Arbitrary quantum states cannot be copied. In fact, to make a copy we must provide complete information about the system. However, can a quantum system self-replicate? This is not answered by the no-cloning theorem. In the classical context, Von Neumann showed that a `universal constructor' can exist which can self-replicate an arbitrary system, provided that it had access to instructions for making copy of the system. We question the existence of a universal constructor that may allow for the self-replication of an arbitrary quantum system. We prove that there is no deterministic universal quantum constructor which can operate with finite resources. Further, we delineate conditions under which such a universal constructor can be designed to operate dterministically and probabilistically.
The issue of irreversibility in a universe with time-reversal-symmetric laws is a central problem in physics. % , and, in particular, to statistical mechanics, information theory and quantum thermodynamics. In this letter, we discuss for the first time how irreversibility can emerge within the recently proposed constructor theory framework. Here irreversibility is expressed as the requirement that a task is possible, while its inverse is not. In particular, we demonstrate that this irreversibility is compatible with quantum theory's time reversal symmetric laws, by exploiting a specific model,…
We derive and investigate an expression for the dynamically modified decay of states coupled to an arbitrary continuum. This expression is universally valid for weak temporal perturbations. The resulting insights can serve as useful recipes for optimized control of decay and decoherence.
How much time does a tunneling wave packet spent in traversing a barrier? Quantum mechanical calculations result in zero time inside a barrier . In the nineties analogous tunneling experiments with microwaves were carried out. The results agreed with quantum mechanical calculations. Electron tunneling time is hard to measure being extremely short and parasitic effects due to the electric charge of electrons may be dominant. However, quite recently the atomic ionization tunneling time has been measured. Experimental data of photonic, phononic, and electronic tunneling time is available now and …
Quantum entanglement has been actively sought for in optomechanical and electromechanical systems. The simplest such system is a mechanical oscillator interacting with a coherent beam, while the oscillator also suffers from thermal decoherence. For this system, we show that quantum entanglement is always present between the oscillator and continuous outgoing fields -- even when the environmental temperature is high and the oscillator is highly classical. Such universal entanglement is also shown to be able to survive more than one oscillation cycle if characteristic frequency of the optomechan…
Very first time Elzaki transform is used in non relativistic quantum mechanics to solve $N$-dimensional Schrödinger equation in a closed form for different solvable potential models. A universal transformation scheme is introduced and a formula based approach is developed which shows how to apply Elzaki transform to differential equation with non-constant coefficients that generally appear in solving quantum mechanical initial value problems specially for multidimensional Schrödinger equation.
Based on quantum mechanical approach the polarization transport of photons which propagate in a medium with slow varying refractive index is studied. The photon polarizations are separated in opposite directions normal to the ray which is called "Spin Hall effect" of photons, and also the rotation of polarization plane, a manifestation of the Berry phase, occurs. This approach can be generalized to other spinning particles in inhomogeneous media as a universal approach.
On classical phase spaces admitting just one complex-differentiable structure, there is no indeterminacy in the choice of the creation operators that create quanta out of a given vacuum. In these cases the notion of a quantum is universal, i.e., independent of the observer on classical phase space. Such is the case in all standard applications of quantum mechanics. However, recent developments suggest that the notion of a quantum may not be universal. Transformations between observers that do not agree on the notion of an elementary quantum are called dualities. Classical phase spaces admittin…
We summarize the theoretical description of wave packets on molecular energy levels. We review the various quantum mechanical effects which can be studied and the models that can be verified on this system. This justifies our claim that the wave packet constitutes a universal quantum object.
In some of the earliest work on quantum mechanical computers, Feynman showed how to implement universal quantum computation by the dynamics of a time-independent Hamiltonian. I show that this remains possible even if the Hamiltonian is restricted to be a sparse matrix with all entries equal to 0 or 1, i.e., the adjacency matrix of a low-degree graph. Thus quantum walk can be regarded as a universal computational primitive, with any desired quantum computation encoded entirely in some underlying graph. The main idea of the construction is to implement quantum gates by scattering processes.
