We propose a criterion which defines whether a superposition of two photonic components is macroscopic. It is based on the ability to discriminate these components with a particular class of "classical" detectors, namely a photon number measurement with a resolution coarse-grained by noise. We show how our criterion can be extended to a measure of the size of macroscopic superpositions by quantifying the amount of noise that can be tolerated and taking the distinctness of two Fock states differing by N photons as a reference. After applying our measure to several well-known examples, we demonstrate that the superpositions which meet our criterion are very sensitive to phase fluctuations. This suggests that quantifying the macroscopicity of a superposition state through the distinguishability of its components with "classical" detectors is not only a natural measure but also explains why it is difficult to observe superpositions at the macroscopic scale.
The entangled state that results when a detector measures a superposed quantum system has spawned decades of concern about the problem of definite outcomes or "Schrodinger's cat." This state seems to describe a detector in an indefinite or "smeared" situation of indicating two macroscopic configurations simultaneously. This would be paradoxical. Since all entangled states are known to have nonlocal properties, and since measurements have obvious nonlocal characteristics, it's natural to turn to nonlocality experiments for insight into this question. Unlike the measurement situation where the p…
According to Bohr's principle of complementarity, a quanton can behave either as a wave or a particle, depending on the choice of the experimental setup. Some recent two-path interference experiments have devised methods where one can have a quantum superposition of the two choices, thus indicating that a quanton may be in a superposition of wave and particle nature. These experiments have been of interest from the point of view of Wheeler's delayed-choice experiment. However, it has also been claimed that this experiment can violate complementarity. Here we theoretically analyze a multipath i…
We present a scheme to conditionally generate an arbitrary superposition of a pair of coherent states from a squeezed vacuum by means of the modified photon subtraction where a coherent state ancilla and two on/off type detectors are used. We show that, even including realistic imperfections of the detectors, our scheme can generate a target state with a high fidelity. The amplitude of the generated states can be amplified by conditional homodyne detections.
Unruh-deWitt detectors have been utilised widely as probes for quantum particles, entanglement and spacetime curvature. Here, we extend the standard treatment of an Unruh-deWitt detector interacting with a massless, scalar field to include the detector travelling in a quantum superposition of classical trajectories. We derive perturbative expressions for the final state of the detector, and show that it depends on field correlation functions evaluated locally along the individual trajectories, as well as non-locally between the superposed trajectories. By applying our general approach to a det…
The Unruh effect is the phenomenon that accelerated observers detect particles even when inertial observers experience the vacuum state. In particular, uniformly accelerated observers are predicted to measure thermal radiation that is proportional to the acceleration. Here we consider the Unruh effect for a detector that follows a quantum superposition of different accelerated trajectories in Minkowski spacetime. More precisely, we analyse the excitations of a pointlike multilevel particle detector coupled to a massless real scalar field and moving in the superposition of accelerated trajector…
Quantum field theory is completely characterized by the field correlations between spacetime points. In turn, some of these can be accessed by locally coupling to the field simple quantum systems, a.k.a. particle detectors. In this work, we consider what happens when a quantum-controlled superposition of detectors at different space-time points is used to probe the correlations of the field. We show that, due to quantum interference effects, two detectors can gain information on field correlations which would not be otherwise accessible. This has relevant consequences for information theoretic…
The evolution of a measured system and an experimental apparatus is presented in an unified form. Conditions under which the state of such a total system forms, evaluates and declines from a superposition of states are defined. The problem of definite outcomes in the quantum-mechanical measurement theory is considered.
We generalize the Unruh-DeWitt detector model to second quantization. We illustrate this model by applying it to an excited particle in a superposition of relativistic velocities. We calculate, to first order, how its decay depends on whether its superposition of velocities is coherent or incoherent. Further, we generalize the framework of quantum reference frames to allow transformations to the rest frames of second-quantized Unruh DeWitt detectors. As an application, we show how to transform into the rest frame of a decaying particle that, in the laboratory frame, is in a linear superpositio…
In a recent criticism (arXiv:2111.13357) of our paper arXiv:2111.09347, Drezet argues that we have forgotten to consider superpositions of detector eigenstates. However, such superpositions do not occur in the models our paper is concerned with. We also note that no one has ever observed such detector superpositions.
