The problem of reduction (wave packet reduction) is reexamined under two simple conditions: Reduction is a last step completing decoherence. It acts in commonplace circumstances and should be therefore compatible with the mathematical frame of quantum field theory and the standard model.
These conditions lead to an essentially unique model for reduction. Consistency with renormalization and time-reversal violation suggest however a primary action in the vicinity of Planck's length. The inclusion of quantum gravity and the uniqueness of space-time point moreover to generalized quantum theory, first proposed by Gell-Mann and Hartle, as a convenient framework for developing this model into a more complete theory.
A reduction mechanism resulting directly from the basic principles of quantum mechanics is proposed, inseparably from decoherence. A rather consistent theory of this effect is given and the next problems it raises are indicated.
The well-known increase of the decoherence rate with the temperature, for a quantum system coupled to a linear thermal bath, holds no longer for a different bath dynamics. This is shown by means of a simple classical non-linear bath, as well as a quantum spin-boson model. The anomalous effect is due to the temperature dependence of the bath spectral profile. The decoherence reduction via the temperature increase can be relevant for the design of quantum computers.
We describe exchange-only universal quantum computation and leakage reduction in the 3-qubit decoherence free subsystem (DFS). We discuss the angular momentum structure of the DFS, the proper forms for the DFS CNOT and leakage reduction operators in the total angular momentum basis, and new exchange-only pulse sequences for the CNOT and leakage reduction operators. Our new DFS CNOT sequence requires 22 pulses in 13 time steps. The DFS leakage reduction sequence, the first explicit leakage reduction sequence of its kind, requires 30 pulses in 20 time steps. Although the search for sequences was…
We study decoherence in a simple quantum mechanical model using two approaches. Firstly, we follow the conventional approach to decoherence where one is interested in solving the reduced density matrix from the perturbative master equation. Secondly, we consider our novel correlator approach to decoherence where entropy is generated by neglecting observationally inaccessible correlators. We show that both methods can accurately predict decoherence time scales. However, the perturbative master equation generically suffers from instabilities which prevents us to reliably calculate the system's t…
We formulate a novel approach to decoherence based on neglecting observationally inaccessible correlators. We apply our formalism to a renormalised interacting quantum field theoretical model. Using out-of-equilibrium field theory techniques we show that the Gaussian von Neumann entropy for a pure quantum state increases to the interacting thermal entropy. This quantifies decoherence and thus measures how classical our pure state has become. The decoherence rate is equal to the single particle decay rate in our model. We also compare our approach to existing approaches to decoherence in a simp…
We present a discussion of the fundamental loss of unitarity that appears in quantum mechanics due to the use of a physical apparatus to measure time. This induces a decoherence effect that is independent of any interaction with the environment and appears in addition to any usual environmental decoherence. The discussion is framed self consistently and aimed to general physicists. We derive the modified Schroedinger equation that arises in quantum mechanics with real clocks and discuss the theoretical and potential experimental implications of this process of decoherence.
Lisi, Marrone, and Montanino have recently proposed a test for quantum gravity induced decoherence effects in neutrino oscillations observed at Super-Kamiokande. We comment here that their equations have the same qualitative form as the energy conserving objective state vector reduction equations discussed by a number of authors. However, using the Planckian parameter value proposed to explain state vector reduction leads to a neutrino oscillation effect many orders of magnitude smaller than would be detectable at Super-Kamiokande. Similar estimates hold for the Ghirardi, Rimini, and Weber spo…
We make a novel observation about the decoherence phenomenon of the fermion in the Witten's supersymmetric (SUSY) quantum mechanical model. It is shown that, when the bosonic partner in the SUNY model is unobservable in a certain energy scale, the quantum coherence meant by the superposition of fermion states can not be preserved for a long time due to the quantum decoherence induced by the overlooked boson. This refers to a supercharge superselection rule similar to the charge superselection. We numerically calculate the decoherence factor characterizing the extent of decoherence . The obtain…
Quantum spin squeezing is an important resource for quantum information processing, but its squeezing degree is not easy to preserve in an open system with decoherence. Here, we propose a scheme to implement single-photon-triggered spin squeezing with decoherence reduction in an open system. In our system, a Dicke model (DM) is introduced into the quadratic optomechanics, which can be equivalent to an effective DM manipulated by the photon number. Besides, the phonon mode of the optomechanical system is coupled to a squeezed vacuum reservoir with a phase matching, resulting in that the thermal…
To discuss the quantum to classical transition in quantum cosmology, we study the decoherence factor and the peak of the Wigner function, which respectively represent the degree of decoherence and the degree to which the classical motion of the Universe is defined, in a Robertson-Walker universe model coupled with a scalar field. It is known that the decoherence factor is divergent in some cases. This implies that perfect decoherence occurs, and classical correlation criterion fails. In this paper we discuss the divergence of the decoherence factor in some detail and obtain the constraints for…
