We construct a model of quantum metrology inspired by the computational model known as deterministic quantum computation with one quantum bit (DQC1). Using only one pure qubit together with $l$ fully-mixed qubits we obtain measurement precision at the standard quantum limit, which is typically obtained using the same number of uncorrelated qubits in fully-pure states. The standard quantum limit can be exceeded using an additional qubit, which adds only a small amount of purity. We show that the discord in the final state vanishes only in the limit of attaining infinite precision for the parameter being estimated.
We derive a bound on the ability of a linear optical network to estimate a linear combination of independent phase shifts by using an arbitrary non-classical but unentangled input state, thereby elucidating the quantum resources required to obtain the Heisenberg limit with a multi-port interferometer. Our bound reveals that while linear networks can generate highly entangled states, they cannot effectively combine quantum resources that are well distributed across multiple modes for the purposes of metrology: in this sense linear networks endowed with well-distributed quantum resources behave …
The impact of measurement imperfections on quantum metrology protocols has not been approached in a systematic manner so far. In this work, we tackle this issue by generalising firstly the notion of quantum Fisher information to account for noisy detection, and propose tractable methods allowing for its approximate evaluation. We then show that in canonical scenarios involving $N$ probes with local measurements undergoing readout noise, the optimal sensitivity depends crucially on the control operations allowed to counterbalance the measurement imperfections -- with global control operations, …
We explore the role of $\textit{collective measurements}$ on precision in estimation of a single parameter. Collective measurements are represented by observables which commute with all permutations of the probe particles. We show that with this constraint, quantum bits(qubits) outperform classical bits(non-superposable bits) in optimizing precision. Specifically, we prove that while precision in a collective measurement is loosely bounded by $O\left(\frac{1}{N}\right)$ for $N$ classical bits, using qubits it is tightly bounded by $O\left(\frac{1}{N^2}\right)$. This bound is consistent with qu…
Quantum systems can be exploited for disruptive technologies but in practice quantum features are fragile due to noisy environments. Quantum coherence, a fundamental such feature, is a basis-dependent property that is known to exhibit a resilience to certain types of Markovian noise. Yet, it is still unclear whether this resilience can be relevant in practical tasks. Here, we experimentally investigate the resilient effect of quantum coherence in a photonic Greenberger-Horne-Zeilinger state under Markovian bit-flip noise, and explore its applications in a noisy metrology scenario. In particula…
Quantum Metrology calculates the ultimate precision of all estimation strategies, measuring what is their root mean-square error (RMSE) and their Fisher information. Here, instead, we ask how many bits of the parameter we can recover, namely we derive an information-theoretic quantum metrology. In this setting we redefine "Heisenberg bound" and "standard quantum limit" (the usual benchmarks in quantum estimation theory), and show that the former can be attained only by sequential strategies or parallel strategies that employ entanglement among probes, whereas parallel-separable strategies are …
We establish the nonclassicality of continuous-variable states as a resource for quantum metrology. Based on the quantum Fisher information of multimode quadratures, we introduce the metrological power as a measure of nonclassicality with a concrete operational meaning of displacement sensitivity beyond the classical limit. This measure belongs to the resource theory of nonclassicality, which is nonincreasing under linear optical elements. Our Letter reveals that a single copy, highly nonclassical quantum state is intrinsically advantageous when compared to multiple copies of a quantum state w…
We improve the precision of the interferometric weak-value-based beam deflection measurement by introducing a power recycling mirror, creating a resonant cavity. This results in \emph{all} the light exiting to the detector with a large deflection, thus eliminating the inefficiency of the rare postselection. The signal-to-noise ratio of the deflection is itself magnified by the weak value. We discuss ways to realize this proposal, using a transverse beam filter and different cavity designs.
