Under the assumption that every material object can ultimately be described by quantum theory, we ask how a probe system evolves in a device prepared and kept in a superposition state of values of its classical parameter. We find that, under ideal conditions, the evolution of the system would be unitary, generated by an effective Hamiltonian. We describe also an incoherent use of the device that achieves the same effective evolution on an ensemble. The effective Hamiltonian thus generated may have qualitatively different features from that associated to a classical value of the parameter.
We consider fundamental limits on the detectable size of macroscopic quantum superpositions. We argue that a full quantum mechanical treatment of system plus measurement device is required, and that a (classical) reference frame for phase or direction needs to be established to certify the quantum state. When taking the size of such a classical reference frame into account, we show that to reliably distinguish a quantum superposition state from an incoherent mixture requires a measurement device that is quadratically bigger than the superposition state. Whereas for moderate system sizes such a…
Quantum computing is an emerging field of science which will eventually lead us to new and powerful logic devices with capabilities far beyond the limits of current transistor-based technology. There are certain types of problems which quantum computers can solve fundamentally faster than the tradition digital computers. There are quantum algorithms which require both superposition and entanglement (e.g. Shor algorithm). But neither the Grover algorithm nor the very first quantum algorithm due to Deutsch and Jozsa need entanglement. Is it possible to utilize classical wave superposition to spe…
Overlapping resonances are shown to provide new insights into the extent of decoherence experienced by a system superposition state in the regime of strong system- environment coupling. As an example of this general approach, a generic system comprising spin-half particles interacting with a thermalized oscillator environment is considered. We find that (a) amongst the collection of parametrized Hamiltonians, the larger the overlapping resonances contribution, the greater the maximum possible purity, and (b) for a fixed Hamiltonian, the larger the overlapping resonances contribution, the large…
We study the question of what kind of a macroscopic superposition can(not) naturally exist as a ground state of some gapped local many-body Hamiltonian. We derive an upper bound on the energy gap of an arbitrary physical Hamiltonian provided that its ground state is a superposition of two well-distinguishable macroscopic "semi-classical" states. For a large class of macroscopic superposition states we show that the gap vanishes in the macroscopic limit. This in turn shows that preparation of such states by simple cooling to the ground state is not experimentally feasible and requires different…
Simulating quantum measurements without superposition devices
Lund University（隆德大学）；Instituto de física Teórica, IFT-UAM/CSIC, Universidad Autónoma de Madrid（马德里自治大学理论物理研究所）；Uppsala University（乌普萨拉大学）；Nordita, KTH Royal Institute of Technology and Stockholm University（诺迪塔，皇家理工学院与斯德哥尔摩大学）
We present a scheme for achieving macroscopic quantum superpositions in optomechanical systems by using single photon postselection and detecting them with nested interferometers. This method relieves many of the challenges associated with previous optical schemes for measuring macroscopic superpositions, and only requires the devices to be in the weak coupling regime. It requires only small improvements on currently achievable device parameters, and allows observation of decoherence on a timescale unconstrained by the system's optical decay time. Prospects for observing novel decoherence mech…
Measurement-device-independent quantum key distribution (MDI-QKD) with decoy-state method is believed to be securely applied to defeat various hacking attacks in practical quantum key distribution systems. Recently, the coherent-state superpositions (CSS) have emerged as an alternative to single-photon qubits for quantum information processing and metrology. Here, in this Letter, CSS are exploited as the source in MDI-QKD. We present an analytical method which gives two tight formulas to estimate the lower bound of yield and the upper bound of bit error rate. We exploit the standard statistica…
We show that a nonlinear Hamiltonian evolution can transform an SU(3) coherent state into a superposition of distinct SU(3) coherent states, with a superposition of two SU(2) coherent states presented as a special case. A phase space representation is depicted by projecting the multi-dimensional $Q$-symbol for the state to a spherical subdomain of the coset space. We discuss realizations of this nonlinear evolution in the contexts of nonlinear optics and Bose--Einstein condensates.