It is well known, that the causal Schrödinger evolution of a quantum state is not compatible with the reduction postulate, even when decoherence is taken into account. The violation of the causal evolution, introduced by the standard reduction postulate distinguishes certain systems (as the measurement devices), whose states are very close to statistical mixtures (as the ones resulting from the process of decoherence). In these systems, this violation has not any observable effect. In arbitrary quantum systems, the transition from the initial density matrix to a diagonal matrix predicted by th…
Quantum decoherence, which appears when a system interacts with its environment in an irreversible way, plays a fundamental role in the description of quantum-to-classical transitions and has been successfully applied in some important experiments. Here, we study the decoherence in noninertial frames for the first time. It is shown that the decoherence and loss of the entanglement generated by the Unruh effect will influence each other remarkably. It is interesting to note that in the case of the total system under decoherence, the sudden death of entanglement may appear for any acceleration. …
Macroscopic quantum systems (MQS) are macroscopic systems driven by quantum rather than classical mechanics, a long studied area with minimal success till recently. Harnessing the benefits of quantum mechanics on a macroscopic level would revolutionize fields ranging from telecommunication to biology, the latter focused on here for reasons discussed. Contrary to misconceptions, there are no known physical laws that prevent the development of MQS. Instead, they are generally believed universally lost in complex systems from environmental entanglements (decoherence). But we argue success is achi…
We study and compare the decoherent histories approach, the environment-induced decoherence and the localization properties of thesolutions to the stochastic Schrödinger equation in quantum jump simulationand quantum state diffusion approaches, for a quantum two-level system model. We show, in particular, that there is a close connection between the decoherent histories and the quantum jump simulation, complementing a connection with the quantum state diffusion approach noted earlier by Diósi, Gisin, Halliwell and Percival. In the case of the decoherent histories analysis, the degree of approx…
The Conditional Probability Interpretation of Quantum Mechanics replaces the abstract notion of time used in standard Quantum Mechanics by the time that can be read off from a physical clock. The use of physical clocks leads to apparent non-unitary and decoherence. Here we show that a close approximation to standard Quantum Mechanics can be recovered from conditional Quantum Mechanics for semi-classical clocks, and we use these clocks to compute the minimum decoherence predicted by the Conditional Probability Interpretation.
The quantum to classical transition maybe caused by decoherence or by dynamical collapse of the wave-function. We propose quantum discord as a tool, 1) for comparing and contrasting the role of a collapse model (Continuous Spontaneous Localization) and various sources of decoherence (environmental and fundamental), 2) for detecting collapse model and fundamental decoherence for an experimentally demonstrated macroscopic entanglement. We discuss the experimental times which will lead to the detection of either Continuous Spontaneous Localization or fundamental decoherence. We further put bounds…
The fact that we rarely directly observe much quantum uncertainty is often attributed to decoherence. However, decoherence does not reduce the quantum uncertainty in the full quantum state. Whether or not it reduces the quantum uncertainties in observations depends on the yet-unknown rules for getting observations (and their measures or `probabilities') from the quantum state. These points are illustrated by a simple toy model with a baseball at 100 miles per hour, which has the Planck momentum.
We show via an explicit example that quantum anomalies can lead to decoherence of a single quantum qubit through phase relaxation. The anomaly causes the Hamiltonian to develop a non-self-adjoint piece due to the non-invariance of the domain of the Hamiltonian under symmetry transformation. The resulting decoherence originates completely from the dynamics of the system itself and not, as usually considered, from interactions with the environment.
A theory of dynamical control by modulation for optimal decoherence reduction is developed. It is based on the non-Markovian Euler-Lagrange equation for the energy-constrained field that minimizes the average dephasing rate of a qubit for any given dephasing spectrum.
Quantum decoherence plays a pivotal role in the dynamical description of the quantum-to-classical transition and is the main impediment to the realization of devices for quantum information processing. This paper gives an overview of the theory and experimental observation of the decoherence mechanism. We introduce the essential concepts and the mathematical formalism of decoherence, focusing on the picture of the decoherence process as a continuous monitoring of a quantum system by its environment. We review several classes of decoherence models and discuss the description of the decoherence …
A protocol for considering decoherence in quantum games is presented. Results for two-player, two-strategy quantum games subject to decoherence are derived and some specific examples are given. Decoherence in other types of quantum games is also considered. As expected, the advantage that a quantum player achieves over a player restricted to classical strategies is diminished for increasing decoherence but only vanishes in the limit of maximum decoherence.
