Massimiliano F. Sacchi
We show how to quantify the optimal tradeoff between the amount of information retrieved by a quantum measurement in estimating an unknown spin coherent state and the disturbance on the state itself, and how to derive the corresponding minimum-disturbing measurement.
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We demonstrate a fundamental principle of disturbance tradeoff for quantum measurements, along the lines of the celebrated uncertainty principle: The disturbances associated with measurements performed on distinct yet identically prepared ensembles of systems in a pure state cannot all be made arbitrarily small. Indeed, we show that the average of the disturbances associated with a set of projective measurements is strictly greater than zero whenever the associated observables do not have a common eigenvector. For such measurements, we show an equivalence between disturbance tradeoff measured …
We present a simple information-disturbance tradeoff relation valid for any general measurement apparatus: The disturbance between input and output states is lower bounded by the information the apparatus provides in distinguishing these two states.
Heisenberg's uncertainty principle is quantified by error-disturbance tradeoff relations, which have been tested experimentally in various scenarios. Here we shall report improved new versions of various error-disturbance tradeoff relations by decomposing the measurement errors into two different components, namely, operator bias and fuzziness. Our improved uncertainty relations reveal the tradeoffs between these two components of errors, and imply various conditionally valid error-tradeoff relations for the unbiased and projective measurements. We also design a quantum circuit to measure the …
We derive the amount of information retrieved by a quantum measurement in estimating an unknown maximally entangled state, along with the pertaining disturbance on the state itself. The optimal tradeoff between information and disturbance is obtained, and a corresponding optimal measurement is provided.
We discuss the relation between entropic uncertainty relations by Buscemi et al. and by Barchielli et al.
We show the flaws found in the customary fidelity-based definitions of disturbance in quantum measurements and evolutions. We introduce the "entropic disturbance" D and show that it adequately measures the degree of disturbance, intended essentially as an irreversible change in the state of the system. We also find that it complies with an information-disturbance tradeoff, namely the mutual information between the eigenvalues of the initial state and the measurement results is less than or equal to D.
We show that the global balance of information dynamics for general quantum measurements given in [F. Buscemi, M. Hayashi, and M. Horodecki, Phys.Rev.Lett. 100, 210504 (2008)] makes it possible to unify various and generally inequivalent approaches adopted in order to derive information-disturbance tradeoffs in quantum theory. We focus in particular on those tradeoffs, constituting the vast majority of the literature on the subject, where disturbance is defined either in terms of average output fidelity or of entanglement fidelity.
When discriminating between two pure quantum states, there exists a quantitative tradeoff between the information retrieved by the measurement and the disturbance caused on the unknown state. We derive the optimal tradeoff and provide the corresponding quantum measurement. Such an optimal measurement smoothly interpolates between the two limiting cases of maximal information extraction and no measurement at all.
The uncertainty principle is often interpreted by the tradeoff between the error of a measurement and the consequential disturbance to the followed ones, which originated long ago from Heisenberg himself but now falls into reexamination and even heated debate. Here we show that the tradeoff is switched on or off by the quantum uncertainties of two involved non-commuting observables: if one is more certain than the other, there is no tradeoff; otherwise, they do have tradeoff and the Jensen-Shannon divergence gives it a good characterization.
We provide a general framework for quantifying the optimal tradeoff between the information retrieved by a quantum measurement and the disturbance on the quantum state in covariant quantum state estimation.
We consider measurement disturbance tradeoffs in quantum machine learning protocols which seek to learn about quantum data. We study the simplest example of a binary classification task, in the unsupervised regime. Specifically, we investigate how a classification of two qubits, that can each be in one of two unknown states, affects our ability to perform a subsequent classification on three qubits when a third is added. Surprisingly, we find a range of strategies in which a non-trivial first classification does not affect the success rate of the second classification. There is, however, a non…
For sending unknown direction information, antiparallel spins contains more direction information than parallel spins(Gisin and Popescu, 1999, \textit{Phys. Rev. Lett.} 83, 432).In this paper, the optimal information-disturbance tradeoff bound for antiparallel spins is derived. The quantum measurements which attain the optimal tradeoff bound are obtained. This result can be of practical relevance for posing some general limits on Eve's eavesdropping process. Finally, we also present a comparison between the bound for antiparallel spins and the bound for parallel spins.