We investigate the time evolution of statistical properties of a single mode radiation field after its interaction with a two-level atom. The entire system is described by a dispersive Jaynes-Cummings Hamiltonian assuming the atomic state evolving from an initial superposition of its excited and ground states, $\vert e\rangle +\vert g\rangle ,$ and the field evolving from an initial superposition of two excited levels, $\vert n_{1}\rangle+ \vert n_{2}\rangle$. It is found that the field evolution is periodic, the period depending on the ratio $n_{2}/n_{1}.$ The energy excitation oscillates bet…
We examine heralded nondeterministic noiseless amplification based on the quantum scissors device, which has been shown to increase the one-photon amplitude of a state at the expense of the vacuum-state amplitude. Here we propose using the same basic design to perform perfect amplification in a basis set of up to two photons. The device is much more efficient than several one-photon amplifiers working in tandem. When used to amplify coherent states this advantage is shown using either fidelity or in terms of probability of sucessful action, or more strikingly in a combination of the two.
The higher order susy partners of Schroedinger Hamiltonians can be explicitly constructed by iterating a nonlinear difference algorithm coinciding with the Backlund superposition principle used in soliton theory. As an example, it is applied in the construction of new higher order susy partners of the free particle potential, which can be used as a handy tool in soliton theory.
In this paper we detail some results advanced in a recent letter [Prado et al., Phys. Rev. Lett. 102 073008 (2009)] showing how to engineer reservoirs for two-level systems at absolute zero by means of a time-dependent master equation leading to a nonstationary superposition equilibrium state. We also present a general recipe showing how to build nonadiabatic coherent evolutions of a fermionic system interacting with a bosonic mode and investigate the influence of thermal reservoirs at finite temperature on the fidelity of the protected superposition state. Our analytical results are supported…
We propose an experimental protocol to realize discrete variable quantum teleportation using optomechanical devices. The photonic polarization superposition state of a single photon is teleported to a phononic superposition of two micromechanical oscillators by means of photon/phonon entanglement generation and optical Bell state measurement using two-photon interference. Verification of the protocol is performed by coherent state transfer between the mechanical devices and light. Simulations show the feasibility of the proposed scheme at millikelvin temperatures using state-of-the-art gigaher…
We study the functioning of associative memory on three-level quantum elements, qutrites represented by spins with S = 1. The recording of patterns into the superposition of quantum states and their recall are carried out by adiabatic variation of the Hamiltonian with time. To equalize the probabilities of finding the system in different states of superposition, an auxiliary Hamiltonian is proposed, which is turned off at the end of evolution. Simulations were performed on two and three qutrits and an increase in the memory capacity after replacing qubits with qutrits is shown.
Many delayed-choice experiments based on Mach-Zehnder interferometers (MZI) have been thought and made to address the fundamental problem of wave-particle duality. Conventional wisdoms long hold that by inserting or removing the second beam splitter (BS2) in a controllable way, microscopic particles (photons, electrons, etc.) transporting within the MZI can lie in the quantum superposition of the wave and particle state as ψ=a_wψ_wave+a_pψ_particle. Here we present an alternative interpretation to these delayed-choice experiments. We notice that as all composite devices of MZI including BS2 ar…
We propose a method to create superpositions of two macroscopic quantum states of a single-mode microwave cavity field interacting with a superconducting charge qubit. The decoherence of such superpositions can be determined by measuring either the Wigner function of the cavity field or the charge qubit states. Then the quality factor Q of the cavity can be inferred from the decoherence of the superposed states. The proposed method is experimentally realizable within current technology even when the $Q$ value is relatively low, and the interaction between the qubit and the cavity field is weak…
A series of recent works has shown that placing communication channels in a coherent superposition of alternative configurations can boost their ability to transmit information. Instances of this phenomenon are the advantages arising from the use of communication devices in a superposition of alternative causal orders, and those arising from the transmission of information along a superposition of alternative trajectories. The relation among these advantages has been the subject of recent debate, with some authors claiming that the advantages of the superposition of orders could be reproduced,…
The time evolution of the Wigner function for Gaussian states generated by Lindblad quantum dynamics is investigated in the semiclassical limit. A new type of phase-space dynamics is obtained for the centre of a Gaussian Wigner function, where the Lindblad terms generally introduce a non-Hamiltonian flow. In addition to this, the Gaussian approximation yields dynamical equations for the covariances. The approximation becomes exact for linear Lindblad operators and a quadratic Hamiltonian. By viewing the Wigner function as a wave function on a coordinate space of doubled dimension, and the phas…
We provide a general method for efficiently simulating time-dependent Hamiltonian dynamics on a circuit-model based quantum computer. Our approach is based on approximating the truncated Dyson series of the evolution operator, extending the earlier proposal by Berry to evolution generated by explicitly time-dependent Hamiltonians. Two alternative strategies are proposed to implement time ordering while exploiting the superposition principle for sampling the Hamiltonian at different times. The resource cost of our simulation algorithm retains the optimal logarithmic dependence on the inverse of…