Universal sensing the motion of mechanical resonators with high precision and low back-action is of paramount importance in ultra-weak signal detection which plays a fundamental role in modern physics. Here we present a universal scheme that transfer mechanically the motion of the resonator not directly measurable to the one can be precisely measured using mechanical frequency conversion. Demonstration of the scheme at room temperature shows that both the motion imprecision and the back-action force are below the intrinsic level of the objective resonator, which agree well with our theoretical…
Quantum algorithms profit from the interference of quantum states in an exponentially large Hilbert space and the fact that unitary transformations on that Hilbert space can be broken down to universal gates that act only on one or two qubits at the same time. The former aspect renders the direct classical simulation of quantum algorithms difficult. Here we introduce higher-order partial derivatives of a probability distribution of particle positions as a new object that shares these basic properties of quantum mechanical states needed for a quantum algorithm. Discretization of the positions a…
We consider opto- and electro-mechanical quantum systems composed of a driven cavity mode interacting with a set of mechanical resonators. It has been proposed that the latter can be initialized in arbitrary cluster states, including universal resource states for Measurement Based Quantum Computation (MBQC). We show that, despite the unavailability in this set-up of direct measurements over the mechanical resonators, computation can still be performed to a high degree of accuracy. In particular, it is possible to indirectly implement the measurements necessary for arbitrary Gaussian MBQC by pr…
Quantum teleportation enables networking participants to move an unknown quantum state between the nodes of a quantum network, and hence constitutes an essential element in constructing large-sale quantum processors with a quantum modular architecture. Herein, we propose two protocols for teleporting qubits through an N-node quantum network in a highly-entangled box-cluster state or chain-type cluster state. The proposed protocols are systematically scalable to an arbitrary finite number N and applicable to arbitrary size of modules. The protocol based on a box-cluster state is implemented on …
We present a quantum-mechanical generalization of the work penalty equation (Eq. (6) in Phys. Rev. Lett., 127, 190602 (2021)) with an alternative derivation.
In this work we define an universal arithmetical algorithm, by means of the standard quantum mechanical formalism, called universal qm-arithmetical algorithm. By universal qm-arithmetical algorithm any decidable arithmetical formula (operation) can be decided (realized, calculated. Arithmetic defined by universal qm-arithmetical algorithm called qm-arithmetic one-to-one corresponds to decidable part of the usual arithmetic. We prove that in the qm-arithmetic the undecidable arithmetical formulas (operations) cannot exist (cannot be consistently defined). Or, we prove that qm-arithmetic has no …
We propose to realize effective beam-splitter-like and two-mode-squeezing photon-photon interactions in a strong coupling optomechanical interface by exploiting detuned driving lasers. In this interface, the transitions between the optical system and the mechanical oscillator are suppressed by the large energy offsets, therefore protecting the photon-photon interactions from mechanical dissipations. Moreover, the destructive quantum interference between the eigenmodes of the interface is capable of further reducing the effects of initial mechanical thermal occupations. The interface can serve …
If the unitary quantum mechanical state evolution is universally valid, quantized systems evolve uniformly, deterministically, and reversible; that is, one-to-one. Hence, what is considered an irreversible measurement might be a purely subjective, conventional, and convenient abstraction of the situation that, although in principal totally reversible, for all practical purposes (fapp), measurements cannot be undone. If this is granted, then Schroedinger's "quantum jellification" arises because of the inevitability of the physical co-existence of classically mutually exclusive states through qu…