It is well-known that the precision of a phase measurement with a Mach-Zehnder interferometer employing strong (macroscopic) classic light can be greatly enhanced with the addition of a weak (microscopic) light field in a non-classical state. The resulting precision is much greater than that possible with either the macroscopic classical or microscopic quantum states alone. In the context of quantifying non-classicality, the amount by which a non-classical state can enhance precision in this way has been termed its "metrological power". Given the technological difficulty of producing high-ampl…
We identify a fundamental difference between classical and quantum dynamics in the linear response regime by showing that the latter is in general contextual. This allows us to provide an example of a quantum engine whose favorable power output scaling \emph{unavoidably} requires nonclassical effects in the form of contextuality. Furthermore, we describe contextual advantages for local metrology. Given the ubiquity of linear response theory, we anticipate that these tools will allow one to certify the nonclassicality of a wide array of quantum phenomena.
We devise powerful algorithms based on differential evolution for adaptive many-particle quantum metrology. Our new approach delivers adaptive quantum metrology policies for feedback control that are orders-of-magnitude more efficient and surpass the few-dozen-particle limitation arising in methods based on particle-swarm optimization. We apply our method to the binary-decision-tree model for quantum-enhanced phase estimation as well as to a new problem: a decision tree for adaptive estimation of the unknown bias of a quantum coin in a quantum walk and show how this latter case can be realized…
Entanglement is recognized as a key resource for quantum computation and quantum cryptography. For quantum metrology, the use of entangled states has been discussed and demonstrated as a means of improving the signal-to-noise ratio. In addition, entangled states have been used in experiments for efficient quantum state detection and for the measurement of scattering lengths. In quantum information processing, manipulation of individual quantum bits allows for the tailored design of specific states that are insensitive to the detrimental influences of an environment. Such 'decoherence-free subs…
We show that when a suitable entanglement generating unitary operator depending on a parameter is applied on N qubits in parallel, and an appropriate observable is measured, a precision of order 2 raised to the power (-N) in estimating the parameter may be achieved. This exponentially improves the precision achievable in classical and in quantum non-entangling parallel strategies. We propose a quantum-optics model of laser light interacting with an N-qubit system, say a polyatomic molecule, via a generalized Jaynes-Cummings interaction which, in principle, could achieve the exponentially enhan…
We carefully examine critical metrology and present an improved critical quantum metrology protocol which relies on quenching a system exhibiting a superradiant quantum phase transition beyond its critical point. We show that this approach can lead to an exponential increase of the quantum Fisher information in time with respect to existing critical quantum metrology protocols relying on quenching close to the critical point and observing power law behaviour. We demonstrate that the Cramér-Rao bound can be saturated in our protocol through the standard homodyne detection scheme. We explicitly …
Quantum metrology is supposed to significantly improve the precision of parameter estimation by utilizing suitable quantum resources. However, the predicted precision can be severely distorted by realistic noises. Here, we propose a control-enhanced quantum metrology scheme to defend against these noises for improving the metrology performance. Our scheme can automatically alter the parameter encoding dynamics with adjustable controls, thus leading to optimal resultant states that are less sensitive to the noises under consideration. As a demonstration, we numerically apply it to the problem o…
Noise-Symmetry Optimization of Quantum Error-Corrected Metrology
School of Physics, Sun Yat-sen University（中山大学物理学院）；State Key Laboratory for Mesoscopic Physics, Department of Physics, Peking University（北京大学物理学院介观物理国家重点实验室）；Hefei National Laboratory, University of Science and Technology of China（中国科学技术大学合肥国家实验室）
Experimental realization of quantum Zeno dynamics for robust quantum metrology
Shenzhen University（深圳大学）；Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area (Guangdong)（粤港澳大湾区量子科学中心（广东））；China Jiliang University（中国计量大学）；Southern University of Science and Technology（南方科技大学）
Quantum optical metrology aims to identify ultimate sensitivity bounds for the estimation of parameters encoded into quantum states of the electromagnetic field. In many practical applications, including imaging, microscopy, and remote sensing, the parameter of interest is not only encoded in the quantum state of the field, but also in its spatio-temporal distribution, i.e. in its mode structure. In this mode-encoded parameter estimation setting, we derive an analytical expression for the quantum Fisher information valid for arbitrary multimode Gaussian fields. To illustrate the power of our a…
