Although quantum mechanics is a mature theory, fundamental problems discussed during its time of foundation have remained with us to this day. These problems are centered on the problematic relation between the quantum and classical worlds. The most famous element is the measurement problem, i.e., the measurement of a quantum system by a classical apparatus, and the concomitant phenomena of wave packet reduction, the appearance of probability, and the problems related to Schrödinger cat states. A fundamental question in this context is whether quantum mechanics can bootstrap itself to the classical world: is quantum mechanics self-consistent, such that the measurement process can be understood within quantum mechanics itself, or does this process require additional elements from the realm outside of traditional quantum mechanics? Here, we point to a problematic aspect in the traditional Schrödinger cat argument which can be overcome through its extension with a proper macroscopic preparation device; the deliberate creation of a cat state and its identification then turns into a non-trivial problem requiring the determination of the evolution of a quantum system entangled with a macroscopic reservoir. We describe a new type of wave-function correlator testing for the appearance of Schrödinger cat states and discuss its implications for theories deriving the wave function collapse from a unitary evolution.
We know that the original Schrödinger cat states has no amplitude-squared squeezing. In this paper, we investigate the amplitude-squared squeezing of Schrödinger cat states using postselected von Neumann measurement. The results show that after postselected von Neumann measurement, the amplitude-squared squeezing of Schrödinger cat states change dramatically and this can be considered a result of weak value amplification. The squeezing effect also investigated by studying the Wigner function of Schrödinger cat states after postselected measurement.
Schrödinger's cat puzzle is resolved. The reason why we do not see a macroscopic superposition of states is cleared in the light of Everett's formulation of quantum mechanics.
The Schrödinger cat male and female states are discussed. The Wigner and Q--functions of generalized correlated light are given. Linear transformator of photon statistics is reviewed.
We extensively discuss how Schrodinger cat states (superpositions of well-separated coherent states) in optical systems can be used for quantum information processing.
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.
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.
A scheme for preparing Schrödinger cat (SC) states is proposed beyond the Lamb-Dicke limit in a Raman-$Λ$-type configuration. It is shown that SC states can be obtained more efficiently with our scheme than with the former ones.
The replica method for calculating the von Neumann entropy is reviewed. Explicit expression for the entropy of the mixed coherent states $|α>$ and $|β>$ is obtained using this method. The purity inequality for bipartite system for separable states is studied on example of even and odd Schrödinger cat state.
We propose a postselecting parity-swap amplifier for Schrödinger cat states that does not require the amplified state to be known a priori. The device is based on a previously-implemented state comparison amplifier for coherent states. It consumes only Gaussian resource states, which provides an advantage over some cat state amplifiers. It requires simple Geiger-mode photodetectors and works with high fidelity and approximately twofold gain.
Particle distributions in squeezed states, even and odd coherent states are given in terms of multivariable Hermite polynomials. The Q--function and Wigner function for nonclassical field states are discussed.
We proposed and analyzed a scheme to generate large-size Schrödinger cat states based on linear operations of Fock states and squeezed vacuum states and conditional measurements. By conducting conditional measurements via photon number detectors, two unbalanced Schrödinger kitten states combined by a beam splitter can be amplified to a large-size cat state with the same parity. According to simulation results, two Schrödinger odd kitten states of $β=1.06$ and $β=1.11$ generated from one-photon-subtracted squeezed vacuum states of $-$3 dB, are amplified to an odd cat state of $β=1.73$ with a fi…
We show, in the context of quantum combinatorial optimization, or quantum annealing, how the nonlinear Schrödinger-Langevin-Kostin equation can dynamically drive the system toward its ground state. We illustrate, moreover, how a frictional force of Kostin type can prevent the appearance of genuinely quantum problems such as Bloch oscillations and Anderson localization which would hinder an exhaustive search.
