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 quantities, like entanglement and mutual information harvested from the field. In particular, the quantum control allows for extraction of entanglement in scenarios where this is otherwise provably impossible.
We present efficient methods to interpolate data with a quantum computer that complement uploading techniques and quantum post-processing. The quantum algorithms are supported by the efficient Quantum Fourier Transform (QFT) and classical signal and imaging processing techniques, and open the door of quantum advantage to relevant families of data. We showcase a QFT interpolation method, a Quantum Cosine Transform (QCT) interpolation geared towards natural data, and we improve upon them by utilizing a quantum circuit's capabilities of processing data in superposition. A novel circuit for the QC…
States in quantum field theory (QFT) are represented by many-particle wave functions, such that a state describing n particles depends on n spacetime positions. Since a general state is a superposition of states with different numbers of particles, the wave function lives in the configuration space identified with a product of an infinite number of 4-dimensional Minkowski spacetimes. The squared absolute value of the wave function is interpreted as the probability density in the configuration space, from which the standard probabilistic predictions of QFT can be recovered. Such a formulation a…
We propose a method for the realization of the two-qubit quantum Fourier transform (QFT) using a Hamiltonian which possesses the circulant symmetry. Importantly, the eigenvectors of the circulant matrices are the Fourier modes and do not depend on the magnitude of the Hamiltonian elements as long as the circulant symmetry is preserved. The QFT implementation relies on the adiabatic transition from each of the spin product states to the respective quantum Fourier superposition states. We show that in ion traps one can obtain a Hamiltonian with the circulant symmetry by tuning the spin-spin inte…
Quantum mechanics allows coherent superposition between different states of matter. This quality is responsible for major non-classical phenomena that occur in quantum systems. Beyond states, coherent superpositions are also possible between quantum evolutions. We characterize such superpositions here. A resource theoretic framework is developed to quantify superposition present in an arbitrary quantum evolution. In addition to characterization, the framework considers superposition as a quantum resource. This resource can be exploited to perform certain quantum tasks that are otherwise imposs…
Models for quantum computation with circuit connections subject to the quantum superposition principle have been recently proposed. There, a control quantum system can coherently determine the order in which a target quantum system undergoes $N$ gate operations. This process, known as the quantum $N$-switch, is a resource for several information-processing tasks. In particular, it provides a computational advantage -- over fixed-gate-order quantum circuits -- for phase-estimation problems involving $N$ unknown unitary gates. However, the corresponding algorithm requires an experimentally unfea…
Proposed quantum experiments in deep space will be able to explore quantum information issues in regimes where relativistic effects are important. In this essay, we argue that a proper extension of Quantum Information theory into the relativistic domain requires the expression of all informational notions in terms of quantum field theoretic (QFT) concepts. This task requires a working and practicable theory of QFT measurements. We present the foundational problems in constructing such a theory, especially in relation to longstanding causality and locality issues in the foundations of QFT. Fina…
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…
The General Boundary Formulation (GBF) is a new framework for studying quantum theories. After concise overviews of the GBF and Schrödinger-Feynman quantization we apply the GBF to resolve a well known problem on Anti-deSitter spacetime where due to the lack of temporally asymptotic free states the usual S-matrix cannot be defined. We construct a different type of S-matrix plus propagators for free and interacting real Klein-Gordon theory.
A class of models with a dynamics of generalized quantum cat maps on a product of quantum tori is described. These tori are defined by an algebra of clock-shift matrices of dimension $N$. The dynamics is such that the Lyapunov exponents can be computed analytically at large $N$. Some of these systems can be thought of as a toy model for quantum fields on a lattice under a time evolution with nearest neighbor interactions, resembling a quantum version of a cellular automaton. The dynamics of entangling is studied for initial product states. Some of these entangle at rates determined by Lyapunov…
In this work, we describe examples for calculating the 1-D circular convolution of signals represented by 3-qubit superpositions. The case is considered, when the discrete Fourier transform of one of the signals is known and calculated in advance and only the QFT of another signal is calculated. The frequency characteristics of many linear time-invariant systems and filters are well known. Therefore, the considered method of convolution can be used for these systems in quantum computation. The ideal low pass and high pass filters are considered and quantum schemes for convolution are presented…
In this note we describe a simple and intriguing observation: the quantum Fourier transform (QFT) over $Z_q$, which is considered the most ``quantum'' part of Shor's algorithm, can in fact be simulated efficiently by classical computers. More precisely, we observe that the QFT can be performed by a circuit of poly-logarithmic path-width, if the circuit is allowed to apply not only unitary gates but also general linear gates. Recalling the results of Markov and Shi [MaSh] and Jozsa [Jo] which provided classical simulations of such circuits in time exponential in the tree-width, this implies the…
Quantum superpositions and entanglement are at the heart of the quantum information science. There have been only a few investigations of these phenomena at the mesoscopic level, despite the fact that these systems are promising for quantum state storage and processing. Here we present two novel experiments with surface plasmons propagating on cm-long metallic stripe waveguides. We demonstrate that two plasmons can be entangled at remote places. In addition, we create a single plasmon in a temporal superposition state: it exists in a superposition of two widely separated moments. These quantum…
The complementary principle of quantum mechanics relates qualitatively the visibility of quantum interference with path indistinguishability. Here we propose a scheme of constructive quantum interference involving superposition between an $N$-photon state and a single-photon state to characterize quantitatively the degree of temporal distinguishability of the $N$-photon state. This scheme is based on a generalized photon bunching effect. Such a scheme can be extended to other more general cases.
