Noise In Quantum Measurements Research Articles

Practical Trainable Temporal Postprocessor for Multistate Quantum Measurement

We develop and demonstrate a trainable temporal postprocessor (TPP) harnessing a simple but versatile machine learning algorithm to provide optimal processing of quantum measurement data subject to arbitrary noise processes for the readout of an arbitrary number of quantum states. We demonstrate the TPP on the essential task of qubit state readout, which has historically relied on temporal processing via matched filters in spite of their applicability for only specific noise conditions. Our results show that the TPP can reliably outperform standard filtering approaches under complex readout conditions, such as high-power readout. Using simulations of quantum measurement noise sources, we show that this advantage relies on the TPP’s ability to learn optimal linear filters that account for general quantum noise correlations in data, such as those due to quantum jumps, or correlated noise added by a phase-preserving quantum amplifier. Furthermore, we derive an exact analytic form for the optimal TPP weights: this positions the TPP as a linearly scaling generalization of matched filtering, valid for an arbitrary number of states under the most general readout noise conditions, all while preserving a training complexity that is essentially negligible in comparison with that of training neural networks for processing temporal quantum measurement data. The TPP can be autonomously and reliably trained on measurement data and requires only linear operations, making it ideal for field-programmable gate array implementations in circuit QED for real-time processing of measurement data from general quantum systems. Published by the American Physical Society 2024

Rydberg-atom-based single-photon detection for haloscope axion searches

We propose a Rydberg-atom-based single-photon detector for signal readout in dark matter haloscope experiments between 40 μeV and 200 μeV (10 GHz and 50 GHz). At these frequencies, standard haloscope readout using linear amplifiers is limited by quantum measurement noise, which can be avoided by using a single-photon detector. Our single-photon detection scheme can offer scan rate enhancements up to a factor of 104 over traditional linear amplifier readout, and is compatible with many different haloscope cavities. We identify multiple haloscope designs that could use our Rydberg-atom-based single-photon detector to search for QCD axions with masses above 40 μeV (10 GHz), currently a minimally explored parameter space. Published by the American Physical Society 2024

Fundamental quantum limits of magnetic nearfield measurements

Major advances in the precision of magnetic measurements bring us closer to quantum detection of individual spins at the single-atom level. On the quest for reducing both classical and quantum measurement noise, it is intriguing to look forward and search for precision limits arising from the fundamental quantum nature of the measurement process itself. Here, we present the limits of magnetic quantum measurements arising from quantum information considerations, and apply these limits to a concrete example of magnetic force microscopy (MFM). We show how such microscopes have a fundamental limit on their precision arising from the theory of imperfect quantum cloning, manifested by the entanglement between the measured system and the measurement probe. We show that counterintuitively, increasing the probe complexity decreases both the measurement noise and back action, and a judicious design of the magnetic interaction reveals optimal schemes already at spin-1 probes.

Eigen-Spectrum Estimation and Source Detection in a Massive Sensor Array Based on Quantum Assisted Hamiltonian Simulation Framework

In this work, we propose quantum assisted eigenvalue estimation and target detection algorithms for a large sensor array via Hamiltonian simulation. Quantum algorithms provide complexity advantage of a certain class of problems on a quantum computer with fewer physical resources as compared to their classical counterparts. The proposed algorithms make use of the quantum phase estimation (QPE) as its core computing component. We have introduced an analytical quantum framework to map from classical to quantum in the context of target detection. Target detection involves an appropriate choice of threshold based on the probability of detection or false alarm. We exploited the massive sensor array structure and invoked the random matrix theory to propose an optimal threshold. It also takes into account the quantum measurement noise in the framework. Numerical simulations are performed to ascertain the efficacy of the proposed framework. The results suggest near term applications of the quantum algorithm for large-scale linear systems.

The performance of typical QKD scheme under the condition of quantum measurement noise

The performance of typical quantum key distribution protocol under the condition of quantum measurement noise has been explored in this paper. Additionally, the realization steps for quantum key distribution are presented. Based on the successful probability, the performance of quantum key distribution is studied. The results show that the total probability is not influenced by the phase factors, and this probability is relative with the amplitude parameters. The results about quantum key distribution protocol with measurement noise would be useful in the field of quantum communication.

Quantum noise in a transversely-pumped-cavity Bose-Hubbard model

We investigate the quantum measurement noise effects on the dynamics of an atomic Bose lattice gas inside an optical resonator. We describe the dynamics by means of a hybrid model consisting of a Bose--Hubbard Hamiltonian for the atoms and a Heisenberg--Langevin equation for the lossy cavity field mode. We assume that the atoms are prepared initially in the ground state of the lattice Hamiltonian and then start to interact with the cavity mode. We show that the cavity field fluctuations originating from the dissipative outcoupling of photons from the resonator lead to vastly different effects in the different possible ground state phases, i.e., the superfluid, the supersolid, the Mott- and the charge-density-wave phases. In the former two phases with the presence of a superfluid wavefunction, the quantum measurement noise appears as a driving term leading to excess noise depletion of the ground state. The time scale for the system to leave the ground scale is determined analytically. For the latter two incompressible phases, the quantum noise results in the fluctuation of the chemical potential. We derive an analytical expression for the corresponding broadening of the quasiparticle resonances.

