This paper relates both to the metaphysics of probability and to the physics of time asymmetry. Using the formalism of decoherent histories, it investigates whether intuitions about intrinsic time directedness that are often associated with probability can be justified in the context of no-collapse approaches to quantum mechanics. The standard (two-vector) approach to time symmetry in the decoherent histories literature is criticised, and an alternative approach is proposed, based on two decoherence conditions ('forwards' and 'backwards') within the one-vector formalism. In turn, considerations of forwards and backwards decoherence and of decoherence and recoherence suggest that a time-directed interpretation of probabilities, if adopted, should be both contingent and perspectival.
The environment -- external or internal degrees of freedom coupled to the system -- can, in effect, monitor some of its observables. As a result, the eigenstates of these observables decohere and behave like classical states: Continuous destruction of superpositions leads to environment-induced superselection (einselection). Here I investigate it in the context of quantum chaos (i. e., quantum dynamics of systems which are classically chaotic).
Certain intriguing consequences of the discreteness of time on the time evolution of dynamical systems are discussed. In the discrete-time classical mechanics proposed here, there is an {\it arrow of time} that follows from the fact that the replacement of the time derivative by the backward difference operator alone can preserve the non-negativity of the phase space density. It is seen that, even for free particles, all the degrees of freedom are {\it correlated} in principle. The forward evolution of functions of phase space variables by a finite number of time steps, in this discrete-time m…
We consider the superposition of two semiclassical solutions of the Wheeler-DeWitt equation for a de Sitter universe, describing a quantized scalar vacuum propagating in a universe that is contracting in one case and expanding in the other, each identifying a opposite cosmological arrow of time. We discuss the suppression of the interference terms between the two arrows of time due to environment-induced decoherence caused by modes of the scalar vacuum crossing the Hubble horizon. Furthermore, we quantify the effect of the interference on the expectation value of the observable field mode corr…
Recently David Jennings and Terry Rudolph published two papers as reaction on Maccone's paper "Quantum Solution to the Arrow-of-Time Dilemma". In these papers, the authors suppose that second law of thermodynamics is not relevant for quantum systems. Unfortunately, these papers did not get relevant reply from Maccone. The reason of this is following. Both Maccone and the above-mentioned authors use thermodynamic law and thermodynamic-like terminology for non-thermodynamic systems, for example, microscopic system of three qubits. However, big size of a system (quantum or classic) is also not an…
Two manifestations of decoherence, called instantaneous and dynamical, are investigated. The former reflects the suppression of the interference between the components of the current state while the latter reflects that within the initial state. These types of decoherence are computed in the case of the Brownian motion and the harmonic and anharmonic oscillators within the semiclassical approximation. A remarkable phenomenon, namely the opposite orientation of the time arrow of the dynamical variables compared to that of the quantum fluctuations generates a double exponential time dependence o…
The spread of the time arrows from the environment to an observed subsystem is followed within a harmonic model. A similarity is pointed out between irreversibility and a phase with spontaneously broken symmetry. The causal structure of interaction might be lost in the irreversible case, as well. The Closed Time Path formalism is developed for classical systems and shown to handle the time arrow problem in a clear and flexible manner. The quantum case is considered, as well, and the common origin of irreversibility and decoherence is pointed out.
With a choice of boundary conditions for solutions of the Schrödinger equation, state vectors and density operators even for closed systems evolve asymmetrically in time. For open systems, standard quantum mechanics consequently predicts irreversibility and signatures of the extrinsic arrow of time. The result is a new framework for the treatment of decoherence, not based on a reduced dynamics or a master equation. As an application, using a general model we quantitatively match previously puzzling experimental results and can conclude that they are the measurable consequence of the indistingu…
The extrinsic quantum mechanical arrow of time is understood to be a consequence of the interaction between quantum systems and their environment. A choice of boundary conditions for the Schrödinger equation results in a different time asymmetry intrinsic to quantum mechanical dynamics and independent of environmental interactions. Correct application of the intrinsically asymmetric dynamics, however, leads unavoidably to predictions of the experimental signatures of the extrinsic arrow of time. We are led to a new, model-independent mechanism for quantum decoherence. We need not invoke a mast…
Time-arrow $s=+/-$, intrinsic to a concrete physical system, is associated with the direction of information loss $ΔI$ displayed by the random evolution of the given system. When the information loss tends to zero the intrinsic time-arrow becomes uncertain. We propose the heuristic relationship $1/[1+exp(-sΔI)]$ for the probability of the intrinsic time-arrow. The main parts of the present work are trying to confirm this heuristic equation. The probability of intrinsic time arrow is defined by Bayesian inference from the observed random process. From irreversible thermodynamic systems, the pro…
Physical laws for elementary particles can be described by the quantum dynamics equation given a Hamiltonian. The solution are probability amplitudes in Hilbert space that evolve over time. A probability density function over position and time is given as the magnitude square of such probability amplitude. An entropy can be associated with these probability densities characterizing the position information of a particle. Coherent states are localized wave packets and may describe the spatial distribution for some particle states. We show that due to a dispersion property of Hamiltonians in qua…
Most attempts to argue for the second law of thermodynamics fail because (1) they use the unviable frequency theory of probability and (2) they do not explain why the arrow of time seen in experiments is aligned with the thermodynamic arrow of time. I use the decision theoretic interpretation of quantum probability from the many worlds interpretation of quantum mechanics to solve the probability problem. I then derive a correlation between the knowledge arrow of time and the entropy arrow of time using physical constraints on knowledge creation imposed by Popper's evolutionary theory of knowle…