One of the peculiar features in quantum mechanics is that a superposition of macroscopically distinct states can exits. In optical system, this is highlighted by a superposition of coherent states (SCS), i.e. a superposition of classical states. Recently this highly nontrivial quantum state and its variant have been demonstrated experimentally. Here we demonstrate the superposition of coherent states in quantum measurement which is also a key concept in quantum mechanics. More precisely, we propose and implement a projection measurement onto the arbitrary superposition of the SCS bases in opti…
We present a new operational framework for studying ``superpositions of spacetimes'', which are of fundamental interest in the development of a theory of quantum gravity. Our approach capitalizes on nonlocal correlations in curved spacetime quantum field theory, allowing us to formulate a metric for spacetime superpositions as well as characterizing the coupling of particle detectors to a quantum field. We apply our approach to analyze the dynamics of a detector (using the Unruh-deWitt model) in a spacetime generated by a BTZ black hole in a superposition of masses. We find that the detector e…
We address the peculiarities of the quantum measurement process in the course of a continuous weak linear measurement (CWLM). As a tool, we implement an efficient numerical simulation scheme that allows us to generate single quantum trajectories of the measured system state as well as the recorded detector signal, and study statistics of these trajectories with and without post-selection. In this scheme, a linear detector is modelled with a qubit that is weakly coupled to the quantum system measured and is subject to projective measurement and re-initialization after a time interval at each si…
Entanglement can modify the interference patterns of multi-particle systems. We analyse, using the path integral formalism, a novel example of multi-particle interference and some unexplored aspects of this phenomenon by considering the two-slit arrangement with two distinguishable particles in a superposition state. The two components of entanglement, multiplicity of multi-particle terms and their coherence, can be studied separately by comparing the patterns of product, mixed and superposition states. This suggests a scheme to detect multi-particle superposition in some favourable cases. Mor…
We explore quantum properties of a which-way detector using three versions of an idealized two slit arrangements. Firstly we derive complementarity relations for the detector; secondly we show how the "experiment" may be altered in such a way that using single position measurement on the screen we can obtain quantum erasure. Finally we show how to construct a superposition of "wave" and "particle" components.
Over decades quantum cryptography has been intensively studied for unconditionally secured data transmission in a quantum regime. Due to the quantum loopholes caused by imperfect single photon detectors and/or lossy quantum channels, however, the quantum cryptography is practically inefficient and even vulnerable to eavesdropping. Here, a method of unconditionally secured key distribution potentially compatible with current fiber-optic communications networks is proposed in a classical regime for high-speed optical backbone networks. The unconditional security is due to the quantum superpositi…
We study characteristics of superpositions and entanglement of thermal states at high temperatures and discuss their applications to quantum information processing. We introduce thermal-state qubits and thermal-Bell states, which are a generalization of pure-state qubits and Bell states to thermal mixtures. A scheme is then presented to discriminate between the four thermal-Bell states without photon number resolving detection but with Kerr nonlinear interactions and two single-photon detectors. This enables one to perform quantum teleportation and gate operations for quantum computation with …
Within any anticipated unifying theory of quantum gravity, it should be meaningful to combine the fundamental notions of quantum superposition and spacetime to obtain so-called "spacetime superpositions": that is, quantum superpositions of different spacetimes not related by a global coordinate transformation. Here we consider the quantum-gravitational effects produced by superpositions of periodically identified Minkowski spacetime (i.e.\ Minkowski spacetime with a periodic boundary condition) with different characteristic lengths. By coupling relativistic quantum matter to fields on such a s…
It has been shown that a macroscopic system being in a high-temperature thermal coherent state can be, in principle, driven into a non-classical state by coupling to a microscopic system. Therefore, thermal coherent states do not truly represent the classical limit of quantum description. Here, we study the classical limit of quantum state of a more relevant macroscopic system, namely the pointer of a detector, after the phase-preserving linear amplification process. In particular, we examine to what extent it is possible to find the corresponding amplified state in a superposition state, by c…
Coincidence detection is a key technique used in nonlocal quantum-correlation measurements to test Bell inequality violation between remotely separated local detectors. With individual uniform intensity of local measurements, the nonlocal correlation fringe is a mysterious quantum feature that cannot be achieved classically. Here, the coincidence detection is coherently investigated to understand the fundamental physics of the nonlocal correlation fringe via second-order quantum superposition between selected nonlocal measurement events. Because of the coherence feature of paired photons, the …
