Homodyne Measurement Research Articles

Quantum fluctuations spatial mode profiler

The spatial mode is an essential component of an electromagnetic field description, yet it is challenging to characterize it for optical fields with the low average photon number, such as in a squeezed vacuum. We present a method for the reconstruction of the spatial modes of such fields based on the homodyne measurements of their quadrature noise variance performed with a set of structured masks. We show theoretically that under certain conditions, we can recover individual spatial mode distributions by using the weighted sum of the basis masks, where weights are determined using measured variance values and phases. We apply this approach to analyze the spatial structure of a squeezed vacuum field with various amount of excess thermal noise generated in Rb vapor.

Near-perfect discrimination of chiral molecules based on steady states of a cavity mode

We propose a protocol to realize discrimination of chiral molecules based on steady states of a cavity mode. Using the closed-loop three-level structure of a molecule, an effective Hamiltonian of the molecule-cavity-coupled system is derived. The effective Hamiltonian is similar to a linear driving of the cavity mode, but the driving strength depends on the chirality of the molecule. In the presence of photon loss, the cavity behaves like a driven damped harmonic oscillator, and it will evolve to different steady coherence states according to the chirality of the molecule. By selecting proper parameters, it is possible to obtain steady coherence states with large-enough amplitudes that can be well determined by homodyne measurements on the cavity. Consequently, the chirality of the molecules can be discriminated near perfectly, according to the measurement result of the cavity. Numerical simulations show that the protocol is insensitive to the systematic errors of the control fields and the energy relaxation of the molecules. Therefore, the protocol may provide an effective approach to realize chirality discrimination with high accuracy.

High-threshold fault-tolerant quantum computation with the Gottesman-Kitaev-Preskill qubit under noise in an optical setup

To implement fault-tolerant quantum computation (FTQC) with continuous variables, continuous variables need to be digitized using an appropriate code such as the Gottesman--Kitaev--Preskill (GKP) qubit. The scheme introduced in [K. Fukui et. al., Phys. Rev. X 8, 021054 (2018)] has reduced the threshold of a squeezing level required for continuous-variable FTQC to less than 10 dB, assuming noise derived from the GKP qubit itself. In this work, we propose a scheme to improve noise tolerance during the construction of large-scale cluster state used for FTQC with the GKP qubits. In our scheme, a small-scale cluster state is prepared by employing a maximum-likelihood method, the entanglement generation via the Bell measurement, and a probabilistic reliable measurement. Then, a large-scale cluster state is construct from the small-scale cluster states via the encoded Bell measurement. In the numerical calculations, we assume errors derived from the two-mode gate and loss in the homodyne measurement in addition to noise from the GKP qubit itself. The results show that the thresholds of a squeezing level are around 8.1, 9.6, and 12.4 dB for loss in the homodyne measurement 0, 5, and 10 %, respectively. Hence, this work provides a way toward continuous-variable FTQC with a feasible squeezing level.

Imaging-Based Quantum Tomography of Orbital-Angular-Momentum-Multiplexed Continuous-Variable Entangled States

Multiplexing techniques combine multiple signals into one channel, in order to increase the channel capacity and speed. Here we propose a correlation-based imaging method to efficiently measure the quantum states of orbital-angular-momentum (OAM)-multiplexed Gaussian light. The covariance matrices for all OAM components of the multiplexed Gaussian light can be efficiently reconstructed by one homodyne measurement on each beam. We also show that the proposed scheme can be simplified and implemented with only two charge coupled device detectors.

Unbalanced beam splitters enabling enhanced phase sensitivity of a Mach-Zehnder interferometer using coherent and squeezed vacuum states

An optical interferometer seeded by coherent and squeezed vacuum states seems to be the most promising platform for gravitational wave detection. Prior studies regarding this estimation protocol focus on the scenario in which the transmittances of two beam splitters are $\frac{1}{2}$. In this paper, with respect to the same inputs, we analyze the phase sensitivity of an unbalanced Mach-Zehnder interferometer (MZI) followed by balanced homodyne measurement. We give the optimal transmittance and demonstrate the advantage of our scheme over a balanced MZI scheme. Additionally, when the average photon number of the coherent state is dominant, the phase sensitivity of our scheme can nearly saturate the single-parameter quantum Cram\'er-Rao bound. Our results may contribute to the development of practical quantum sensing.