Quantum sensors based on the superposition of neutral atoms are promising for sensing the nature of dark matter (DM). In this study, we utilize the Stern-Gerlach (SG) interferometer configuration to seek a novel method for the detection of detect axion-like particles (ALPs). Using an SG interferometer, we create a spatial quantum superposition of neutral atoms such as $^{3}$He and $^{87}$Rb. It is shown that the interaction of ALPs with this superposition induces a relative phase between superposed quantum components. We use the quantum Boltzmann equation (QBE) to introduce a first-principles …
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…
Leveraging Quantum Superposition to Infer the Dynamic Behavior of a Spatial-Temporal Neural Network Signaling Model
Department of Bioengineering and Department of Neurosciences（生物工程系和神经科学系）；Center for Engineered Natural Intelligence（工程化自然智能中心）；Kavli Institute for Brain and Mind（脑与心智研究所）；University of California San Diego（加州大学圣地亚哥分校）
Two-photon time-frequency entanglement is a valuable resource in quantum information. Resolving the wavepacket of ultrashort pulsed single-photons, however, is a challenge. Here, we demonstrate remote spectral shaping of single photon states and probe the coherence properties of two-photon quantum correlations in the time-frequency domain, using engineered parametric down-conversion (PDC) and a quantum pulse gate (QPG) in nonlinear waveguides. Through tailoring the joint spectral amplitude function of our PDC source we control the temporal mode structure between the generated photon pairs and …
Encoding quantum information in the photon temporal mode (TM) offers a robust platform for high-dimensional quantum protocols. The main practical challenge, however, is to design a device that operates on single photons in specific TMs and all coherent superpositions. The quantum pulse gate (QPG) is a mode-selective sum-frequency generation designed for this task. Here, we perform a full modal characterisation of a QPG using weak coherent states in well-defined TMs. We reconstruct a full set of measurement operators, which show an average fidelity of 0.85 to a theoretically ideal device when o…
Conditional preparation is a well-established technique for quantum state engineering of light. A general trend is to increase the number of heralding detection events in such realization to reach larger photon-number states or their arbitrary superpositions. In contrast to pulsed implementations, where detections only occur within the pulse window, for continuous-wave light the temporal separation of the conditioning detections is an additional degree of freedom and a critical parameter. Based on the theoretical study by A.E.B. Nielsen and K. Molmer and on a continuous-wave two-mode squeezed …
Quantum interference arising from superposition of states is a striking evidence of the validity of Quantum Mechanics, confirmed in many experiments and also exploited in applications. However, as for any scientific theory, Quantum Mechanics is valid within the limits in which it has been experimentally verified. In order to extend such limits, it is necessary to observe quantum interference in unexplored conditions such as moving terminals at large distance in Space. Here we experimentally demonstrate single photon interference at a ground station due to the coherent superposition of two temp…
The photonic temporal degree of freedom is one of the most promising platforms for quantum communication over fiber networks and free-space channels. In particular, time-bin states of photons are robust to environmental disturbances, support high-rate communication, and can be used in high-dimensional schemes. However, the detection of photonic time-bin states remains a challenging task, particularly for the case of photons that are in a superposition of different time-bins. Here, we experimentally demonstrate the feasibility of picosecond time-bin states of light, known as ultrafast time-bins…
Clarifying the nature of the quantum state $|Ψ\rangle$ is at the root of the problems with insight into counter-intuitive quantum postulates. We provide a direct-and math-axiom free-empirical derivation of this object as an element of a vector space. Establishing the linearity of this structure--quantum superposition--is based on a set-theoretic creation of ensemble formations and invokes the following three principia: ($\textsf{I}$) quantum statics, ($\textsf{II}$) doctrine of the number in the physical theory, and ($\textsf{III}$) mathematization of matching the two observations with each ot…
Time has a fundamentally different character in quantum mechanics and in general relativity. In quantum theory events unfold in a fixed time order while in general relativity temporal order is influenced by the distribution of matter. When the distribution of matter requires a quantum description, temporal order is expected to become non-classical -- a scenario beyond the scope of current theories. Here we provide a direct description of such a scenario. We consider a massive body in a spatial superposition and show how it leads to "entanglement" of temporal orders between time-like events in …
