach is demonstrated on the experimental twin beams with increasing intensity and the squeezed super-Gaussian beams composed of photon pairs. Our method is readily applicable to multibeam Gaussian fields to characterize their quantum correlations.

Ultra-high-precision detection of single microwave photons based on a hybrid system between a Majorana zero mode and a quantum dot

The ability to detect single photons has become increasingly essential due to the rise of photon-based quantum computing. In this theoretical work, we propose a system consisting of a quantum dot (QD) side-coupled to a superconducting nanowire. The coupling opens a gap in both the QD mode and the Majorana zero mode (MZM) at the nanowire edge, enabling photon absorption in the system. We show that the absorbed photoelectron decays via rapid (subnanosecond to nanosecond) nonradiative heat transfer to the nanowire phonon modes rather than by spontaneous emission. Furthermore, we calculate the temperature increase and associated resistance increase induced by the absorption of a photon for a given appropriate set of material and environmental parameters, yielding a temperature increase in the millikelvin range and a resistance increase in the kiloohm range, vastly exceeding the photon-absorption-induced temperature and resistance increases for competing 2D-3D hybrid systems by 5 and 9 orders of magnitude, respectively. Last, we determine the detector efficiency and discuss the system density required for deterministic photon number measurement, demonstrating that a photon absorption probability of over 99.9 percent can be achieved for an integrated system consisting of an array of nanowire-QD complexes on-chip inside a cavity. Our results thus provide a basis for a deterministic microwave photon number detector with an unprecedented photon-number-detection resolution.

Achieving the ultimate end-to-end rates of lossy quantum communication networks

The field of quantum communications promises the faithful distribution of quantum information, quantum entanglement, and absolutely secret keys, however, the highest rates of these tasks are fundamentally limited by the transmission distance between quantum repeaters. The ultimate end-to-end rates of quantum communication networks are known to be achievable by an optimal entanglement distillation protocol followed by teleportation. In this work, we give a practical design for this achievability. Our ultimate design is an iterative approach, where each purification step operates on shared entangled states and detects loss errors at the highest rates allowed by physics. As a simpler design, we show that the first round of iterations can purify completely at high rates. We propose an experimental implementation using linear optics and photon-number measurements which is robust to inefficient operations and measurements, showcasing its near-term potential for real-world practical applications.

Remote switch for Schrödinger's cat state using Einstein-Podolsky-Rosen entanglement.

We propose a 'remote switch' for Schrödinger's cat state (SCS). Resorting to nonlocal correlations, we demonstrate that an approximate SCS can be heralded at one mode of an Einstein-Podolsky-Rosen entangled state, via a conditional 'hybrid projective measurement' (HPM) performed on the other one mode. The HPM is able to fully manipulate both size and parity of the generated SCS. Here, the HPM consists of both photon number measurement and homodyne conditioning. Such a remote switch for SCS will open up new ideas in subsequent protocols, including fundamental tests and nonlocal manipulation of non-Gaussian states.

Quantum nondemolition measurements of photon number in monolithic microcavities

We revisit the idea of quantum nondemolition measurement (QND) of optical quanta via a resonantly enhanced Kerr nonlinearity taking into account quantum backaction. We show that the monolithic microcavities enable QND measurement of the number of quanta in a weak signal field using a classical probe field spatially overlapping with the signal. The phase of the probe field acquires information about the signal number of quanta without altering it due to the cross-phase modulation effect. We find the exact solution to the Heisenberg equations of motion of this system and calculate the measurement error, accounting for the optical losses in the measurement path. We identify a realistic approximation to obtain the explicit form of the final conditional quantum state of the signal field, accounting for the undesirable self-phase modulation effect and designing the optimal homodyne measurement of the probe beam to evade this effect. We show that the best modern monolithic microcavities allow achieving the measurement imprecision several times better than the standard quantum limit.

Weak Measurement Effects on Dynamics of Quantum Correlations in a Two-Atom System in Thermal Reservoirs

The dynamical behavior of quantum correlations captured by different forms Measurement-Induced Nonlocality (MIN) between two atoms coupled with thermal reservoirs is investigated and compared with the entanglement. It is shown that the MIN quantities are more robust, while noise causes sudden death in entanglement. Further, we quantified the quantum correlation with weak measurement, and the effect of measurement strength is observed. The role of mean photon number and weak measurement on quantum correlation is also highlighted.