When we extract information from a system by performing a quantum measurement, the state of the system is disturbed due to the backaction of the measurement. Numerous studies have been performed to quantitatively formulate tradeoff relations between information and disturbance. We formulate a tradeoff relation between information and disturbance from an estimation-theoretic point of view, and derive an inequality between them. The information is defined as the classical Fisher information obtained by the measurement, and the disturbance is defined as the average loss of the quantum Fisher info…
We address the problem of the information-disturbance trade-off associated to the estimation of a quantum transformation, and show how the extraction of information about the a black box causes a perturbation of the corresponding input-output evolution. In the case of a black box performing a unitary transformation, randomly distributed according to the invariant measure, we give a complete solution of the problem, deriving the optimal trade-off curve and presenting an explicit construction of the optimal quantum network.
One of the characteristic features of quantum mechanics is that every measurement that extracts information about a general quantum system necessarily causes an unavoidable disturbance to the state of this system. A plethora of different approaches has been developed to characterize and optimize this tradeoff. Here, we apply the framework of quantum instruments to investigate the optimal tradeoff and to derive a class of procedures that is optimal with respect to most meaningful measures. We focus our analysis on binary measurements on qubits as commonly used in communication and computation p…
We address the class of positive operator-valued measures (POVMs) for qubit systems that are obtained by coupling the signal qubit with a probe qubit and then performing a projective measurement on the sole probe system. These POVMs, which represent the simplest class of qubit POVMs, depends on 3+3+2=8 free parameters describing the initial preparation of the probe qubit, the Cartan representative of the unitary coupling, and the projective measurement at the output, respectively. We analyze in some details the properties of the POVM matrix elements, and investigate their values for given rang…
Stinespring's dilation theorem is the basic structure theorem for quantum channels: it states that any quantum channel arises from a unitary evolution on a larger system. Here we prove a continuity theorem for Stinespring's dilation: if two quantum channels are close in cb-norm, then it is always possible to find unitary implementations which are close in operator norm, with dimension-independent bounds. This result generalizes Uhlmann's theorem from states to channels and allows to derive a formulation of the information-disturbance tradeoff in terms of quantum channels, as well as a continui…
In general, classical measurement statistics of a quantum measurement is disturbed by performing an additional incompatible quantum measurement beforehand. Using this observation, we introduce a state-independent definition of disturbance by relating it to the distinguishability problem between two classical statistical distributions --- one resulting from a single quantum measurement and the other from a succession of two quantum measurements. Interestingly, we find an error-disturbance trade-off relation for any measurements in two-dimensional Hilbert space and for measurements with mutually…
I consider the tradeoff between the information gained about an initially unknown quantum state, and the disturbance caused to that state by the measurement process. I show that for any distribution of initial states, the information-disturbance frontier is convex, and disturbance is nondecreasing with information gain. I consider the most general model of quantum measurements, and all post-measurement dynamics compatible with a given measurement. For the uniform initial distribution over states, I show that the least-disturbing way of making any measurement is with conditional dynamics satisf…
Measurement sharpness and disturbance tradeoff
本文研究了量子测量中信息获取与状态扰动之间的权衡问题，提出了多种方法解决无偏二元量子比特测量中的最小扰动和最佳信息获取问题，并揭示了测量锐度与平均保真度、量子资源之间的权衡关系。
Information Disturbance Tradeoff in Bidirectional QKD
本文基于量子网络形式构建网络，证明区分互偏酉基算子的信息扰动权衡等同于基于 Haar 测度估计 SU(2) 算子，并将其作为针对双向量子密码协议的自然攻击策略。
Information-theoretic definitions for the noise associated with a quantum measurement and the corresponding disturbance to the state of the system have recently been introduced [F. Buscemi et al., Phys. Rev. Lett. 112, 050401 (2014)]. These definitions are invariant under relabelling of measurement outcomes, and lend themselves readily to the formulation of state-independent uncertainty relations both for the joint estimate of observables (noise-noise relations) and the noise-disturbance tradeoff. Here we derive such relations for incompatible qubit observables, which we prove to be tight in t…
We introduce information-theoretic definitions for noise and disturbance in quantum measurements and prove a state-independent noise-disturbance tradeoff relation that these quantities have to satisfy in any conceivable setup. Contrary to previous approaches, the information-theoretic quantities we define are invariant under relabelling of outcomes, and allow for the possibility of using quantum or classical operations to `correct' for the disturbance. We also show how our bound implies strong tradeoff relations for mean square deviations.