By sending a classical two-level system, one can transfer information about only \emph{two} distinguishable outcomes. Here we show that in quantum mechanics, using both the spin and path degrees of freedom of a spin-1/2 particle, and a Mach-Zehnder type interferometric arrangement with two suitable Stern-Gerlach detectors, it is possible to transfer information about \emph{four} distinguishable outcomes. This procedure does \emph{not} require using quantum entanglement as a resource as in the well-known protocol of dense coding, but instead hinges entirely on the quantum superposition principl…
Quantum mechanical complementarity ensures the security of the key-distribution scheme reported by Brassard and Bennet in 1984 (BB84), but does not prohibit use of multi-photons as a signal carrier. We describe a novel BB84 scheme in which two nearly orthogonal coherent states carry the key, and the superposition of these states (cat states) protects the communication channel from eavesdropping. Information leakage to eavesdroppers can be determined from the visibility of the interferential fringes in the distribution of the outcome when a certain quadrature component is measured through homod…
We propose and experimentally realize a novel versatile protocol that allows the quantum state engineering of heralded optical coherent-state superpositions. This scheme relies on a two-mode squeezed state, linear mixing and a $n$-photon detection. It is optimally using expensive non-Gaussian resources to build up only the key non-Gaussian part of the targeted state. In the experimental case of a two-photon detection based on high-efficiency superconducting nanowire single-photon detectors, the freely propagating state exhibits a 67% fidelity with a squeezed even coherent-state superposition w…
We examine an experimental setup implementing a family of quantum non-Gaussian filters. The filters can be applied to an arbitrary two-mode input state. We assume realistic photodetection in the filtering process and explore two different models of inefficient detection: a beam splitter of a small reflectivity located in front of a perfect detector and a Weierstrass transform applied to the unperturbed measurement outcomes. We explicitly give an operator which describes the coherent action of the filters in the realistic experimental conditions. The filtered states may find applications in qua…
We derive stochastic master equations for a quantum system interacting with a Bose field prepared in a superposition of continuous-mode coherent states. To determine a conditional evolution of the quantum system we use a collision model with an environment given as an infinite chain of not interacting between themselves qubits prepared initially in a entangled state being a discrete analogue of a superposition of coherent states of the Bose field. The elements of the environment chain interact with the quantum system in turn one by one and they are subsequently measured. We determine a conditi…
Error correction will add so much overhead to large quantum computations that we suspect the most efficient algorithms will use a classical co-processor to do as much work as possible. We present a method to offload portions of a quantum computation to a classical computer by producing a superposition of masks which hide a quantum input. With the masks, we can measure the result without altering the original input and then perform classical computations on the measured output. If the task has enough structure, the classical computations will be equivalent to a quantum computation performed in …
Spontaneous collapse models of state vector reduction represent a possible solution to the quantum measurement problem. In the present paper we focus our attention on the Ghirardi-Rimini-Weber (GRW) theory and the corresponding continuous localisation models in the form of a Brownian-driven motion in Hilbert space. We consider experimental setups in which a single photon hits a beam splitter and is subsequently detected by photon detector(s), generating a superposition of photon-detector quantum states. Through a numerical approach we study the dependence of collapse times on the physical feat…
We study a class of quantum measurement models. A microscopic object is entangled with a macroscopic pointer such that a distinct pointer position is tied to each eigenvalue of the measured object observable. Those different pointer positions mutually decohere under the influence of an environment. Overcoming limitations of previous approaches we (i) cope with initial correlations between pointer and environment by considering them initially in a metastable local thermal equilibrium, (ii) allow for object-pointer entanglement and environment-induced decoherence of distinct pointer readouts to …
A method for the determination of absolute quantum detection efficiency is suggested based on the measurement of photocount statistics of twin beams. The measured histograms of joint signal-idler photocount statistics allow to eliminate an additional noise superimposed on an ideal calibration field composed of only photon pairs. This makes the method superior above other approaches presently used. Twin beams are described using a paired variant of quantum superposition of signal and noise.