A longstanding problem in quantum metrology is how to extract as much information as possible in realistic scenarios with not only multiple unknown parameters, but also limited measurement data and some degree of prior information. Here we present a practical solution to this: we derive a new Bayesian multi-parameter quantum bound, construct the optimal measurement when our bound can be saturated for a single shot and consider experiments involving a repeated sequence of these measurements. Our method properly accounts for the number of measurements and the degree of prior information, and we …
We investigate how the Hilbert-Schmidt speed (HSS), a special type of quantum statistical speed, can be exploited as a powerful and easily computable tool for quantum phase estimation in a $n$-qubit system. We find that, when both the HSS and quantum Fisher information (QFI) are computed with respect to the phase parameter encoded into the initial state of the $n$-qubit register, the zeros of the HSS dynamics are essentially the same as those of the QFI dynamics. Moreover, the positivity (negativity) of the time-derivative of the HSS exactly coincides with the positivity (negativity) of the ti…
The heat dissipation in quantum metrology represents not only an unavoidable problem towards practical applications of quantum sensing devices but also a fundamental relationship between thermodynamics and quantum metrology. However, a general thermodynamic principle which governs the rule of energy consumption in quantum metrology, similar to Landauer's principle for heat dissipation in computations, has remained elusive. Here, we establish such a physical principle for energy consumption in order to achieve a certain level of measurement precision in quantum metrology, and show that it is in…
Randomized measurements for multi-parameter quantum metrology
Perimeter Institute for Theoretical Physics（珀蒂默理论物理研究所）；University of Waterloo（滑铁卢大学）；The University of Chicago（芝加哥大学）；California Institute of Technology（加州理工学院）
Coherence time is an important resource to generate enhancement in quantum metrology. In this work, based on continuous-variable models, we propose a new design of the signal-probe Hamiltonian which generates an exponential enhancement of measurement sensitivity. The key idea is to include into the system an ancilla that does not couple directly to the signal. An immediate benefit of such design is one can expand quantum Fisher information(QFI) into a power series in time, making it possible to achieve a higher-order time scaling in QFI. Specifically, one can design the interaction for a qubit…
In this review, we introduce the notion of quantum nonclassicality of light, and the role of nonclassicality in optical quantum metrology. The first part of the paper focuses on defining and characterizing the notion of nonclassicality and how it may be quantified in radiation fields. Several prominent examples of nonclassical light is also discussed. The second part of the paper looks at quantum metrology through the lens of nonclassicality. We introduce key concepts such as the Quantum Fisher information, the Cram{é}r-Rao bound, the standard quantum limit and the Heisenberg limit, and discus…
Quantum Fisher information (QFI) has potential applications in quantum metrology tasks. We investigate QFI when the consecutive actions of a quantum channel on the sequence of qubits have partial classical correlations. Our results showed that while the decoherence effect is detrimental to QFI, effects of such classical correlations on QFI are channel-dependent. For the Bell-type probe states, the classical correlations on consecutive actions of the depolarizing and phase flip channels can be harnessed to improve QFI, while the classical correlations in the bit flip and bit-phase flip channels…
Photon number states are assigned a parity of if their photon number is even and a parity of if odd. The parity operator, which is minus one to the power of the photon number operator, is a Hermitian operator and thus a quantum mechanical observable though it has no classical analog, the concept being meaningless in the context of classical light waves. In this paper we review work on the application of the parity operator to the problem of quantum metrology for the detection of small phase shifts with quantum optical interferometry using highly entangled field states such as the so-called N00…
We present experimental and theoretical results on a new interferometer topology that nests a SU(2) interferometer, e.g., a Mach-Zehnder or Michelson interferometer, inside a SU(1,1) interferometer, i.e., a Mach-Zehnder interferometer with parametric amplifiers in place of beam splitters. This SU(2)-in-SU(1,1) nested interferometer (SISNI) simultaneously achieves high signal-to-noise ratio (SNR), sensitivity beyond the standard quantum limit (SQL) and tolerance to photon losses external to the interferometer, e.g., in detectors. We implement a SISNI using parametric amplification by four-wave …