Bennett-Brassard 1984 quantum key distribution using conjugate homodyne detection

Optical homodyne detection has been widely used in continuous-variable (CV) quantum information processing for measuring field quadrature values. In this paper we explore the possibility of operating a conjugate homodyne detection system in "photon counting" mode to implement discrete-variable (DV) quantum key distribution (QKD) protocols. A conjugate homodyne detection system, which consists of a beam splitter followed by two optical homodyne detectors, can simultaneously measure a pair of conjugate quadratures X and P of the incoming quantum state. In classical electrodynamics, X^2 + P^2 is proportional to the energy (the photon number) of the input light. In quantum optics, X and P do not commute and thus the above photon-number measurement is intrinsically noisy. This suggests that a blind application of the standard security proof could result pessimistic QKD performance. We overcome this obstacle by taking advantage of two special features of the proposed detection scheme. First, the fundamental detection noise associated with vacuum fluctuation cannot be manipulated by an external adversary. Second, the ability to reconstruct the photon number statistics at the receiver's end can place additional constraints on possible attacks from the adversary. As an example, we study the security of the BB84 QKD using conjugate homodyne detection and evaluate its performance through numerical simulations. This study may open the door to a new family of QKD protocols, in complementary to the well-established DV-QKD based on single photon detection and CV-QKD based on coherent detection.

Quantum illumination via quantum-enhanced sensing

Quantum-enhanced sensing has a goal of enhancing a parameter sensitivity with input quantum states, while quantum illumination has a goal of enhancing a target detection capability with input entangled states in a heavy noise environment. Here we propose a concatenation between quantum-enhanced sensing and quantum illumination that can take quantum advantage over the classical limit. First, phase sensing in an interferometry is connected to a target sensing via quantum Fisher information. Second, the target sensitivity is investigated in noisy quantum-enhanced sensing. Under the same input state energy, for example, $N$-photon entangled states can exhibit better performance than a two-mode squeezed vacuum state and a separable coherent state. Incorporating a photon-number difference measurement, finally, the noisy target sensitivity is connected to a signal-to-noise ratio which is associated with a minimum error probability of discriminating the presence and absence of the target. We show that both the target sensitivity and the signal-to-noise ratio can be enhanced with increasing thermal noise.

Generation of optical Schrödinger cat states by generalized photon subtraction

We propose a high-rate generation method of optical Schr\"odinger cat states. Thus far, photon subtraction from squeezed vacuum states has been a standard method in cat-state generation, but its constraints on experimental parameters limit the generation rate. In this paper, we consider the state generation by photon number measurement in one mode of two-mode Gaussian states, which is a generalization of conventional photon subtraction, and derive the conditions to generate high-fidelity and large-amplitude cat states. Our method relaxes the constraints on experimental parameters, allowing us to optimize them and attain a high generation rate. Supposing realistic experimental conditions, the generation rate of cat states with large amplitudes ($|\ensuremath{\alpha}|\ensuremath{\ge}2)$ can exceed megacounts per second, about ${10}^{3}$ to ${10}^{6}$ times better than typical rates of conventional photon subtraction. This rate would be improved further by the progress of related technologies. The ability to generate non-Gaussian states at a high rate is important in quantum computing using optical continuous variables, where scalability has been demonstrated but preparation of non-Gaussian states of light remains as a challenging task for universality and fault tolerance. Our proposal reduces the difficulty of the state preparation and opens a way for practical applications in quantum optics.

Improved phase sensitivity in a quantum optical interferometer based on multiphoton catalytic two-mode squeezed vacuum states

The usage of non-Gaussian states to improve the phase sensitivity of interferometers has been studied before. In this paper, we introduce the multiphoton catalysis two-mode squeezed vacuum (MC-TMSV) state as an input of the Mach-Zehnder interferometer (MZI) and study its phase sensitivity with photon-number parity measurement and the influence of photon losses. We also study the statistical properties of the MC-TMSV state in terms of the average photon number, the Wigner function, and the Mandel-$Q$ parameter. Our results show that the MC-TMSV state can exhibit stronger nonclassical characteristics, thereby making the phase sensitivity more precise with either the increase of the photon-catalyzed number or the decrease of the transmissivity. Furthermore, we also consider the effects of photon losses involving external- and internal-loss processes of the MZI, and we find that in both cases the sensitivity with the MC-TMSV state can be significantly better than that with the TMSV state under the same parameters especially in the serious photon losses and small initial squeezing regimes. We also find that the multiphoton catalysis is more sensitive to the external photon losses compared with the internal ones. Our results here can find important applications in quantum metrology.