We study a quantum repeater which is based on decoherence free quantum gates recently proposed by Klein et al. [Phys. Rev. A 73, 012332 (2006)]. A number of operations on the decoherence free subspace in this scheme makes use of an ancilla qubit, which undergoes dephasing and thus introduces decoherence to the system. We examine how this decoherence affects entanglement swapping and purification as well as the performance of a quantum repeater. We compare the decoherence free quantum repeater with a quantum repeater based on qubits that are subject to decoherence and show that it outperforms t…
We prove a quantum version of the second law of thermodynamics: the (quantum) Boltzmann entropy increases if the initial (zero time) density matrix decoheres, a condition generally satisfied in Nature. It is illustrated by a model of wave-packet reduction, the Coleman-Hepp model, along the framework introduced by Sewell in his approach to the quantum measurement problem. Further models illustrate the monotonic-versus-non-monotonic behavior of the quantum Boltzmann entropy in time. As a last closely related topic, decoherence, which was shown by Narnhofer and Thirring to enforce macroscopic pur…
We study the ultimate limits to the decoherence rate associated with dephasing processes. Fluctuating chaotic quantum systems are shown to exhibit extreme decoherence, with a rate that scales exponentially with the particle number, thus exceeding the polynomial dependence of systems with fluctuating $k$-body interactions. Our findings suggest the use of quantum chaotic systems as a natural test-bed for spontaneous wave function collapse models. We further discuss the implications on the decoherence of AdS/CFT black holes resulting from the unitarity loss associated with energy dephasing.
Quantum Fourier transform is of primary importance in many quantum algorithms. In order to eliminate the destructive effects of decoherence induced by couplings between the quantum system and its environment, we propose a robust scheme for quantum Fourier transform over the intrinsic decoherence-free subspaces. The scheme is then applied to the circuit design of quantum Fourier transform over quantum networks under collective decoherence. The encoding efficiency and possible improvements are also discussed.
Taming decoherence is essential in realizing quantum computation and quantum communication. Here we experimentally demonstrate that decoherence due to amplitude damping can be suppressed by exploiting quantum measurement reversal in which a weak measurement and the reversing measurement are introduced before and after the decoherence channel, respectively. We have also investigated the trade-off relation between the degree of decoherence suppression and the channel transmittance.
The following statements belonging to the folklore of the theory of environmental decoherence are shown to be incorrect: 1) linear coupling to harmonic oscillator bath is a universal model of decoherence, 2) chaotic environments are more efficient decoherers.
A direct classical analog of the quantum dynamics of intrinsic decoherence in Hamiltonian systems, characterized by the time dependence of the linear entropy of the reduced density operator, is introduced. The similarities and differences between the classical and quantum decoherence dynamics of an initial quantum state are exposed using both analytical and computational results. In particular, the classicality of early-time intrinsic decoherence dynamics is explored analytically using a second-order perturbative treatment, and an interesting connection between decoherence rates and the stabil…
We describe quantum controllability under the influences of the quantum decoherence induced by the quantum control itself. It is shown that, when the controller is considered as a quantum system, it will entangle with its controlled system and then cause quantum decoherence in the controlled system. In competition with this induced decoherence, the controllability will be limited by some uncertainty relation in a well-armed quantum control process. In association with the phase uncertainty and the standard quantum limit, a general model is studied to demonstrate the possibility of realizing a …
I give a pedagogical overview of decoherence and its role in providing a dynamical account of the quantum-to-classical transition. The formalism and concepts of decoherence theory are reviewed, followed by a survey of master equations and decoherence models. I also discuss methods for mitigating decoherence in quantum information processing and describe selected experimental investigations of decoherence processes.