Quantum walks are the quantum-mechanical analog of random walks, in which a quantum `walker' evolves between initial and final states by traversing the edges of a graph, either in discrete steps from node to node or via continuous evolution under the Hamiltonian furnished by the adjacency matrix of the graph. We present a hybrid scheme for universal quantum computation in which a quantum walker takes discrete steps of continuous evolution. This `discontinuous' quantum walk employs perfect quantum state transfer between two nodes of specific subgraphs chosen to implement a universal gate set, t…
Processing quantum information on continuous variables requires a highly nonlinear element in order to attain universality. Noise reduction in processing such quantum information involves the use of a nonlinear phase state as a non-Gaussian ancilla. A necessary condition for a nonlinear phase state to implement a nonlinear phase gate is that noise in a selected nonlinear quadrature should decrease below the level of classical states. A reduction of the variance in this nonlinear quadrature below the ground state of the ancilla, a type of nonlinear squeezing, is the resource embedded in these n…
Mechanical trisqueezing in circuit quantum acoustodynamics with SNAIL devices
Institute of Physics, Chinese Academy of Science（中国科学院物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Department of Physics, ETH Zürich（苏黎世联邦理工学院物理系）
Universal quantum computation encoded over continuous variables can be achieved via Gaussian measurements acting on entangled non-Gaussian states. However, due to the weakness of available nonlinearities, generally these states can only be prepared conditionally, potentially with low probability. Here we show how universal quantum computation could be implemented unconditionally using an integrated platform able to sustain both linear and quadratic optomechanical-like interactions. Specifically, considering cavity opto- and electro-mechanical systems, we propose a realisation of a driven-dissi…
It has recently been shown that a parametrically driven oscillator with Kerr nonlinearity yields a Schrödinger cat state via quantum adiabatic evolution through its bifurcation point and a network of such nonlinear oscillators can be used for solving combinatorial optimization problems by bifurcation-based adiabatic quantum computation [H. Goto, Sci. Rep. \textbf{6}, 21686 (2016)]. Here we theoretically show that such a nonlinear oscillator network with controllable parameters can also be used for universal quantum computation. The initialization is achieved by a quantum-mechanical bifurcation…
We report on the utility of using Shannons Sampling theorem to solve Quantum Mechanical systems. We show that by extending the logic of Shannons interpolation theorem we can define a Universal Lattice Basis, which has superior interpolating properties compared to traditional methods. This basis is orthonormal, semi-local, has a Euclidean norm, and a simple analytic expression for the derivatives. Additionally, we can define a bounded domain for which band-limited functions, such as Gaussians, show quadratic convergence in the representation error in respect to the sampling frequency. This theo…
Conservation laws are discussed in conjunction with quantum-mechanical indeterminacies of the corresponding observables. The considered examples show that the connections between energy and its indeterminacy may be quite intricate. The indeterminacies of the parts of a composite system may be correlated in such a way that the net value of the considered observable is definite. This may be the case with specific entangled superposition of eigenstates in a composite system. In some cases the fact of energy conservation cannot be convincingly established and generally the concept of conserving ob…
Can quantum-mechanical particles propagating on a fixed spacetime background be approximated as test bodies satisfying the weak equivalence principle? We ultimately answer the question in the negative but find that, when universality of free-fall is assessed locally, a nontrivial agreement between quantum mechanics and the weak equivalence principle exists. Implications for mass sensing by quantum probes are discussed in some details.