Particle detector in a position-superposed black hole spacetime
University of York（约克大学）；International Iberian Nanotechnology Laboratory (INL)（伊比利亚纳米技术国际实验室）；University of Vienna（维也纳大学）；Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences（奥地利科学院量子光学与量子信息研究所）
We consider an entanglement harvesting protocol between two Unruh-deWitt detectors in quantum superpositions of static trajectories in the static de Sitter and thermal Minkowski spacetimes. We demonstrate for the first time that the spatial superposition of each detector's path allows entanglement to be harvested from the quantum field in regimes where it would be otherwise impossible for detectors on classical trajectories. Surprisingly, for detectors on sufficiently delocalised trajectories in a thermal bath, the amount of harvested entanglement grows with the temperature of the field, viola…
We study the two-path interference of single-particle pulses measured by the Unruh-DeWitt-type quantum detector, which itself is a quantum state as well as the incoming pulse, and of which the interaction with the pulse is described by unitary quantum evolution instead of a nonunitary collapsing process. Provided that the quantum detector remains coherent in time long enough, the detection probability still manifests the two-path interference pattern even if the length difference between the two paths considerably exceeds the coherence length of the single-particle pulse, contrary to the resul…
We study dynamics of the measurement process in quantum dot systems, where a particular state out of coherent superposition is observed. The ballistic point-contact placed near one of the dots is taken as a noninvasive detector. We demonstrate that the measurement process is fully described by the Bloch-type equations applied to the whole system. These equations clearly reproduce the collapse of the density-matrix into the statistical mixture in the course of the measurement process. The corresponding dephasing width is uniquely defined. We show that the continuous observation of one of the st…
A misunderstanding of entangled states has spawned decades of concern about quantum measurements and a plethora of quantum interpretations. The "measurement state" or "Schrodinger's cat state" of a superposed quantum system and its detector is nonlocally entangled, suggesting that we turn to nonlocality experiments for insight into measurements. By studying the full range of superposition phases, these experiments show precisely what the measurement state does and does not superpose. These experiments reveal that the measurement state is not, as had been supposed, a paradoxical superposition o…
We study a class of quantum measurement models. A microscopic object is entangled with a macroscopic pointer such that each eigenvalue of the measured object observable is tied up with a specific pointer deflection. Different pointer positions mutually decohere under the influence of a bath. Object-pointer entanglement and decoherence of distinct pointer readouts proceed simultaneously. Mixtures of macroscopically distinct object-pointer states may then arise without intervening macroscopic superpositions. Initially, object and apparatus are statistically independent while the latter has point…
This paper reviews and suggests a resolution of the problem of definite outcomes of measurement. This problem, also known as "Schrodinger's cat," has long posed an apparent paradox because the state resulting from a measurement appears to be a quantum superposition in which the detector is in two macroscopically distinct states (alive and dead in the case of the cat) simultaneously. Many alternative interpretations of the quantum mathematical formalism, and several alternative modifications of the theory, have been proposed to resolve this problem, but no consensus has formed supporting any on…
Wave function collapse models postulate a fundamental breakdown of the quantum superposition principle at the macroscale. Therefore, experimental tests of collapse models are also fundamental tests of quantum mechanics. Here, we compute the upper bounds on the collapse parameters, which can be inferred by the gravitational wave detectors LIGO, LISA Pathfinder, and AURIGA. We consider the most widely used collapse model, the continuous spontaneous localization (CSL) model. We show that these experiments exclude a huge portion of the CSL parameter space, the strongest bound being set by the rece…
With the example of a Stern-Gerlach measurement on a spin-1/2 atom, we show that a superposition of both paths may be observed compatibly with properties attributed to state collapse - for example, the singleness (or mutual exclusivity) of outcomes. This is done by inserting a quantum two-state system (an ancilla) in each path, capable of responding to the passage of the atom, and thus acting as a virtual detector. We then consider real measurements on the compound system of atomic spin and two ancillae. Nondestructive measurements of a set of compatible joint observables can be performed, one…