The possible effect of environment on the efficiency of a quantum algorithm is considered explicitely. It is illustrated through the example of Shor's prime factorization algorithm that this effect may be disastrous. The influence of environment on quantum computation is probed on the basis of its analogy to the problem of wave function collapse in quantum measurement.Techniques from the Hepp-Colemen approach and its generalization are used to deal with decoherence problems in quantum computation including dynamic mechanism of decoherence, quantum error avoiding tricks and calculation of decoh…
We propose and analyse a robust quantum state transfer protocol by the use of a combination of coherent quantum coupling and decoherence-free subspaces in a coupled quantum spin chain. Under decoherence, an arbitrary unknown quantum state embedded in a decoherence-free subspace can be perfectly transferred through a noisy channel being weakly coupled to two end registers. The method protects quantum information from both the channel noise and the environmental decoherence. A special case of utilizing two physical qubits to encode one logical qubit is considered as an example and the robustness…
It is shown how environmental decoherence plays an essential and constructive role in a quantum mechanical theory of brain process that has significant explanatory power.
Griffiths' ``quantum trajectories'' formalism is extended to describe weak decoherence. The decoherence conditions are shown to severely limit the complexity of histories composed of fine-grained events.
A direct classical analog of quantum decoherence is introduced. Similarities and differences between decoherence dynamics examined quantum mechanically and classically are exposed via a second-order perturbative treatment and via a strong decoherence theory, showing a strong dependence on the nature of the system-environment coupling. For example, for the traditionally assumed linear coupling, the classical and quantum results are shown to be in exact agreement.
Decoherence in quantum computer memory due to the inevitable coupling to the external environment is examined. We take the assumption that all quantum bits (qubits) interact with the same environment rather than the assumption of separate environments for different qubits. It is found that the qubits are decohered collectively. For some kinds of entangled input states, no decoherence occurs at all in the memory even if the qubits are interacting with the environment. Based on this phenomenon, a scheme is proposed for reducing the collective decoherence. We also discuss possible implications of…
In the framework of the Lindblad theory for open quantum systems, we determine the degree of quantum decoherence of a harmonic oscillator interacting with a thermal bath. It is found that the system manifests a quantum decoherence which is more and more significant in time. We calculate also the decoherence time scale and analyze the transition from quantum to classical behaviour of the considered system.
In this paper we study decoherence in the quantum walk on the line. We generalize the method of decoherent coin quantum walk, introduced by Brun et al [Phys. Rev. A {\bf 67}, 32304 (2003)]. Our analytical expressions are applicable for all kinds of decoherence. As an example of the coin-position decoherence, we study the broken line quantum walk and compare our results with the numerical one. We also show that our analytical results reduce to the Brun formalism when only the coin is subjected to decoherence.
When the nonlinearity of nanomechanical resonator is not negligible, the quantum decoherence of charge qubit is studied analytically. Using nonlinear Jaynes-Cummings model, one explores the possibility of being quantum data bus for nonlinear nanomechanical resonator, the nonlinearity destroys the dynamical quantum information-storage and maintains the revival of quantum coherence of charge qubit. With the calculation of decoherence factor, we demonstrate the influence of the nonlinearity of nanomechanical resonator on engineered decoherence of charge qubit.
We have studied how decoherence affects a quantum walk on the line. As expected, it is highly sensitive, consisting as it does of an extremely delocalized particle. We obtain an expression for the rate at which the standard deviation falls from the quantum value as decoherence increases and show that it is proportional to the number of decoherence "events" occuring during the walk.
To resist decoherence from destroying the phase factor of qubit state, it is important to use decoherence-free states for processing, transmitting and storing quantum information in quantum computing and quantum communication. We propose a practical scheme using four atoms with decoherence-free states in a single-mode cavity to realize the entanglement and fundamental quantum logic gates. The transmission of quantum information can be made directly from one atom to another, in which the cavity is only virtually excited. The possible application and the experimental requirement of our proposal …
Two initially correlated coherent states, each interacting with its own independent dissipative environment exhibit a sudden transition from classical to quantum decoherence. This change in the dynamics is a turning point in the decoherence, in the sense that depending on the average number of photons of each cavity, decoherence can even be suppressed. Indeed, the quantum state is time-independent for a time span in the mesoscopic regime, revealing a decoherence-free subspace. Furthermore, the absence of decoherence is manifested in the apparition of a metastable pointer state basis.
Marshall et al. gedanken experiment of the quantum superpposition of a mirror (oscilating part of a Michelson interferometer) interacting with single photon is consequently interpreted by relative decoherence.Such relative decoherence (based on the spontaneous superposition breaking (effective hiding)) on the photon (quantum object) caused by mirror (measurement device) is sufficient to model real measurement.
New feasible cavity QED experiment is proposed to analyse reversible quantum decoherence in consequence of quantum complementarity and entanglement. Utilizing the phase selective manipulations with enviroment, it is demonstrated how the complementarity particularly induces a preservation of visibility, whereas quantum decoherence is more progressive due to pronounced entanglement between system and enviroment. This effect can be directly observed using the proposed cavity QED measurements.