Modeling the Schrödinger cat by a two state system and assuming that the cat is coupled to the environment we look for the least paradoxical states of the Schrödinger cat in the following way. We require the reduced density matrix of the cat for one of the two states in the superposition to be the same as the one for the total state while distinct from the reduced density matrix of the cat for the other state in the superposition. We then look for the reduced density matrices for which the cat is as alive as possible for the first state (and as dead as possible for the second state). The resul…
We present what is to our knowledge the first implementation of a Schrödinger cat states "breeding" operation, which allows an iterative growth of these states. We thus report the experimental generation of a squeezed Schrödinger cat state from two single photon Fock states, which can be seen as cat states with zero amplitude. These Fock states are mixed on a symmetrical beamsplitter and the generation is heralded by a homodyne measurement in one of the two output arms. The output state has a fidelity of 61% with an even squeezed Schrödinger cat state of amplitude $α=1.63$. This hybrid operati…
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.
The manuscript investigates the entropy squeezing of a qubit (two-level atom) interacting with the cavity field in the Schrödinger cat states. The effects of the Schrödinger cat states of the field on the squeezing are examined. Our results suggest that entropy squeezing is not sensitive to the superposition features of two coherent states of the Schrödinger cat states. Furthermore, it is found that entropy squeezing occurs as the qubit initially close to its maximally coherent state, and the qubit initially in the maximally coherent state can generate optimal squeezing. This also demonstrates…
We study the dephasing of a single qubit coupled to a bosonic bath. In particular, we investigate the case when the bath is initially prepared in a pure state known as the Schrödinger cat. In clear contradistinction to the time-evolution of an initial coherent state, the time evolutions of the purity and the coherence factor now depend on the particular choice of the Schrödinger cat state. We also demonstrate that the evolution of the entanglement of a two--qubit system depends on the initial conditions in a similar way.
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.
Though scientifically unconvincing, the Broglie-Bohm model has the virtue of reproducing the observational predictions of quantum mechanics while being conceptually crystal-clear. Hence, even if we do not believe in it, we may find it useful in suggesting ways of removing conceptual difficulties. This procedure is here applied to the Schrödinger cat riddle (in its Wigner version). The outcome yields tentative views on the relationship between mentality and physical reality.
Overcomplete families of states of the type of Barut-Girardello coherent states (BG CS) are constructed for noncompact algebras $u(p,q)$ and $sp(N,C)$ in quadratic bosonic representation. The $sp(N,C)$ BG CS are obtained in the form of multimode ordinary Schrödinger cat states. A set of such macroscopic superpositions is pointed out which is overcomplete in the whole $N$ mode Hilbert space (while the associated $sp(N,C)$ representation is reducible). The multimode squared amplitude Schrödinger cat states are introduced as macroscopic superpositions of the obtained $sp(N,C)$ BG CS.}
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…
We propose a scheme to prepare optical Schrödinger-cat states in a traveling wave setting. Two states are similarly prepared via the self-Kerr effect and after mixing them, one mode is measured by homodyne detection. In the other mode a superposition of coherent states is conditionally prepared. The advantage of the scheme is that assuming a small Kerr effect one can prepare with high probability one from a set of Schrödinger-cat states. The measured value of the quadrature provides the information, which state from the set is actually prepared.
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…
Deep in the ultrastrong light-matter coupling regime, it has been predicted that the ground state of a two-level atom interacting with a cavity mode takes the form of a "virtual" Schrödinger cat entangled state between light and matter. We propose a method to convert this Schrödinger cat state from virtual to real, and back again, by driving the atom with optimally chosen pulses. Our system consists of a four-level atom, with two of these levels ultrastrongly coupled to a cavity mode. We show that the Schrödinger cat state can be converted between virtual and real by making use of either an id…
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…
Until now, Schrödinger's cat states are generated by subtracting single photons from the whole bandwidth of squeezed vacua. However, it was pointed out recently that the achievable purities are limited in such method (J. Yoshikawa, W. Asavanant, and A. Furusawa, arXiv:1707.08146 [quant-ph] (2017)). In this paper, we used our new photon subtraction method with a narrowband filtering cavity and generated a highly pure Schrödinger's cat state with the value of $-0.184$ at the origin of the Wigner function. To our knowledge, this is the highest value ever reported without any loss corrections. The…
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.
