In this paper, we are interested in detecting the presence of a nearby phase-sensitive object, where traveling light works out under a low-photon loss rate. Here we investigate the optimal quantum phase estimation with generalized multi-component Schrodinger cat states. In addition, we show the optimal conditions of the generalized multi-component cat states for the phase estimation in a lossless scenario. We then demonstrate that the generalized multi-component cat states can beat the performances of the NOON and two-mode squeezed vacuum states in the presence of small loss, while maintaining the quantum advantage over the standard quantum limit, attainable by coherent states. Finally, we propose a generation scheme of the entangled multi-component cat states with current or near-term optical technologies.
We investigate complex PT and non-PT-symmetric forms of the generalized Woods- Saxon potential. We also look for exact solutions of the Schrodinger equation for the PT and/or non-PT-symmetric potentials of the kind mentioned above. Nikiforov-Uvarov method is used to obtain their energy eigenvalues and associated eigenfunctions.
We show in this paper that the basic representations of position and momentum in a quantum mechanical system, that are guided by a generalized uncertainty principle and lead to a corresponding one-parameter eigenvalue problem, can be interpreted in terms of an extended Schrodinger equation embodying momentum-dependent mass. Some simple consequences are pointed out.
The derivation of the Schrödinger-like equations from the system of equations of the quantum hydrodynamic analogy (QHA) is analyzed in presence of fluctuations. If in absence of fluctuation each QHA solution can be tracked back to the equivalent one of the Schrödinger problem, in presence of fluctuations the work shows that the ensemble of solution of the QHA equations is wider than the Schrödinger one and the tracking-back procedure from the QHA problem to the original Schrödinger equation is not generally possible. The break-down of the mathematical correspondence is inspected and correlated…
In this work, we derive a generalization of the so-called Schrödinger-Langevin or Kostin equation for a Brownian particle interacting with a heat bath. This generalization is based on a nonlinear interaction model providing a state-dependent dissipation process exhibiting multiplicative noise. Two straightforward applications to the measurement process are then analyzed, continuous and weak measurements in terms of the quantum Bohmian trajectory formalism. Finally, it is also shown that the generalized uncertainty principle, which appears in some approaches to quantum gravity, can be expressed…
The Darboux transformation operator technique in differential and integral forms is applied to the generalized Schrodinger equation with a position-dependent effective mass and with linearly energy-dependent potentials. Intertwining operators are obtained in an explicit form and used for constructing generalized Darboux transformations of an arbitrary order. A relation between supersymmetry and the generalized Darboux transformation is considered. The method is applied to generation of isospectral potentials with additional or removal bound states or construction of new partner potentials with…
We extensively discuss how Schrodinger cat states (superpositions of well-separated coherent states) in optical systems can be used for quantum information processing.
We analyze condition of orthogonality between optical Schrodinger cat-like-states constructed as superposition of two coherent states. We show that the orthogonality condition leads to quantization of values of a naturally emerging symplectic form, while values of the corresponding metric form are continuous. A complete analytical solution of the problem is presented.
Macroscopic objects appear to have definite positions. In a many-worlds interpretation of quantum theory, this appearance is an illusion; the correct view is the "view from outside" in which even macroscopic objects are in general in a superposition of different positions. In the Bohm model, objects really are in definite positions. This additional aspect of reality is accessible only from the "inside"; thus in the Bohm model the view from inside can be more correct than is the view from outside.
The purpose of this manuscript is to provide a short pedagogical explanation why "quantum collapse" is not a metaphysical event, by pointing out the analogy with a "classical collapse" which is associated with the Monty Hall Paradox.
We propose a scheme to engineer Schrödinger-cat states of propagating optical pulses. Multi-dimensional and multi-partite cat states can be generated simply by reflecting coherent optical pulses successively from a single-atom cavity. The influences of various sources of noise, including the atomic spontaneous emission and the pulse shape distortion, are characterized through detailed numerical simulation, which demonstrates practicality of this scheme within the reach of current experimental technology.
Pseudopure "cat" state, a superposition of quantum states with all spins up and all spins down, is experimentally demonstrated for a system of twelve dipolar-coupled nuclear spins of fully 13C-labeled benzene molecule oriented in a liquid-crystalline matrix.
From the following thought experiments, it is demonstrated that the collapse of wave function of an isolated system is possible without external observer. It will be shown that the analysis by Feynman path integral method supports this conclusion. The argument is based on two assumptions: 1. The condition of Schrodinger's cat experiment 2. Feynman path integral; This could explain Schrodinger's cat paradox and its implication on the black hole information paradox will be discussed.