We analyze quantum states formed as superpositions of an initial pure product state and its image under local unitary evolution, using two measurement-based measures of superposition size: one based on the optimal quantum binary distinguishability of the branches of the superposition and another based on the ratio of the maximal quantum Fisher information of the superposition to that of its branches, i.e., the relative metrological usefulness of the superposition. A general formula for the effective sizes of these states according to the branch distinguishability measure is obtained and applie…
We present the point-coupling Hamiltonian as a model for frequency-independent linear optical devices acting on propagating optical modes described as a continua of harmonic oscillators. We formally integrate the Heisenberg equations of motion for this Hamiltonian, calculate its quantum scattering matrix, and show that an application of the quantum scattering matrix on an input state is equivalent to applying the inverse of classical scattering matrix on the annihilation operators describing the optical modes. We show how to construct the point-coupling Hamiltonian corresponding to a general l…
We analyze three different quantum search algorithms, the traditional Grover's algorithm, its continuous-time analogue by Hamiltonian evolution, and finally the quantum search by local adiabatic evolution. We show that they are closely related algorithms in the sense that they all perform a rotation, at a constant angular velocity, from a uniform superposition of all states to the solution state. This make it possible to implement the last two algorithms by Hamiltonian evolution on a conventional quantum circuit, while keeping the quadratic speedup of Grover's original algorithm.
For any choice of initial state and weak assumptions about the Hamiltonian, large isolated quantum systems undergoing Schrodinger evolution spend most of their time in macroscopic superposition states. The result follows from von Neumann's 1929 Quantum Ergodic Theorem. As a specific example, we consider a box containing a solid ball and some gas molecules. Regardless of the initial state, the system will evolve into a quantum superposition of states with the ball in macroscopically different positions. Thus, despite their seeming fragility, macroscopic superposition states are ubiquitous conse…
We consider environment induced decoherence of quantum superpositions to mixtures in the limit in which that process is much faster than any competing one generated by the Hamiltonian $H_{\rm sys}$ of the isolated system. While the golden rule then does not apply we can discard $H_{\rm sys}$. By allowing for simultaneous couplings to different reservoirs, we reveal decoherence as a universal short-time phenomenon independent of the character of the system as well as the bath and of the basis the superimposed states are taken from. We discuss consequences for the classical behavior of the macro…
We study the behaviour of the Negativity of Wigner Function (NWF) as a measure of entanglement in non-Gaussian states under quantum polarisation converter devices. We analyze comparatively this quantity with other measures of entanglement in a system prepared in a superposition of two-mode coherent states. We show that the (WF) can be identified as a quantifier of non-Gaussian entanglement.
The process of cavity mode quantum state photodetection subject to a nonideal measurement device is under consideration. A set of nonorthogonal probabilistic operator valued measures (POVMs) describing the photodetection process is suggested. The superoperators of conditional system evolution and their Kraus representations are obtained. Developed formalism is used to the quantum state reconstruction problem. We recalculate the probabilities of hypotheses about the initial state of cavity quantum mode in the case of unknown superposition of vacuum and single photon states.
Projective Simulation was introduced as a novel approach to Artificial Intelligence. It involves a deliberation procedure that consists of a random walk on a graph of clips and allows for the learning agent to project itself into the future before committing to an action. Here we study and analyze a quantum mechanical version in which the random walk is performed by two kinds of Hamiltonians. The first kind is implemented by naively embedding the classical model in a quantum model by turning the clips into qubits. The other allows for storing clips in superpositions of qubits allowing for a po…
High fidelity models, which support accurate device characterization and correctly account for environmental effects, are crucial to the engineering of scalable quantum technologies. As it ensures positivity of the density matrix, one preferred model for open systems describes the dynamics with a master equation in Lindblad form. The Linblad operators are rarely derived from first principles, resulting in dynamical models which miss those additional terms that must generally be added to bring the master equation into Lindblad form, together with concomitant other terms that must be assimilated…
We propose a quantum-classical hybrid algorithm of the power method, here dubbed as quantum power method, to evaluate $\hat{\cal H}^n |ψ\rangle$ with quantum computers, where $n$ is a nonnegative integer, $\hat{\cal H}$ is a time-independent Hamiltonian of interest, and $|ψ\rangle$ is a quantum state. We show that the number of gates required for approximating $\hat{\cal H}^n$ scales linearly in the power and the number of qubits, making it a promising application for near term quantum computers. Using numerical simulation, we show that the power method can control systematic errors in approxi…
We show how recent state-reconstruction techniques can be used to determine the Hamiltonian of an optical device that evolves the quantum state of radiation. A simple experimental setup is proposed for measuring the Liouvillian of phase-insensitive devices. The feasibility of the method with current technology is demonstrated on the basis of Monte Carlo simulated experiments.