Taking the decoherence into account, we investigate nonclassical features of the optical Schrödinger cat states in one mode and two coupled-modes systems with two-photon driving. In the one mode system, the relationship between the Schrödinger cat states and the system parameters is derived. We observe that in the presence of single-photon decay the steady states would be a mixture of Schrödinger cats. The dynamics and steady states of such a cat versus single-photon decay are examined. In the two coupled-modes cases with linear and nonlinear couplings, the dynamics of entanglement and mutual …
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…
Preparation of Schrödinger-cat-like states via conditional output measurement on a beam splitter is studied. In the scheme, a mode prepared in a squeezed vacuum is mixed with a mode prepared in a Fock state and photocounting is performed in one of the output channels of the beam splitter. In this way the mode in the other output channel is prepared in a Schrödinger-cat-like state that is either a photon-subtracted or a photon-added Jacobi polynomial squeezed vacuum state, depending upon the difference between the number of photons in the input Fock state and the number of photons in the output…
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
This report experimentally demonstrates that the theoretical background of the atom-field scenario points out that the NMR quadrupolar Hamiltonian works as an effective Hamiltonian to generate Schrödinger's cat states in a $2I+1$ low dimensional Hilbert space. The versatility of this nuclear spin setup is verified by monitoring the $^{23}$Na nucleus of a lyotropic liquid crystal sample at the nematic phase. The quantum state tomography and the Wigner quasiprobability distribution function are performed to characterize the accuracy of the experimental implementation.
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 study the effects of continuous measurement of the field mode during the collapse and revival of spin Schrödinger cat states in the Tavis-Cummings model of N qubits (two-level quantum systems) coupled to a field mode. We show that a compromise between relatively weak and relatively strong continuous measurement will not completely destroy the collapse and revival dynamics while still providing enough signal-to-noise resolution to identify the signatures of the process in the measurement record. This type of measurement would in principle allow the verification of the occurrence of the colla…
Quantum superpositions of distinct coherent states in a single-mode harmonic oscillator, known as "cat states", have been an elegant demonstration of Schrodinger's famous cat paradox. Here, we realize a two-mode cat state of electromagnetic fields in two microwave cavities bridged by a superconducting artificial atom, which can also be viewed as an entangled pair of single-cavity cat states. We present full quantum state tomography of this complex cat state over a Hilbert space exceeding 100 dimensions via quantum non-demolition measurements of the joint photon number parity. The ability to ma…
In a previous paper we examined the role of a conscious observer in a typical quantum mechanical measurement. Four rules were given that were found to govern the stochastic choice and state reduction in several cases of continuous and intermittent observation. It was shown that consciousness always accompanies a state reduction leading to observation, but its presence is not sufficient to 'cause' a reduction. The distinction is clarified and codified by the rules that are repeated below. In this paper, these rules are successfully applied to two different versions of the Schrodinger cat experi…
The Schrödinger cat state plays a crucial role in quantum theory, and has important fundamental as well as technological implications, ranging from quantum measurement theory to quantum computers. The power of the potential implications of the cat state lies in the quantum coherence, as measured by the degree of entanglement, between its microscopic and macroscopic sectors. We show that in contrast to other cat states, it is possible to choose the states of the macroscopic sector in a way that the resulting cat state, which we term as the W-cat state, has quantum coherence that is resistant to…
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…
Favored schemes for trapped-ion quantum logic gates use bichromatic laser fields to couple internal qubit states with external motion through a "spin-dependent force." We introduce a new degree of freedom in this coupling that reduces its sensitivity to phase decoherence. We demonstrate bichromatic spin-dependent forces on a single trapped $^{111}$Cd$^+$ ion, and show that phase coherence of the resulting "Schrödinger-cat" states of motion depends critically upon the spectral arrangement of the optical fields. This applies directly to the operation of entangling gates on multiple ions.
Given a source of two coherent state superpositions with small separation in a traveling wave optical setting, we show that by interference and balanced homodyne measurement it is possible to conditionally prepare a symmetrically placed superposition of coherent states around the origo of the phase space. The separation of the coherent states in the superposition will be amplified during the process.
A measurement-induced continuous-variable logical gate is able to prepare Schrödinger cat states if the gate uses a non-Gaussian resource state, such as cubic phase state [I. V. Sokolov, Phys. Lett. A 384, 126762 (2020)]. Our scheme provides an alternative to hybrid circuits which use photon subtraction and (or) Fock resource states and photon number detectors. We reveal the conditions under which the gate conditionally prepares quantum superposition of two undistorted "copies" of an arbitrary input state that occupies a finite area in phase space. A detailed analysis of the fidelity between t…