Full-state information-disturbance tradeoff for direction estimation with antiparallel spin-coherent pairs
通过旋转协方差和Choi问题，推导了反平行自旋1/2系统的最优信息-干扰权衡，发现最优操作是标量-矢量相干协变滤波器，其干扰小于平行自旋基准和反平行测量-重制备策略，并推广到任意自旋j的反平行自旋相干态。
We derive new Heisenberg-type uncertainty relations for both joint measurability and the error-disturbance tradeoff for arbitrary observables of finite-dimensional systems. The relations are formulated in terms of a directly operational quantity, namely the probability of distinguishing the actual operation of a device from its hypothetical ideal, by any possible testing procedure whatsoever. Moreover, they may be directly applied in information processing settings, for example to infer that devices which can faithfully transmit information regarding one observable do not leak any information …
We investigate the tradeoff between the quality of an approximate version of a given measurement and the disturbance it induces in the measured quantum system. We prove that if the target measurement is a non-degenerate von Neumann measurement, then the optimal tradeoff can always be achieved within a two-parameter family of quantum devices that is independent of the chosen distance measures. This form of almost universal optimality holds under mild assumptions on the distance measures such as convexity and basis-independence, which are satisfied for all the usual cases that are based on norms…
Covariant correlation-disturbance and its experimental realization with spin-1/2 particles
本文提出了任意维度空间中序列$n$-结果量子测量的关联与扰动精确折中关系，通过中子光学实验验证了其有效性，并利用该最优关系直接估计了单光子探测器的特征噪声。
We investigate the optimal tradeoff between information gained about an unknown coherent state and the state disturbance caused by the measurement process. We propose several optical schemes that can enable this task, and we implement one of them, a scheme which relies on only linear optics and homodyne detection. Experimentally we reach near optimal performance, limited only by detection inefficiencies. In addition we show that such a scheme can be used to enhance the transmission fidelity of a class of noisy channels.
When an observer wants to identify a quantum state, which is known to be one of a given set of non-orthogonal states, the act of observation causes a disturbance to that state. We investigate the tradeoff between the information gain and that disturbance. This issue has important applications in quantum cryptography. The optimal detection method, for a given tolerated disturbance, is explicitly found in the case of two equiprobable non-orthogonal pure states.
Optimal quantum measurements for additive information and disturbance measures
本文从乘性保真度出发，通过对数定义加性信息与扰动度量，并证明加性会改变相对信息量仅引入最小扰动的最优量子测量，进而给出具有权衡关系的最优测量。
The notions of error and disturbance appearing in quantum uncertainty relations are often quantified by the discrepancy of a physical quantity from its ideal value. However, these real and ideal values are not the outcomes of simultaneous measurements, and comparing the values of unmeasured observables is not necessarily meaningful according to quantum theory. To overcome these conceptual difficulties, we take a different approach and define error and disturbance in an operational manner. In particular, we formulate both in terms of the probability that one can successfully distinguish the act…
A unitary interaction coupling two parties enables quantum communication in both the forward and backward directions. Each communication capacity can be thought of as a tradeoff between the achievable rates of specific types of forward and backward communication. Our first result shows that for any bipartite unitary gate, coherent classical communication is no more difficult than classical communication -- they have the same achievable rate regions. Previously this result was known only for the unidirectional capacities (i.e., the boundaries of the tradeoff). We then relate the tradeoff curve …
Heisenberg's intuition was that there should be a tradeoff between measuring a particle's position with greater precision and disturbing its momentum. Recent formulations of this idea have focused on the question of how well two complementary observables can be jointly measured. Here, we provide an alternative approach based on how enhancing the predictability of one observable necessarily disturbs a complementary one. Our measurement-disturbance relation refers to a clear operational scenario and is expressed by entropic quantities with clear statistical meaning. We show that our relation is …
In standard coherent state teleportation with shared two-mode squeezed vacuum (TMSV) state there is a trade-off between the teleportation fidelity and the fidelity of estimation of the teleported state from results of the Bell measurement. Within the class of Gaussian operations this trade-off is optimal, i.e. there is not a Gaussian operation which would give for a given output fidelity a larger estimation fidelity. We show that this trade-off can be improved by up to 2.77% if we use a suitable non-Gaussian operation. This operation can be implemented by the standard teleportation protocol in…
In quantum physics, measurement error and disturbance were first naively thought to be simply constrained by the Heisenberg uncertainty relation. Later, more rigorous analysis showed that the error and disturbance satisfy more subtle inequalities. Several versions of universally valid error-disturbance relations (EDR) have already been obtained and experimentally verified in the regimes where naive applications of the Heisenberg uncertainty relation failed. However, these EDRs were formulated for discrete measurements. In this paper, we consider continuous measurement processes and obtain new …
In 1927, Heisenberg heuristically disclosed the tradeoff between the error in the measurement and the caused disturbance on another complementary observable. In the quantum theory, most of uncertainty relations are proposed to reveal the amount of unavoidable uncertainty in the measuring process. In this paper, we study the error-disturbance relation from the information viewpoint. We ask how much information, rather than how much uncertainty, can be obtained during the two sequential measurements. To achieve optimal information gain, we argue that the strategy for the "intelligent" prior appa…