Non-Gaussian quantum state generation by multi-photon subtraction at the telecommunication wavelength.

In the field of continuous-variable quantum information processing, non-Gaussian states with negative values of the Wigner function are crucial for the development of a fault-tolerant universal quantum computer. While several non-Gaussian states have been generated experimentally, none have been created using ultrashort optical wave packets, which are necessary for high-speed quantum computation, in the telecommunication wavelength band where mature optical communication technology is available. In this paper, we present the generation of non-Gaussian states on wave packets with a short 8-ps duration in the 1545.32 nm telecommunication wavelength band using photon subtraction up to three photons. We used a low-loss, quasi-single spatial mode waveguide optical parametric amplifier, a superconducting transition edge sensor, and a phase-locked pulsed homodyne measurement system to observe negative values of the Wigner function without loss correction up to three-photon subtraction. These results can be extended to the generation of more complicated non-Gaussian states and are a key technology in the pursuit of high-speed optical quantum computation.

Bayesian quantum parameter estimation with Gaussian states and homodyne measurements in a dissipative environment

The deterioration of precision caused by quantum decoherence in dissipative environments is a longstanding problem in the development of quantum metrology. Therefore, it is significant to effectively analyze the evolution of quantum systems under dissipative environments and quantitatively estimate the parameters given a certain probe. Here, we propose a continuous-variable (CV) quantum metrology scheme within the Bayesian paradigm to estimate phase shift, loss coefficient and temperature of a dissipative environment. Through numerical evaluation and concrete analysis, we investigate the achievable precision of Bayesian quantum parameter estimation with Gaussian states and homodyne measurements, and the influence of different parameters on the estimation process. More interestingly, the scheme can be applied in more practical scenarios where not enough measurements are obtained and the frequentist analysis is not well defined.

Bosonic Pair Production and Squeezing for Optical Phase Measurements in Long-Lived Dipoles Coupled to a Cavity.

We propose to simulate bosonic pair creation using large arrays of long-lived dipoles with multilevel internal structure coupled to an undriven optical cavity. Entanglement between the atoms, generated by the exchange of virtual photons through a common cavity mode, grows exponentially fast and is described by two-mode squeezing of effective bosonic quadratures. The mapping between an effective bosonic model and the natural spin description of the dipoles allows us to realize the analog of optical homodyne measurements via straightforward global rotations and population measurements of the electronic states, and we propose to exploit this for quantum-enhanced sensing of an optical phase (common and differential between two ensembles). We discuss a specific implementation based on Sr atoms and show that our sensing protocol is robust to sources of decoherence intrinsic to cavity platforms. Our proposal can open unique opportunities for next-generation optical atomic clocks.

Precise Nondestructive Parity Measurement of Artificial Atoms Using a Superconducting Resonator and Homodyne Measurement

AbstractIn this paper, a robust and accurate protocol is proposed to realize nondestructive parity measurement of artificial atoms using a superconducting resonator and homodyne measurement. With the help of an additional microwave driving field, the cavity field evolves into a coherent state or remains in a vacuum state according to the parity of the atoms. Consequently, the parity information of atoms can be read out by a homodyne measurement on the cavity. Parity information can be obtained without destroying the original state of the system, which means that the state can be further applied to other quantum information processing tasks after a parity measurement. The numerical simulation results show that the protocol is robust against systematic error, random noise, and decoherence. Therefore, this protocol can provide a feasible viewpoint for nondestructive parity measurement.