We establish general limits on how precise a parameter, e.g. frequency or the strength of a magnetic field, can be estimated with the aid of full and fast quantum control. We consider uncorrelated noisy evolutions of N qubits and show that fast control allows to fully restore the Heisenberg scaling (~1/N^2) for all rank-one Pauli noise except dephasing. For all other types of noise the asymptotic quantum enhancement is unavoidably limited to a constant-factor improvement over the standard quantum limit (~1/N) even when allowing for the full power of fast control. The latter holds both in the s…
Entanglement is the central yet fleeting phenomena of quantum physics. Once being considered a peculiar counter-intuitive property of quantum theory it has developed into the most central element of quantum technology providing speed up to quantum computers, a path towards long distance quantum cryptography and increased sensitivity in quantum metrology. Consequently, there have been a number of experimental demonstration of entanglement between photons, atoms, ions as well as solid state systems like spins or quantum dots, superconducting circuits and macroscopic diamond. Here we experimental…
In standard quantum computation, the initial state is pure and the answer is determined by making a measurement of some of the bits in the computational basis. What can be accomplished if the initial state is a highly mixed state and the answer is determined by measuring the expectation of $σ_z$ on the first bit with bounded sensitivity? This is the situation in high temperature ensemble quantum computation. We show that in this model it is possible to perform interesting physics simulations which have no known efficient classical algorithms, even though the model is less powerful then standar…
We demonstrate new experimental procedures for measuring small errors in a superconducting quantum bit (qubit). By carefully separating out gate and measurement errors, we construct a complete error budget and demonstrate single qubit gate fidelities of 0.98, limited by energy relaxation. We also introduce a new metrology tool -- a Ramsey interference error filter -- that can measure the occupation probability of the state $\ket{2}$ down to $10^{-4}$, a magnitude near the fault tolerant threshold.
Joint Attosecond Science Laboratory (JASLab), National Research Council of Canada and University of Ottawa（联合阿秒科学实验室，加拿大国家研究委员会和渥太华大学）；Department of Physics, University of Ottawa（渥太华大学物理系）；Laboratory for Laser Energetics, University of Rochester（罗切斯特大学激光能量学实验室）；Nexus for Quantum Technologies, University of Ottawa（渥太华大学量子技术枢纽）；Department of Physics, University of Windsor（温莎大学物理系）
Photoelectron interferograms, manifested in photoelectron angular distributions (PADs), are a high-information, coherent observable. In order to obtain the maximum information from angle-resolved photoionization experiments it is desirable to record the full, 3D, photoelectron momentum distribution. Here we apply tomographic reconstruction techniques to obtain such 3D distributions from multiphoton ionization of potassium atoms, and fully analyse the energy and angular content of the 3D data. The PADs obtained as a function of energy indicate good agreement with previous 2D data and detailed a…
All communication channels are at bottom quantum mechanical. Quantum mechanics contributes both obstacles to communication in the form of noise, and opportunities in the use of intrinsically quantum representations for information. This paper investigates the trade-off between power and communication rate for coupled quantum channels. By exploiting quantum correlations such as entanglement, coupled quantum channels can communicate at a potentially higher rate than unentangled quantum channels given the same power. In particular, given the same overall power, M coupled, entangled quantum channe…
The nonclassical properties of quantum states are of tremendous interest due to their potential applications in future technologies. It has recently been realized that the concept of a "resource theory" is a powerful approach to quantifying and understanding nonclassicality. To realize the potential of this approach one must first find resource theoretic measures of nonclassicality that are "operational", meaning that they also quantify the ability of quantum states to provide enhanced performance for specific tasks, such as precision sensing. Here we achieve a significant milestone in this en…
Reciprocal Quantum Logic combines the speed and power-efficiency of single-flux quantum superconductor devices with design features that are similar to CMOS. We have demonstrated an 8-bit carry look-ahead adder in the technology using combinational gates with fanout of four and non-local interconnect. Measured power dissipation of the fully active circuit is only 510 nW at 6.2GHz. Latency is only 150 ps at a clock rate of 10GHz.