Heisenberg's original uncertainty relation is related to measurement effect, which is different from the preparation uncertainty relation. However, it has been shown that Heisenberg's error-disturbance uncertainty relation can be violated in some cases. We experimentally test the error-tradeoff uncertainty relation by using a continuous-variable Einstein-Podolsky-Rosen (EPR) entangled state. Based on the quantum correlation between the two entangled optical beams, the errors on amplitude and phase quadratures of one EPR optical beam coming from joint measurement are estimated respectively, whi…
A quantum string seal encodes the value of a (bit) string as a quantum state in such a way that everyone can extract a non-negligible amount of available information on the string by a suitable measurement. Moreover, such measurement must disturb the quantum state and is likely to be detected by an authorized verifier. In this way, the intactness of the encoded quantum state plays the role of a wax seal in the digital world. Here I analyze the security of quantum string seal by studying the information disturbance tradeoff of a measurement. This information disturbance tradeoff analysis extend…
We analyze in details a conditional measurement scheme based on linear optical components, feed-forward loop and homodyne detection. The scheme may be used to achieve two different tasks. On the one hand it allows the extraction of information with minimum disturbance about a set of coherent states. On the other hand, it represents a nondemolitive measurement scheme for the annihilation operator, i.e. an indirect measurement of the Q-function. We investigate the information/disturbance trade-off for state inference and introduce the estimation/distortion trade-off to assess estimation of the Q…
In this paper we give a new way to quantify the folklore notion that quantum measurements bring a disturbance to the system being measured. We consider two observers who initially assign identical mixed-state density operators to a two-state quantum system. The question we address is to what extent one observer can, by measurement, increase the purity of his density operator without affecting the purity of the other observer's. If there were no restrictions on the first observer's measurements, then he could carry this out trivially by measuring the initial density operator's eigenbasis. If, h…
We propose and experimentally demonstrate an optimal non-unity gain Gaussian scheme for partial measurement of an unknown coherent state that causes minimal disturbance of the state. The information gain and the state disturbance are quantified by the noise added to the measurement outcomes and to the output state, respectively. We derive the optimal trade-off relation between the two noises and we show that the trade-off is saturated by non-unity gain teleportation. Optimal partial measurement is demonstrated experimentally using a linear optics scheme with feed-forward.
We give an explicit construction for a quantum observer coherently mimicking the dynamics of a cavity mode system and without any disturbance of the system's dynamics. This gives the exact analogue of the Luenberger observer used in controller design in engineering
We consider a strategic problem of the Evesdropping to quantum key distribution. Evesdropper hopes to obtain the maxium information given the disturbance to the qubits is often For this strategy, the optimized individual attack have been extensively constructed under various conditions. However, it seems a difficult task in the case of coherent attack, i.e., Eve may treat a number of intercepted qubits collectively, including the collective unitary transformations and the measurements. It was conjectured by Cirac and Gisin that no coherent attack can be more powerful for this strategy for BB84…
We address the problem of energy-error tradeoff in the discrimination between two linear passive quantum optical devices with a single use. We provide an analytical derivation of the optimal strategy for beamsplitters and an iterative algorithm converging to the optimum in the general case. We then compare the optimal strategy with a simpler strategy using coherent input states and homodyne detection. It turns out that the former requires much less energy in order to achieve the same performances.
We propose a mechanism to describe how a physical quantity, which initially can take continuous values, is restricted within some discrete values after a measurement. As an example of the present theory, in which interplay between coherence of motion and fluctuation from disturbance plays an important role, we investigate motion of a spin state in a magnetic field. First, we point out that discrete eigenstates are formed from continuous states as a result of coherence of precession motion of a spin. Next, by assuming disturbance from environmental electromagnetic fields, we investigate tempora…
We propose two experimental schemes for quantum state discrimination that achieve the optimal tradeoff between the probability of correct identification and the disturbance on the quantum state.
Heisenberg formulated a noise-disturbance principle stating that there is a tradeoff between noise and disturbance when a measurement of position and a measurement of momentum are performed sequentially, and another principle imposing a limitation on the product of the uncertainties in a joint measurement of position and momentum. We prove that the former, the Heisenberg sequential noise-disturbance principle, holds when the detectors are assumed to be initially uncorrelated from each other, but that it can be violated for some properly correlated initial preparations of the detectors.