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…
With the exception of superselection rules, there are no known explicit violations of the Principle of quantum Superposition. However, quantum measurement and the emergence of classicality seem to imply that the Principle of Superposition is not universal, so perhaps new superselection rules or something similar wait to be found. This invites us to search for explicit violations of superposition, even in places where we expect it to hold. Given that many quantum measurement devices rely on atoms absorbing photons, these processes are natural places for a first search for such violations. We pr…
Generation of arbitrary superposition of vacuum and one-photon states using quantum scissors device (QSD) is studied. The device allows the preparation of states by truncating an input coherent light. Optimum values of the intensity of the coherent light for the generation of any desired state using the experimentally feasible QSD scheme are found.
The transition from quantum to classical physics remains an intensely debated question even though it has been investigated for more than a century. Further clarifications could be obtained by preparing macroscopic objects in spatial quantum superpositions and proposals for generating such states for nano-mechanical devices either in a transient or a probabilistic fashion have been put forward. Here we introduce a method to deterministically obtain spatial superpositions of arbitrary lifetime via dissipative state preparation. In our approach, we engineer a double-well potential for the motion…
Analog quantum simulators rely on programmable quantum devices to emulate Hamiltonians describing various physical phenomenon. Photonic coupled cavity arrays are a promising platform for realizing such devices. Using a silicon photonic coupled cavity array made up of 8 high quality-factor resonators and equipped with specially designed thermo-optic island heaters for independent control of cavities, we demonstrate a programmable device implementing tight-binding Hamiltonians with access to the full eigen-energy spectrum. We report a ~50% reduction in the thermal crosstalk between neighboring s…
Aim of this work is to calculate explicitly the result of the experiment of superposition of a mirror in the Michelson photon cavities interferometric device proposed by Marshall, Simon, Penrose and Bownmeester, as expected within a recently proposed model of non-unitary self-gravity inducing localization. As for other proposals of modifications of Quantum Mechanics in a non-unitary sense, aimed to account for both unitary evolution and irreversible collapse, like in the famous Ghirardi-Rimini-Weber and Pearle's models, it turns out that, for the experimental parameters proposed, no effect is …
Analog quantum simulation offers a hardware-specific approach to studying quantum dynamics, but mapping a model Hamiltonian onto the available device parameters requires matching the hardware dynamics. We introduce a paradigm for quantum Hamiltonian simulation that leverages digital decomposition techniques and optimal control to perform analog simulation. We validate this approach by constructing the optimal analog controls for a superconducting transmon device to emulate the dynamics of an extended Bose-Hubbard model. We demonstrate the role of control time, digital error, and pulse complexi…
The geometric phases of the cyclic states of a generalized harmonic oscillator with nonadiabatic time-periodic parameters are discussed in the framework of squeezed state. It is shown that the cyclic and quasicyclic squeezed states correspond to the periodic and quasiperiodic solutions of an effective Hamiltonian defined on an extended phase space, respectively. The geometric phase of the cyclic squeezed state is found to be a phase-space area swept out by a periodic orbit. Furthermore, a class of cyclic states are expressed as a superposition of an infinte number of squeezed states. Their geo…
In this perspective we discuss verification of quantum devices in the context of specific examples, formulated as proposed experiments. Our first example is verification of analog quantum simulators as Hamiltonian learning, where the input Hamiltonian as design goal is compared with the parent Hamiltonian for the quantum states prepared on the device. The second example discusses cross-device verification on the quantum level, i.e. by comparing quantum states prepared on different quantum devices. We focus in particular on protocols using randomized measurements, and we propose establishing a …