An average photon number measurement scheme based on balanced homodyne detection

<sec>Quantum key distribution (QKD) has become an alternative technology defensing the security threat resulting from quantum computing. Owing to its superiority in coexistence with optical infrastructures and cost-effective, continuous variable QKD (CV-QKD) is widely studied and developed towards the practical application stage. The standardized measurement of critical parameters of the system should be studied urgently.</sec><sec>In this work we propose a scheme based on balanced homodyne detection with phase-randomized local oscillator to realize the average photon number measurement. By controlling local oscillator phase positively, which obeys <inline-formula><tex-math id="M2">\begin{document}$ [0,\mathrm{ }2\mathrm{\pi }] $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="24-20211216_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="24-20211216_M2.png"/></alternatives></inline-formula> uniform distribution, a linear relationship between average photon numbers and the variance of detector output can be obtained in simulation and experiment. With high-accuracy (～0.1) photons/pulse and large range ～23 dB, this average photon number measurement scheme provides a great reference to evaluating the critical parameters of CV-QKD system in the practical process.</sec>

Bidirectional teleportation using coherent states

In this work, we propose a simple scheme of bidirectional teleportation for transferring unknown coherent superposition states. It consists of exchanging two states by using tripartite entangled coherent states between two parts. This proposed scheme is essentially based on optical devices like beam splitters, phase shifters and photon number measurement detectors. The probability of success and the mean fidelity of quantum teleportation in the presence of quantum noise are evaluated. However, the quantum Fisher information is studied to estimate some parameters such as the weight and the phase of sent states.

Turbulence-free interference induced by the turbulence itself

When a laser beam is incident on a double-slit interferometer without turbulence, the classic Young’s double-slit interference is present in the first-order measurement of the mean photon number (or intensity), while the second-order measurement of photon number fluctuation correlation (or intensity fluctuation correlation) yields a trivial constant. When optical turbulence is introduced, it destroys the classic interference present in the measurement of the photon number; however, two-photon interference appears in the measurement of photon number fluctuation correlation. This interesting observation means that the observed two-photon interference is not only observable through turbulence, i.e., turbulence-free, but also induced by the turbulence itself. Turbulence-free two-photon interference induced by the turbulence itself allows for interferometric sensing through strong turbulence when coherent radiation, such as a laser, is applied.

Temporal array with superconducting nanowire single-photon detectors for photon-number resolution

We present an experimental realization of a 16 element, temporal-array, photon-number-resolving (PNR) detector, which is a multiplexed single-photon detector that splits an input signal over multiple time-bins, and the time-bins are detected using two superconducting nanowire single-photon detectors (SNSPD). A theoretical investigation of the PNR capabilities of the detector is performed and it is concluded that compared to a single-photon detector, our array detector can resolve one order of magnitude higher mean photon numbers, given the same number of input pulses to measure. This claim is experimentally verified and we show that the detector can accurately predict photon numbers between $10^{-3}$ to $10^{2}$. Our present detector is incapable of single-shot photon-number measurements with high precision since its effective quantum efficiency is $49\,\%$. Using SNSPDs with a higher quantum efficiency the PNR performance will improve, but the photon-number resolution will still be limited by the array size.

Implementation of a canonical phase measurement with quantum feedback

Much of modern metrology and communication technology encodes information in electromagnetic waves, typically as an amplitude or phase. While current hardware can perform near-ideal measurements of photon number or field amplitude, to date no device exists that can even in principle perform an ideal phase measurement. In this work, we implement a single-shot canonical phase measurement on a one-photon wave packet, which surpasses the current standard of heterodyne detection and is optimal for single-shot phase estimation. By applying quantum feedback to a Josephson parametric amplifier, our system adaptively changes its measurement basis during photon arrival and allows us to validate the detector's performance by tracking the quantum state of the photon source. These results provide an important capability for optical quantum computing, and demonstrate that quantum feedback can both enhance the precision of a detector and enable it to measure new classes of physical observables.

Nondestructive photon counting in waveguide QED

Number-resolving single-photon detectors represent a key technology for a host of quantum optics protocols, but despite significant efforts, state-of-the-art devices are limited to few photons. In contrast, state-dependent atom counting in arrays can be done with extremely high fidelity up to hundreds of atoms. We show that in waveguide QED, the problem of photon counting can be reduced to atom counting, by entangling the photonic state with an atomic array in the collective number basis. This is possible as the incoming photons couple to collective atomic states and can be achieved by engineering a second decay channel of an excited atom to a metastable state. Our scheme is robust to disorder and finite Purcell factors, and its fidelity increases with atom number. Analyzing the state of the re-emitted photons, we further show that if the initial atomic state is a symmetric Dicke state, dissipation engineering can be used to implement a nondestructive photon-number measurement, in which the incident state is scattered into the waveguide unchanged. Our results generalize to related platforms, including superconducting qubits.