20 MHz resonant photodetector for the homodyne measurement of picosecond pulsed squeezed light

A high-performance resonant balanced homodyne detector is a key element for the measurement of picosecond pulsed squeezed light, which is an important quantum resource in quantum-enhanced microscopic imaging. In this paper, we design and demonstrate a resonant photodetector for homodyne measurement with a maximum signal-to-noise ratio of 22.42 dB at resonant frequency of 20 MHz. Using this detector to pulsed regime, a maximum signal-to-noise ratio at resonant frequency is 10.02 dB, where a 40 dB subtraction capability at 80 MHz repetition rate of pulsed laser is obtained. With this design, the quantum noise of picosecond pulsed squeezed light is measured and the best squeezing level −1.7 dB below the shot noise level is clearly observed at 20 MHz.

Non-Gaussian entanglement criteria for atomic homodyne detection

Homodyne measurement is a crucial tool widely used to address continuous variables for bosonic quantum systems. While an ideal homodyne detection provides a powerful analysis, e.g., to effectively measure quadrature amplitudes of light in quantum optics, it relies on the use of a strong reference field, the so-called local oscillator, typically in a coherent state. Such a strong coherent local oscillator may not be readily available, particularly for a massive quantum system like a Bose-Einstein condensate, posing a substantial challenge in dealing with continuous variables appropriately. It is necessary to establish a practical framework that includes the effects of nonideal local oscillators for a rigorous assessment of various quantum tests and applications. We here develop entanglement criteria beyond a Gaussian regime applicable for this realistic homodyne measurement that do not require assumptions on the state of local oscillators. We discuss the working conditions of homodyne detection to effectively detect non-Gaussian quantum entanglement under various states of local oscillators.

Квантовое измерение амплитуды и фазы электромагнитного поля методом оптического гомодинирования

The possibility of measuring the amplitude and phase of the electromagnetic field by optical light homodyning is shown. A new method for determining the relative phase of the field using the interference scheme of balanced homodyne detection is proposed. The method is based on direct measurement of the average complex amplitude of a quantum field mixed with a classical field using a passive symmetric beam splitter under conditions of a balanced homodyne measurement scheme. A "direct" measurement of the average field amplitude is a direct measurement of the real and imaginary parts of the average quantum mechanical value of the complex field amplitude by homodyning. By comparison with the quantum theory of the Hermitian phase operator of the electromagnetic field, the accuracy of this measurement is estimated for various quantum states of the microscopic electromagnetic field.

Homodyne measurement with a Schrödinger cat state as a local oscillator

Homodyne measurements are a widely used quantum measurement. Using a coherent state of large amplitude as the local oscillator, it can be shown that the quantum homodyne measurement limits to a field quadrature measurement. In this work, we give an example of a general idea: injecting nonclassical states as a local oscillator can lead to nonclassical measurements. Specifically, we consider injecting a superposition of coherent states, a Schr\"odinger cat state, as a local oscillator. We derive the Kraus operators and the positive operator-valued measure in this situation.

Efficient simulation of Gottesman-Kitaev-Preskill states with Gaussian circuits

We study the classical simulatability of Gottesman-Kitaev-Preskill (GKP) states in combination with arbitrary displacements, a large set of symplectic operations and homodyne measurements. For these types of circuits, neither continuous-variable theorems based on the non-negativity of quasi-probability distributions nor discrete-variable theorems such as the Gottesman-Knill theorem can be employed to assess the simulatability. We first develop a method to evaluate the probability density function corresponding to measuring a single GKP state in the position basis following arbitrary squeezing and a large set of rotations. This method involves evaluating a transformed Jacobi theta function using techniques from analytic number theory. We then use this result to identify two large classes of multimode circuits which are classically efficiently simulatable and are not contained by the GKP encoded Clifford group. Our results extend the set of circuits previously known to be classically efficiently simulatable.