In addition to being a very interesting quantum phenomenon, Schrödinger cat swapping has the potential for application in the preparation of quantum states that could be used in metrology and other quantum processing. We study in detail the effects of field decoherence on a cat-swapping system comprising a set of identical qubits, or spins, all coupled to a field mode. We demonstrate that increasing the number of spins actually mitigates the effects of field decoherence on the collapse and revival of a spin Schrödinger cat, which could be of significant utility in quantum metrology and other q…
Schrödinger cat states, consisting of superpositions of macroscopically distinct states, provide key resources for a large number of emerging quantum technologies in quantum information processing. Here we propose how to generate and manipulate mechanical and optical Schrödinger cat states with distinguishable superposition components by exploiting the unique properties of cavity optomechanical systems based on Bose-Einstein condensate. Specifically, we show that in comparison with its solid-state counterparts, almost a $3$ order of magnitude enhancement in the size of the mechanical Schröding…
The Wehrl information entropy and its phase density, the so-called Wehrl phase distribution, are applied to describe Schrödinger cat and cat-like (kitten) states. The advantages of the Wehrl phase distribution over the Wehrl entropy in a description of the superposition principle are presented. The entropic measures are compared with a conventional phase distribution from the Husimi Q-function. Compact-form formulae for the entropic measures are found for superpositions of well-separated states. Examples of Schrödinger cats (including even, odd and Yurke-Stoler coherent states), as well as the…
Schrodinger's famous cat has long been misunderstood. According to quantum theory and experiments with entangled systems, an entangled state such as the Schrodinger's cat state is neither a superposition of states of either subsystem nor a superposition of compound states of the composite system, but rather a nonlocal superposition of correlations between pairs of states of the two subsystems. The entangled post-measurement state that results from an ideal measurement is not paradoxical, but is merely a coherent superposition of two statistical correlations at "zero phase angle," i.e. at 100% …
The marginal distribution of squeezed, rotated and shifted quadrature for two types of nonclassical states of a trapped ion - squeezed correlated states and squeezed even and odd coherent states (squeezed Schrodinger cat states) - is studied.
We carry out probabilistic phase-space sampling of mesoscopic Schrödinger cat quantum states, demonstrating multipartite Bell violations for up to 60 qubits. We use states similar to those generated in photonic and ion-trap experiments. These results show that mesoscopic quantum superpositions are directly accessible to probabilistic sampling, and we analyze the properties of sampling errors. We also demonstrate dynamical simulation of super-decoherence in ion traps. Our computer simulations can be either exponentially faster or slower than experiment, depending on the correlations measured.
We propose a method to generate an optical Schrödinger-cat-like state in a cavity in a substantial decoherence regime. Even when the cavity decay rate is considerably large, a cat-like state can be generated in a laser-like setting if the gain for the field is larger than the loss. Under the condition that opposite-phase atomic dipoles repeatedly traverse the cavity, the cavity field converges to a squeezed vacuum state in a steady state. A Schrödinger-cat-like state is then generated when a single photon decay occurs. The phase-space distribution of the cat state can be revealed in homodyne d…
The recent experiment on superconducting quantum interference device provides new opportunity to clarify the fundamental interpretation of quantum mechanics. After analyzing this and relevant experiments, we claim the point of view that the quantum state in abstract sense contains no information and the wave function is the probability amplitude of fictitious measurement corresponding to the real one which is prepared to be done by the observer. Talking about the quantum state or wave function too materialized in ordinary language would often cause misunderstanding. So basically, the Schröding…
In recent years, there has been an increased interest in the generation of superposition of coherent states with opposite phases, the so-called photonic Schrodinger-cat states. These experiments are very challenging and so far, cats involving small photon numbers only have been implemented. Here, we propose to consider two-mode squeezed states as examples of a Schrodinger-cat-like state. In particular, we are interested in several criteria aiming to identify quantum states that are macroscopic superpositions in a more general sense. We show how these criteria can be extended to continuous vari…
Investigated idea was actuated by the old opinion that a measurement of a quantum observable should be regarded a as a single deterministic sampling. But, according to the last decades studies, such observables are veritable random variables and their measurements must imply significant sets of statistical samplings. So one finds the indubitable caducity of the approached idea. Contiguously the respective finding allows to put into a new light the controversial questions like the Schrodinger's cat thought experiment or description of quantum measurements.