Split-Step Dirac Cellular Automata for Continuous-Time Dirac Dynamics on Finite Spatial Lattices
National Taiwan University（国立台湾大学）；Center for Theoretical Physics, National Taiwan University（国立台湾大学理论物理中心）；National Center for Theoretical Sciences（国家理论科学中心）；Chung Yuan Christian University（中原大学）
Well controlled nonlinear interactions between light field pulses and single atoms could be used to implement optical quantum information technologies based on qubits encoded in superpositions of coherent states of light. Here, we investigate the transformation of a coherent light field input at a single atom sufficiently far from resonance to limit the decoherence effects associated with random excitations of the atom. The conditions for suppressing multi-photon scattering to implement arbitrarily large shifts of the coherent light amplitude without decoherence are studied. It is shown that q…
Nowadays the most intriguing features of wave particle complementarity of single photon is exemplified by the famous Wheeler's delayed choice experiment in linear optics, nuclear magnetic resonance and integrated photonic device systems. Studying the wave particle behavior in light and matter interaction at single photon level is challenging and interesting, which gives how single photons complement in light and matter interaction. Here, we demonstrate a Wheeler's delayed choice experiment in an interface of light and atomic memory, in which the cold atomic memory makes the heralded single pho…
Coherent temporal filtering of multimode parametric down-conversion using a quantum pulse gate
Integrated Quantum Optics Group, Institute for Photonic Quantum Systems (PhoQS), Paderborn University（帕德博恩大学光子量子系统研究所）；School of Mathematics and Physics, University of Queensland（昆士兰大学数学与物理学院）
We considered one-dimensional chain of the two-level quantum systems coupled via tunneling. The chain is driven by the superposition of dc and ac fields in the strong coupling regime. Based on the fundamental principles of electrodynamics and quantum theory, we developed a generalized model of quantum dynamics for such interactions, free of rotating wave approximation (RWA). The system of motion equations was studied numerically. We analyzed the dynamics and spectra of inversion density, dipole current density and tunneling current density. In the case of resonant interaction with ac-component…
Within quantum theory, we can create superpositions of different causal orders of events, and observe interference between them. This raises the question of whether quantum theory can produce results that would be impossible to replicate with any classical causal model, thereby violating a causal inequality. This would be a temporal analogue of Bell inequality violation, which proves that no local hidden variable model can replicate quantum results. However, unlike the case of non-locality, we show that quantum experiments \emph{can} be simulated by a classical causal model, and therefore cann…
A few decades ago, quantum optics stood out as a new domain of physics by exhibiting states of light with no classical equivalent. The first investigations concerned single photons, squeezed states, twin beams and EPR states, that involve only one or two modes of the electromagnetic field. The study of the properties of quantum light then evolved in the direction of more and more complex and rich situations, involving many modes, either spatial, temporal, frequency, or polarization modes. Actually, each mode of the electromagnetic field can be considered as an individual quantum degree of free…
Revealing high-dimensional entanglement through symmetry
Griffith University（格里菲斯大学）；Technische Universität Wien（维也纳工业大学）；AIT- Austrian Institute of Technology（奥地利技术研究院）；University of New South Wales（新南威尔士大学）；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）
Frequency Detuning and Interference-Induced Bohmian Chaos in a Two-Dimensional Anisotropic Harmonic Oscillator
Centre of Foundation Studies in Science of Universiti Putra Malaysia (ASPutra), Universiti Putra Malaysia (UPM)（博特拉大学科学基础研究中心）；Institute for Mathematical Research (INSPEM) Universiti Putra Malaysia (UPM)（博特拉大学数学研究所）；Department of Physics, Faculty of Science, Universiti Putra Malaysia (UPM)（博特拉大学理学院物理系）；Department of Applied Physics, Faculty of Science and Technology Universiti Kebangsaan Malaysia (UKM)（马来西亚国立大学科技与理学院应用物理系）
Quantum Temporal Convolutional Neural Networks for Cross-Sectional Equity Return Prediction: A Comparative Benchmark Study
Beth Israel Deaconess Medical Center \& Harvard Medical School, Boston, MA 02115 USA；Luddy School of Informatics, Computing；Engineering, Indiana University Bloomington, Bloomington, IN 47405 USA；Institute of Electronics Engineering, National Taiwan University, 106319, Taiwan；Department of Mathematics, Boise State University, Boise, ID 83702 USA；Department of Electrophysics, National Yang Ming Chiao Tung University, 30010,Taiwan