Microscopic physical laws are time-symmetric, hence, a priori there exists no preferential temporal direction. However, the second law of thermodynamics allows one to associate the "forward" temporal direction to a positive variation of the total entropy produced in a thermodynamic process, and a negative variation with its "time-reversal" counterpart. This definition of a temporal axis is normally considered to apply in both classical and quantum contexts. Yet, quantum physics admits also superpositions between forward and time-reversal processes, whereby the thermodynamic arrow of time becom…
Quantum detector tomography is a fundamental technique for calibrating quantum devices and performing quantum engineering tasks. In this paper, we design optimal probe states for detector estimation based on the minimum upper bound of the mean squared error (UMSE) and the maximum robustness. We establish the minimum UMSE and the minimum condition number for quantum detectors and provide concrete examples that can achieve optimal detector tomography. In order to enhance the estimation precision, we also propose a two-step adaptive detector tomography algorithm to optimize the probe states adapt…
We study quantum states produced by optimal phase covariant quantum cloners. We argue that cloned quantum superpositions are not macroscopic superpositions in the spirit of Schrödinger's cat, despite their large particle number. This is indicated by calculating several measures for macroscopic superpositions from the literature, as well as by investigating the distinguishability of the two superposed cloned states. The latter rapidly diminishes when considering imperfect detectors or noisy states, and does not increase with the system size. In contrast, we find that cloned quantum states thems…
We propose a method for a weak continuous measurement of the energy eigenstates of a fast quantum system by means of a "slow" detector. Such a detector is only sensitive to slowly-changing variables, e. g. energy, while its back-action can be limited solely to decoherence of the eigenstate superpositions. We apply this scheme to the problem of detection of quantum jumps between energy eigenstates in a harmonic oscillator.
We consider continuously monitored quantum systems and introduce definitions of work and heat along individual quantum trajectories that are valid for coherent superpositions of energy eigenstates. We use these quantities to extend the first and second laws of stochastic thermodynamics to the quantum domain. We illustrate our results with the case of a weakly measured driven two-level system and show how to distinguish between quantum work and heat contributions. We finally employ quantum feedback control to suppress detector backaction and determine the work statistics.
We realized the most fundamental quantum optical experiment to prove the non-classical character of light: Only a single quantum emitter and a single superconducting nanowire detector were used. A particular appeal of our experiment is its elegance and simplicity. Yet its results unambiguously enforce a quantum theory for light. Previous experiments relied on more complex setups, such as the Hanbury-Brown-Twiss configuration, where a beam splitter directs light to two photodetectors, giving the false impression that the beam splitter is required. Our work results in a major simplification of t…
In a macroscopic realm, in which photons are too many for being counted by any photon counting detector, photon statistics can be measured by using detectors simply endowed with linear response. We insert one of such detectors in a conventional photon-counting apparatus, which returns a voltage every time the detector responds to light by generating a number of elementary charges via its primary photo-detection process. We only assume that, when a single charge is photo-generated, the probability density of the voltages is a distribution that is narrow with respect to its mean value. Under thi…
The Feynman Path Integral formalism has long been used for calculations of probability amplitudes. Over the last few years, it has been extensively used to theoretically demonstrate that the usual application of the superposition principle in slit based interference experiments is often incorrect. This has caveat in both optics and quantum mechanics where it is often naively assumed that the boundary condition represented by slits opened individually is same as them being opened together. The correction term comes from exotic sub leading terms in the Path Integral which can be described by wha…
Developing an earlier proposal (Ne'eman, Damnjanovic, etc), we show herein that there is a Landau continuous phase transition from the exact quantum dynamics to the effectively classical one, occurring via spontaneous superposition breaking (effective hiding), as a special case of the corresponding general formalism (Bernstein). Critical values of the order parameters for this transition are determined by Heisenberg's indeterminacy relations, change continuously, and are in excellent agreement with the recent and remarkable experiments with Bose condensation. It is also shown that such a phase…