Detecting quantum capacities of continuous-variable quantum channels

Quantum communication channels and quantum memories are the fundamental building blocks of large-scale quantum communication networks. Estimating their capacity to transmit and store quantum information is crucial in order to assess the performance of quantum communication systems and to detect useful communication paths among the nodes of future quantum networks. However, the estimation of quantum capacities is a challenging task for continuous-variable systems, such as the radiation field, for which a complete characterization via quantum tomography is practically unfeasible. Here we introduce a method for detecting the quantum capacity of continuous-variable communication channels and memories without performing a full process tomography. Our method works in the general scenario where the devices are used a finite number of times, can exhibit correlations across multiple uses, and can change dynamically under the control of a malicious adversary. The method is experimentally friendly and can be implemented using only finitely squeezed states and homodyne measurements.

Quantum dense coding network using multimode squeezed states of light

We present a framework of a multimode dense coding network with multiple senders and a single receiver using continuous variable systems. The protocol is scalable to arbitrary numbers of modes with the encoding being displacements while the decoding involves homodyne measurements of the modes after they are combined in a pairwise manner by a sequence of beam splitters, thereby exhibiting its potentiality to implement in laboratories with currently available resources. We compute the closed form expression of the dense coding capacity for the cases of two and three senders that involve sharing of three- and four-mode states respectively. The dense coding capacity is calculated with the constraint of fixed average energy transmission when the modes of the sender are transferred to the receiver after the encoding operation. In both the cases, we demonstrate the quantum advantage of the protocol using paradigmatic classes of three- and four-mode states. The quantum advantage increases with the increase in the amount of energy that is allowed to be transmitted from the senders to the receiver.

Simple, Reliable, and Noise-Resilient Continuous-Variable Quantum State Tomography with Convex Optimization

Precise reconstruction of unknown quantum states from measurement data, a process commonly called quantum state tomography, is a crucial component in the development of quantum information processing technologies. Many different tomography methods have been proposed over the years. Maximum likelihood estimation is a prominent example, being the most popular method for a long period of time. Recently, more advanced neural network methods have started to emerge. Here, we go back to basics and present a method for continuous variable state reconstruction that is both conceptually and practically simple, based on convex optimization. Convex optimization has been used for process tomography and qubit state tomography, but seems to have been overlooked for continuous variable quantum state tomography. We demonstrate high-fidelity reconstruction of an underlying state from data corrupted by thermal noise and imperfect detection, for both homodyne and heterodyne measurements. A major advantage over other methods is that convex optimization algorithms are guaranteed to converge to the optimal solution.

Steering-based randomness certification with squeezed states and homodyne measurements

We present a scheme for quantum randomness certification based on quantum steering. The protocol is one-sided device independent, providing high security, but requires only states and measurements that are simple to realise on quantum optics platforms - entangled squeezed vacuum states and homodyne detection. This ease of implementation is demonstrated by certifying randomness in existing experimental data and implies that giga-hertz random bit rates should be attainable with current technology. Furthermore, the steering-based setting represents the closest to full device independence that can be achieved using purely Gaussian states and measurements.

Optimal Interferometry for Bell Nonclassicality Induced by a Vacuum–One-Photon Qubit

Bell nonclassicality of a single photon superposition in two modes, often referred to as `nonlocality of a single photon', is one of the most striking nonclassical phenomena discussed in the context of foundations of quantum physics. Here we show how to robustly violate local realism within the weak-field homodyne measurement scheme for \textit{any} superposition of one photon with vacuum. Our modification of the previously proposed setups involves tunable beamsplitters at the measurement stations, and the local oscillator fields significantly varying between the settings, optimally being {\it on} or {\it off}. As photon number resolving measurements are now feasible, we advocate for the use of the Clauser-Horne Bell inequalities for detection events using precisely defined numbers of photons. We find a condition for optimal measurement settings for the maximal violation of the Clauser-Horne inequality with weak-field homodyne detection, which states that the reflectivity of the local beamsplitter must be equal to the strength of the local oscillator field. We show that this condition holds not only for the vacuum-one-photon qubit input state, but also for the superposition of a photon pair with vacuum, which suggests its generality as a property of weak-field homodyne detection with photon-number resolution. Our findings suggest a possible path to employ such scenarios in device-independent quantum protocols.

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.