We examine error-disturbance relations in the quantum measurement of spin systems using an atom-light interface scheme. We model a single spin-1/2 system that interacts with a polarized light meter via a Faraday interaction. We formulate the error and disturbance of the model and examine the uncertainty relations. We found that for the coherent light meter in pure polarization, both the error and disturbance behave the cyclic oscillations due to the Faraday rotation in both the light and spin polarizations. We also examine a class of polarization squeezed light meter, where we apply the phase-…
Quantum space-depth tradeoffs for coherent block encodings
提出一种通过哈密顿模拟实现低辅助量子比特块编码的简单构造，仅需一个辅助量子比特，电路深度接近最优。
Local Gaussian bounds on the non-destructive discrimination of two-mode squeezed states
本研究探究利用局域高斯测量对双模压缩态的非破坏性区分，构造最优协议并扩展至含预共享纠缠的情形，将信息增益与扰动的权衡从有限维系统拓展至连续变量系统。
Information gain and measurement disturbance for quantum agents
将量子测量推广至量子代理，其记忆可存储经典或量子信息，发现量子代理能获取更多信息但代价是更大的测量扰动，并通过实验表征了这种权衡。
Information recycling in coherent state discrimination
针对连续变量量子通信中的相干态识别问题，提出信息回收（IR）策略，通过顺序最小错误识别（MED）回收无歧义识别（UD）的失败态，实现兼顾确定性与无错误子集的最优识别，为长距离CV-QKD接收器设计提供新思路。
When does numerical pulse optimization actually help? Error budgets,robustness tradeoffs, and calibration guidance for transmon single-qubit gates
研究发现DRAG在退相干限制下性能接近最优，GRAPE在短门时间提供零相干误差，但DRAG在频率漂移鲁棒性上更优，为transmon单量子比特门校准提供指导。
All incoherent as well as 2- and 3-qubit coherent eavesdropping strategies on the 6 state protocol of quantum cryptography are classified. For a disturbance of 1/6, the optimal incoherent eavesdropping strategy reduces to the universal quantum cloning machine. Coherent eavesdropping cannot increase Eve's Shannon information, neither on the entire string of bits, nor on the set of bits received undisturbed by Bob. However, coherent eavesdropping can increase as well Eve's Renyi information as her probability of guessing correctly all bits. The case that Eve delays the measurement of her probe u…
We investigate experimentally fundamental properties of coherent ghost imaging using spatially incoherent beams generated from a pseudo-thermal source. A complementarity between the coherence of the beams and the correlation between them is demonstrated by showing a complementarity between ghost diffraction and ordinary diffraction patterns. In order for the ghost imaging scheme to work it is therefore crucial to have incoherent beams. The visibility of the information is shown for the ghost image to become better as the object size relative to the speckle size is decreased, and therefore a re…
It is widely known that `collapse of the wave function' on a quantum system A may be brought about by an interaction with another quantum system B. We will prove that this is not just a possible, but a necessary consequence of information transfer from A to B. We generalize this in order to explain why coherences are normally not observed in macroscopic quantum systems. Finally, we provide a quantitative insight into the balance between information gain and state disturbance. We define the quality of an information transfer. For all information transfers of a certain quality, we find a minimum…
Quantum measurement is a basic tool to manifest intrinsic quantum effects from fundamental tests to quantum information applications. While a measurement is typically performed to gain information on a quantum state, its role in quantum technology is indeed manifold. For instance, quantum measurement is a crucial process element in measurement-based quantum computation. It is also used to detect and correct errors thereby protecting quantum information in error-correcting frameworks. It is therefore important to fully characterize the roles of quantum measurement encompassing information gain,…
For entangled states of light both the amount of entanglement and the sensitivity to noise generally increase with the number of photons in the state. The entanglement-sensitivity tradeoff is investigated for a particular set of states, multi-dimensional entangled coherent states. Those states possess an arbitrarily large amount of entanglement $E$ provided the number of photons is at least of order $2^{2E}$. We calculate how fast that entanglement decays due to photon absorption losses and how much entanglement is left. We find that for very small losses the amount of entanglement lost is equ…
Recent Developments and Perspectives in Variational Quantum Eigensolvers for Molecular Electronic Structure: Methods, Tradeoffs, and Benchmarking
本文综述了VQE算法的最新发展，重点探讨了VQE的不同变体、电路复杂度降低、化学启发型ansatz以及激发态扩展，并评估了VQE方法的准确性和量子模拟器的现状。
Reshaping nonclassical properties and metrological performance of entangled coherent states via post-selected von Neumann measurements
本文通过后选择的von Neumann测量重塑双模纠缠相干态的非经典性质，增强四阶压缩和求和压缩，提升相位灵敏度，为连续变量传感提供了可调的非经典资源工程途径。
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