Epistemological consequences of quantum nonlocality (entanglement) are discussed under the assumption of a universally valid Schrödinger equation in the absence of hidden variables. This leads inevitably to a {\it many-minds interpretation}. The recent foundation of quasi-classical neural states in the brain (based on environmental decoherence) permits in principle a formal description of the whole chain of measurement interactions, including the {\it behavior} of conscious observers, without introducing any intermediate classical concepts (for macroscopic "pointer states") or "observables" (f…
We propose a solid-state hybrid platform based on an array of implanted nitrogen-vacancy (NV) centers in diamond magnetically coupled to a mechanical oscillator. The mechanical oscillator and the NV electronic spins both act as a quantum bus and allow us to induce an effective long-range interaction between distant nuclear spins, relaxing the requirements on their spatial distance. The coherent nuclear spin-spin interaction, having the form of an Ising model, can be maintained in the presence of mechanical damping and spin dephasing via a pulsed dynamical decoupling of the nuclear spins in add…
We propose a scheme for entangling the motion of two massive objects in a hybrid electromechanical architecture. The entanglement is generated due to the interaction of two mechanical oscillators with a mediating superconducting qubit. We show that the generated macroscopic entangled states are non-Gaussian and its lifetime is limited by coherence time of the qubit. The entanglement is attainable in a wide range of parameters with appropriate control of the qubit. We confirm performance of our scheme by numerically solving the quantum optical master equation including sources of noise. The eff…
The circumstances under which a system reaches thermal equilibrium, and how to derive this from basic dynamical laws, has been a major question from the very beginning of thermodynamics and statistical mechanics. Despite considerable progress, it remains an open problem. Motivated by this issue, we address the more general question of equilibration. We prove, with virtually full generality, that reaching equilibrium is a universal property of quantum systems: Almost any subsystem in interaction with a large enough bath will reach an equilibrium state and remain close to it for almost all times…
We measure the propagator length in imaginary time quantum mechanics by Monte Carlo simulation on a lattice and extract the Hausdorff dimension $d_{H}$. We find that all local potentials fall into the same universality class giving $d_{H}=2$ like the free motion. A velocity dependent action ($S \propto \int dt \mid \vec{v} \mid^α$) in the path integral (e.g. electrons moving in solids, or Brueckner's theory of nuclear matter) yields $d_{H}=\frac{α}{α- 1}$ if $α> 2$ and $d_{H}=2$ if $α\leq 2$. We discuss the relevance of fractal pathes in solid state physics and in $QFT$, in particular for the …
In their work [J. Phys. A: Math. Gen. 33, 4427 (2000)], Bender, Brody, and Meister have shown by employing a two-state model of a particle confined in the one-dimensional infinite potential well that it is possible to construct a quantum-mechanical analog of the Carnot engine through the changes of both the width of the well and the quantum state in a specific manner. Here, a discussion is developed about realizing the maximum power of such an engine, where the width of the well moves at low but finite speed. The efficiency of the engine at the maximum power output is found to be universal ind…
We propose a universal, on-chip quantum transducer based on surface acoustic waves in piezo-active materials. Because of the intrinsic piezoelectric (and/or magnetostrictive) properties of the material, our approach provides a universal platform capable of coherently linking a broad array of qubits, including quantum dots, trapped ions, nitrogen-vacancy centers or superconducting qubits. The quantized modes of surface acoustic waves lie in the gigahertz range, can be strongly confined close to the surface in phononic cavities and guided in acoustic waveguides. We show that this type of surface…
We find that the overlapping of a topological quantum color code state, representing a quantum memory, with a factorized state of qubits can be written as the partition function of a 3-body classical Ising model on triangular or Union Jack lattices. This mapping allows us to test that different computational capabilities of color codes correspond to qualitatively different universality classes of their associated classical spin models. By generalizing these statistical mechanical models for arbitrary inhomogeneous and complex couplings, it is possible to study a measurement-based quantum compu…
Highly complex novel critical behavior from the intrinsic randomness of quantum mechanical measurements on critical ground states -- a controlled renormalization group analysis
A positive definite symmetric matrix σ qualifies as a quantum mechanical covariance matrix if and only if σ+(1/2)i\hbarΩ\geq0 where Ω is the standard symplectic matrix. This well-known condition is a strong version of the uncertainty principle, which can be reinterpreted in terms of the topological notion of symplectic capacity, closely related to Gromov's non-squeezing theorem. We show that a recent refinement of the latter leads to a new class of geometric invariants. These are the volumes of the orthogonal projections of the covariance ellipsoid on symplectic subspaces of the phase space. W…