Positive Operator Valued Measures and Feller Markov kernels

A Positive Operator Valued Measure (POVM) is a map F:B(X)→Ls+(H) from the Borel σ-algebra of a topological space X to the space of positive self-adjoint operators on a Hilbert space H. We assume X to be Hausdorff, locally compact and second countable and prove that a POVM F is commutative if and only if it is the smearing of a spectral measure E by means of a Feller Markov kernel. Moreover, we prove that the smearing can be realized by means of a strong Feller Markov kernel if and only if F is uniformly continuous. Finally, we prove that a POVM which is norm bounded by a finite measure ν admits a strong Feller Markov kernel. That provides a characterization of the smearing which connects a commutative POVM F to a spectral measure E and is relevant both from the mathematical and the physical viewpoint since smearings of spectral measures form a large and very relevant subclass of POVMs: they are paradigmatic for the modeling of certain standard forms of noise in quantum measurements, they provide optimal approximators as marginals in joint measurements of incompatible observables [21], they are important for a range of quantum information processing protocols, where classical post-processing plays a role [27]. The mathematical and physical relevance of the results is discussed and particular emphasis is given to the connections between the Markov kernel and the imprecision of the measurement process.

Electrokinetic trapping at the one nanometer limit

Anti-Brownian electrokinetic traps have been used to trap and study the free-solution dynamics of large protein complexes and long chains of DNA. Small molecules in solution have thus far proved too mobile to trap by any means. Here we explore the ultimate limits on trapping single molecules. We developed a feedback-based anti-Brownian electrokinetic trap in which classical thermal noise is compensated to the maximal extent allowed by quantum measurement noise. We trapped single fluorophores with a molecular weight of < 1 kDa and a hydrodynamic radius of 6.7 Å for longer than one second, in aqueous buffer at room temperature. This achievement represents an 800-fold decrease in the mass of objects trapped in solution, and opens the possibility to trap and manipulate any soluble molecule that can be fluorescently labeled. To illustrate the use of this trap, we studied the binding of unlabeled RecA to fluorescently labeled single-stranded DNA. Binding of RecA induced changes in the DNA diffusion coefficient, electrophoretic mobility, and brightness, all of which were measured simultaneously and on a molecule-by-molecule basis. This device greatly extends the size range of molecules that can be studied by room temperature feedback trapping, and opens the door to further studies of the binding of unmodified proteins to DNA in free solution.

Quantum-noise randomized data encryption for wavelength-division-multiplexed fiber-optic networks

We demonstrate high-rate randomized data-encryption through optical fibers using the inherent quantum-measurement noise of coherent states of light. Specifically, we demonstrate 650Mbps data encryption through a 10Gbps data-bearing, in-line amplified 200km-long line. In our protocol, legitimate users (who share a short secret-key) communicate using an M-ry signal set while an attacker (who does not share the secret key) is forced to contend with the fundamental and irreducible quantum-measurement noise of coherent states. Implementations of our protocol using both polarization-encoded signal sets as well as polarization-insensitive phase-keyed signal sets are experimentally and theoretically evaluated. Different from the performance criteria for the cryptographic objective of key generation (quantum key-generation), one possible set of performance criteria for the cryptographic objective of data encryption is established and carefully considered.

Quantum-noise

We demonstrate high data-rate quantum-noise{protected data encryption through optical fibers using coherent states of light. Specifically, we demonstrate 650Mbps data encryption through a 10Gbps data-bearing, in-line amplified 200km-long line. In our protocol, legitimate users (who share a short secret-key) communicate using an M-ry signal set while an attacker (who does not share the secret-key) is forced to contend with the fundamental and irreducible quantum-measurement noise of coherent states. Implementations of our protocol using both polarization-encoded signal sets as well as polarization-insensitive phase-keyed signal sets are experimentally and theoretically evaluated. Different from the performance criteria of the cryptographic objective of key generation (quantum key generation), the performance criteria of data encryption are established and carefully considered.

The action uncertainty principle for continuous measurements

The action uncertainty principle (AUP) for the specification of the most probable readouts of continuous quantum measurements is proved, formulated in different forms and analyzed (for nonlinear as well as linear systems). Continuous monitoring of an observable A(p,q,t) with resolution Δa( t) is considered. The influence of the measurement process on the evolution of the measured system (quantum measurement noise) is presented by an additional term δ F(t)A(p,q,t) in the Hamiltonian where the function δ F (generalized fictitious force) is restricted by the AUP ∫|δ F(t)| Δa( t) d t ≲ and arbitrary otherwise. Quantum-nondemolition (QND) measurements are analyzed with the help of the AUP. A simple uncertainty relation for continuous quantum measurements is derived. It states that the area of a certain band in the phase space should be of the order of. The width of the band depends on the measurement resolution while its length is determined by the deviation of the system, due to the measurement, from classical behavior.

Quantum correlations: A generalized Heisenberg uncertainty relation.

A theoretical result for correlated quantum systems is presented which leads to a noise commutation relation and a generalized Heisenberg uncertainty relation. These relations imply an inherent and unavoidable extra noise in quantum measurements beyond that already included in the Heisenberg lower bound. These relations lead directly to model-independent lower bounds on inherent noise, useful in a variety of applications, including balanced homodyne detection and quantum optical linear amplifiers.

Quantum measurement noise for observation of a particle in a magnetic field

The quantum theory of continuous measurements based on Feynman integration ''in finite limits'' is used in the problem of following the coordinates of a particle moving in a magnetic field. The probability of a particular result of the following for known external force is found, and, conversely, the accuracy with which the external force can be recovered from the known result of measurement is estimated. Allowance is made not only for the spread of the results due to instrumental error but also for the quantum-mechanical influence of the measuring process on the motion of the particle. Three characteristic regimes of measurement are identified: classical, quantum, optimal.