Quantum effects and, in particular, entanglement are by now widely recognized in all areas of physics and related fields. However, we feel that the precise notion of entanglement---though mathematically well-defined---still generates confusion even in the academic environment. Our aim in this article is to point out and clarify some aspects of the notion of entanglement, in particular with respect to observable quantities. We do this by illustrating common misconceptions with Schrödinger's cat paradox, explain them in mathematical terms and provide examples where misunderstandings arise and ho…
Inspired by the generalized uncertainty principle (GUP), which adds gravitational effects to the standard description of quantum uncertainty, we extend the exact uncertainty principle (EUP) approach by Hall and Reginatto [J. Phys. A: Math. Gen. (2002) 35 3289], and obtain a (quasi)nonlinear Schrödinger equation. This quantum evolution equation of unusual form, enjoys several desired properties like separation of non-interacting subsystems or planewave solutions for free particles. Starting with the harmonic oscillator example, we show that every solution of this equation respects the gravitati…
We discuss general properties of the equilibrium state of parametric down-conversion in superconducting quantum circuits with detunings and Kerr anharmonicities, in the strongly nonlinear regime. By comparing moments of the steady state and those of a Schrödinger cat, we show that true Schrödinger cats cannot survive in the steady state if there is any single-photon loss. A delta-function 'cat-like' steady-state distribution can be formed, but this only exists in the limit of an extremely large nonlinearity. The steady state is a mixed state, which is more complex than a mixture or linear comb…
Homodyne measurements are a widely used quantum measurement. Using a coherent state of large amplitude as the local oscillator, it can be shown that the quantum homodyne measurement limits to a field quadrature measurement. In this work, we give an example of a general idea: injecting non-classical states as a local oscillator can led to non-classical measurements. Specifically we consider injecting a superposition of coherent states, a Schrödinger cat state, as a local oscillator. We derive the Kraus operators and the positive operator-valued measure (POVM) in this situation.
Motivated by recent experiments, we consider a Schrödinger cat superposition of two widely separated coherent states in thermal equilibrium. The time development of our system is obtained using Wigner distribution functions. In contrast to our discussion for a two-Gaussian wave packet [Phys. Lett. A 286 (2001) 87], we find that, in the absence of dissipation, the interference term does not decay rapidly in time, but in common with the other two terms, it oscillates in time and persists for all times
Schrödinger's cat originates from the famous thought experiment querying the counterintuitive quantum superposition of macroscopic objects. As a natural extension, several "cats" (quasi-classical objects) can be prepared into coherent quantum superposition states, which is known as multipartite cat states demonstrating quantum entanglement among macroscopically distinct objects. Here we present a highly scalable approach to deterministically create flying multipartite Schrödinger cat states, by reflecting coherent state photons from a microwave cavity containing a superconducting qubit. We per…
We give a mathematical procedure to obtain the adiabatic approximation for the generalized quantum Rabi Hamiltonian both without and with a quadratic interaction. We consider the Hamiltonian as the energy of a model describing the interaction system of a two-level artificial atom and a one-mode microwave photon in circuit QED. In the case without the quadratic interaction, we show in the adiabatic approximation that whether each bare eigenstate forms a Schrodinger-cat-like entangled state or not depends on whether the energy bias of the atom is zero or non-zero, and then, the effect of the tun…
We study the entanglement between a certain qubit and the remaining system in the Schrödinger cat state prepared on the ibmq-melbourne quantum computer. The protocol, which we use for this purpose, is based on the determination of the mean value of spin corresponding to a certain qubit. We explore the dependence of the entanglement on a parameter of the Schrödinger cat state which consists of different numbers of qubits. In addition, we explore the entanglement of each qubit with the remaining system in the maximum entangled Schrödinger cat state.