Many superconducting qubits are highly sensitive to dielectric loss, making the fabrication of coherent quantum circuits challenging. To elucidate this issue, we characterize the interfaces and surfaces of superconducting coplanar waveguide resonators and study the associated microwave loss. We show that contamination induced by traditional qubit lift-off processing is particularly detrimental to quality factors without proper substrate cleaning, while roughness plays at most a small role. Aggressive surface treatment is shown to damage the crystalline substrate and degrade resonator quality. …
In the framework of the Lindblad theory for open quantum systems, we determine the degree of quantum decoherence of a harmonic oscillator interacting with a thermal bath. It is found that the system manifests a quantum decoherence which is more and more significant in time. We also calculate the decoherence time and show that it has the same scale as the time after which thermal fluctuations become comparable with quantum fluctuations.
An open ended spin chain can serves as a quantum data bus for the coherent transfer of quantum state information. In this paper, we investigate the efficiency of such quantum spin channels which work in a decoherence environment. Our results show that, the decoherence will significantly reduce the fidelity of quantum communication through the spin channels. Generally speaking, as the distance increases, the decoherence effects become more serious, which will put some constraints on the spin chains for long distance quantum state transfer.
We suggest that propagation of nonclassical light in lattices of optical waveguides can provide a laboratory tool to simulate quantum decoherence phenomena with high non-Markovian features. As examples, we study decoherence of optical Schrödinger cats in a lattice that mimics a dissipative quantum harmonic oscillator coupled to a quantum bath, showing fractional decoherence in the strong coupling regime, and Bloch oscillations of optical Schrödinger cats, where damped revivals of the coherence can be observed.
A two-slit interference of a massive particle in the presence of environment induced decoherence is theoretically analyzed using a fully quantum mechanical calculation. The Markovian Master equation, derived from coupling the particle to a harmonic-oscillator heat bath, is used to obtain exact solutions which show the existence of an interference. Interestingly, decoherence does not affect the pattern, but only leads to a reduction in the fringe visibility.
We propose a new approach to the implementation of quantum gates in which decoherence during the gate operations is strongly reduced. This is achieved by making use of an environment induced quantum Zeno effect that confines the dynamics effectively to a decoherence-free subspace.
It is shown that the noise process in quantum computation can be described by spatially correlated decoherence and dissipation. We demonstrate that the conventional quantum error correcting codes correcting for single-qubit errors are applicable for reducing spatially correlated noise.
We propose a general approach of protecting a two-level system against decoherence via quantum engineering of non-classical multiple superpositions of coherent states in a non-Markovian reservoir. The scheme surprisingly only uses the system-environment interaction responsible for the decoherence and projective measurements of the two-level system. We demonstrate the method on the example of an excitonic qubit in self-assembled semiconductor quantum dots coupled to super-Ohmic reservoir of acoustic phonons.
Decoherence phenomenon has been widely studied in different types of quantum walks. In this work we show how to model decoherence inspired by percolation on staggered quantum walks. Two models of unitary noise are described: breaking polygons and breaking vertices. The evolution operators subject to these noises are obtained and the equivalence to the coined quantum walk model is presented. Further, we numerically analyze the effect of these decoherence models on the two-dimensional grid of $4$-cliques. We examine how these perturbations affect the quantum walk based search algorithm in this g…
We criticize the Hameroff Penrose model in the context of quantum brain model by gravitational collapse orchestrated objective reduction, orch. OR, assumed by Penrose, and we propose instead that the decoherence process is caused by interaction with the environment. We consider it useful to exploit this possibility because of the growing importance of decoherence theory in quantum measurement, and also because quantum mechanics can be applied to brain study independently of the Hameroff Penrose model for mind and consciousness. Our conclusion is that the Hameroff Penrose model is not compatibl…
An effective force induced by spatially depending decoherence is predicted. The phenomenon is illustrated by a simple model of a 1/2-spin particle subjected to distributed unselective measurement of noncommuting spin components.
Quantum computation that combines the coherence stabilization virtues of decoherence-free subspaces and the fault tolerance of geometric holonomic control is of great practical importance. Some schemes of adiabatic holonomic quantum computation in decoherence-free subspaces have been proposed in the past few years. However, non-adiabatic holonomic quantum computation in decoherence-free subspaces, which avoids long run-time requirement but with all the robust advantages, remains an open problem. Here, we demonstrate how to realize non-adiabatic holonomic quantum computation in decoherence-free…