The bound state energy eigenvalues and the corresponding eigenfunctions of the generalized Woods-Saxon potential reported in [Phys. Rev. C 72, 027001 (2005)] is extended to the fractional forms using the generalized fractional derivative and the fractional Nikiforov-Uvarov (NU) technique. Analytical solutions of bound states of the Schrodinger equation for the present potential are obtained in the terms of fractional Jacobi polynomials. It is demonstrated that the classical results are a special case of the present results at Elfa=Beta=1 Therefore, the present results play important role in mo…
Erwin Schrödinger is famous for presenting his wave equation of motion that jump-started quantum mechanics. His disenchantment with the Copenhagen interpretation of quantum mechanics led him to unveil the Schrödinger's cat paradox, which did not get much attention for nearly half a century. In the meantime, disappointment with quantum mechanics turned his interest to biology facilitating, albeit in a peripheral way, the revelation of the structure of DNA. Interest in Schrödinger's cat has recently come roaring back making its appearance conspicuously in numerous scientific articles. From the a…
Schrödinger's cat is one of the most striking paradoxes of quantum mechanics that reveals the counterintuitive aspects of the microscopic world. Here, I discuss the paradox in the framework of quantum information. Using a quantum networks formalism, I analyse the information flow between the atom and the cat. This reveals that the atom and the cat are connected only through a classical information channel: the detector clicks $\rightarrow$ the poison is released $\rightarrow$ the cat is killed. No amount of local operations and classical communication can entangle the atom and the cat, which a…
We demonstrate that superpositions of coherent and displaced Fock states, also referred to as generalized Schrödinger cats cats, can be created by application of a nonlinear displacement operator which is a deformed version of the Glauber displacement operator. Consequently, such generalized cat states can be formally considered as nonlinear coherent states. We then show that Glauber-Fock photonic lattices endowed with alternating positive and negative coupling coefficients give rise to classical analogs of such cat states. In addition, it is pointed out that the analytic propagator of these d…
The most discussed of ``live'' metaphors in physical sciences is that of the Schrödinger cat. Introduced in the early, but mature days of the new quantum theory, in 1935, the parable of the cat has provoked and enlivened debates on the meaning of the quantum theory, on the ontology of the quantum wavefunction, on the puzzle of the collapse of the wavefunction, on the meaning of quantum measurement, and on the boundary between the quantum world and the classical world. In this article, I will discuss these issues of the quantum theory focussing on various aspects of the metaphor of the Schrödin…
In this article, the following results are obtained: the process of a randomly wandering particle having a size and a continuous trajectory of motion is considered; (b) based on the study of this probabilistic process, a derivation of the Schrodinger equation is proposed; the Planck constant h is expressed in terms of the characteristics of the stationary stochastic process under consideration; the probability distribution density of the n-order derivative for a n-times differentiable stationary stochastic process is determined; it is shown that the obtained generalized Schrodinger equation is…
The question whether quantum mechanics is complete and the nature of the transition between quantum mechanics and classical mechanics have intrigued physicists for decades. There have been many experimental breakthroughs in creating larger and larger quantum superposition and entangled states since Erwin Schrödinger proposed his famous thought experiment of putting a cat in a superposition of both alive and dead states in 1935. Remarkably, recent developments in quantum optomechanics and electromechanics may lead to the realization of quantum superposition of living microbes soon. Recent evide…
We propose to use Bloch oscillation of ultra-cold atoms in a spin-dependent optical lattice to prepare schrodinger cat states. Depending on its internal state, an atom feels different periodic potentials and thus has different energy band structures for its center-of-mass motion. Consequently, under the same gravity force, the wave packets associated with different internal states perform Bloch oscillation of different amplitudes in space and in particular they can be macroscopically displaced with respect to each other. In this way, a cat state can be prepared.
Disentanglement and loss of quantum correlations due to one global collective noise effect are described for two-qubit Schrödinger cat and Werner states of a four level trapped ion quantum system. Once the Jaynes-Cummings ionic interactions are mapped onto a Dirac spinor structure, the elementary tools for computing quantum correlations of two-qubit ionic states are provided. With two-qubit quantum numbers related to the total angular momentum and to its projection onto the direction of an external magnetic field (which lifts the degeneracy of the ion's internal levels), a complete analytical …
We propose a scheme for generating the Schrödinger cat state based on geometric operations by a nanomechanical resonator coupled to a superconducting charge qubit. The charge qubit, driven by two strong classical fields, interacts with a high-frequency phonon mode of the nanomechanical resonator. During the operation, the charge qubit undergoes no real transitions, while the phonon mode of the nanomechanical resonator is displaced along different paths in the phase space, dependent on the states of the charge qubit, which yields the Schrödinger cat state. The robustness of the scheme is justif…
We present a quantum algorithm which allows to simulate chaos-assisted tunneling in deep semiclassical regime on existing quantum computers. This opens new possibilities for investigation of macroscopic quantum tunneling and realization of semiclassical Schrödinger cat oscillations. Our numerical studies determine the decoherence rate induced by noisy gates for these oscillations and propose a suitable parameter regime for their experimental implementation.
We show on the example of the Arnold cat map that classical chaotic systems can be simulated with exponential efficiency on a quantum computer. Although classical computer errors grow exponentially with time, the quantum algorithm with moderate imperfections is able to simulate accurately the unstable chaotic classical dynamics for long times. The algorithm can be easily implemented on systems of a few qubits.