The first paper: We describe principles of new cybernetics and use these principles for resolution of basic physical paradoxes. It demonstrates universality of the principles of new cybernetics. The second paper: recent letter by Maccone presents a solution based on the existing laws of quantum mechanics to the arrow-of-time dilemma. He argues that all phenomena in which the entropy decreases must not leave any information (in the observer's memory) of their having occurred because the observer is a part of the whole system. Maccone concludes that quantum mechanics is necessary to his argument…
We report on the effects of a simple decoherence model on the quantum search algorithm. Despite its simplicity, the decoherence model is an instructive model that can genuinely imitate realistic noisy environment in many situations. As one would expect, as the size of the database gets larger, the effects of decoherence on the efficiency of the quantum search algorithm cannot be ignored. Moreover, with decoherence, it may not be useful to iterate beyond the first maxima in the probability distribution of the search entry. Surprisingly, we also find that the number of iterations for maximum pro…
In this paper, we analyze the quantum counting under the decoherence, which can find the number of solutions satisfying a given oracle. We investigate probability distributions related to the first order term of the error rate on the quantum counting with the depolarizing channel. We also implement two circuits for the quantum counting -- the ascending-order circuit and the descending-order circuit -- by reversing ordering of application of controlled-Grover operations. By theoretical and numerical calculations for probability distributions, we reveal the difference of probability distribution…
An example shows that weak decoherence is more restrictive than the minimal logical decoherence structure that allows probabilities to be used consistently for quantum histories. The probabilities in the sum rules that define minimal decoherence are all calculated by using a projection operator to describe each possibility for the state at each time. Weak decoherence requires more sum rules. They bring in additional variables, that require different measurements and a different way to calculate probabilities, and raise questions of operational meaning. The example shows that extending the line…
We reformulate the quantum Monty Hall problem in the presence of decoherence. The decoherence destroys the fairness of the game. A new Nash equilibrium for a particular strategy profile in the presence of decoherence emerges. It is shown that in the presence of decoherence under the action of amplitude damping channel, Bob's winning probability is always higher than three-forth, irrespective of Alice's strategy, if he does not switch to the other door and always wins for a fully decohered case of the channel. Depolarizing channel damps up Bob's winning probability and gets better off if he sti…
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.
In Everett's many worlds interpretation, quantum measurements are considered to be decoherence events. If so, then inexact decoherence may allow large worlds to mangle the memory of observers in small worlds, creating a cutoff in observable world size. Smaller world are mangled and so not observed. If this cutoff is much closer to the median measure size than to the median world size, the distribution of outcomes seen in unmangled worlds follows the Born rule. Thus deviations from exact decoherence can allow the Born rule to be derived via world counting, with a finite number of worlds and no …
We study time dependence of exchange symmetry properties of Bell states when two qubits interact with local baths having identical parameters. In case of classical noise, we consider a decoherence Hamiltonian which is invariant under swapping the first and second qubits. We find that as the system evolves in time, two of the three symmetric Bell states preserve their qubit exchange symmetry with unit probability, whereas the symmetry of the remaining state survives with a maximum probability of 0.5 at the asymptotic limit. Next, we examine the exchange symmetry properties of the same states un…
We present a simple theoretical description of two recent experiments where damping of Rabi oscillations, which cannot be attributed to dissipative decoherence, has been observed. This is obtained considering the evolution time or the Hamiltonian as random variables and then averaging the usual unitary evolution on a properly defined, model-independent, probability distribution.
We study the dynamics of a two-level quantum system interacting with an external environment that takes the form of an XY spin chain in the presence of an external magnetic field. While the presence of the bath itself can enhance the transition probability from the lower level to the upper level of the system, we show that this noise-assisted phenomenon is sensitive to a change of the quantum phase of the environment. The derivative of the transition probability displays a maximum in correspondence with the critical value of the applied field both in the case of isotropic and anisotropic chain…
For a discrete time quantum walk (QW) on the $N$-cycle, allowing for decoherence on the coin, we derive a number of new results, including an explicit formula for the position probability distribution. For a QW of this type, we show that the mixing behavior tends, in the long-run, to a uniform distribution, regardless of the initial state of the system and irrespective of the parity of the number of nodes $N$. These results confirm the findings of previous authors who arrived at similar conclusions through extensive numerical simulations. In particular, we infer that the mixing time $\bar{M(ε)…
In this paper we study the protection of N-qubit Greenberger-Horne- Zeilinger (GHZ) state and generalized N-qubit GHZ states in amplitude damping channel by means of quantum weak measurement and flip operations. We derive the explicit formulas of the performances of the protection scheme: average fidelity, average probability and the average quantum fisher information (QFI). Moreover, the analytical results for maximizing the average fidelity and probability are obtained. We show that our scheme can effectively protect the average QFI of phase for GHZ states and generalized GHZ states. The pro…
We analyse the effects of intrinsic decoherence on the probability of generating a tripartite GHZ state using a cool trapped ion coupled to a single mode of the cavity field and interacting with a resonant laser field. Milburn equation is solved for this tripartite system to obtain the time evolution of density matrix as a function of cavity-ion coupling, laser-ion coupling, and the size of unitary time step relative to the time scale determined by system parameters. Starting with the system prepared initially in a separable state, density matrix is used to calculate the probability of tripart…
This paper is motivated by the suggestion [W. Zurek, Physica Scripta, T76, 186 (1998)] that the chaotic tumbling of the satellite Hyperion would become non-classical within 20 years, but for the effects of environmental decoherence. The dynamics of quantum and classical probability distributions are compared for a satellite rotating perpendicular to its orbital plane, driven by the gravitational gradient. The model is studied with and without environmental decoherence. Without decoherence, the maximum quantum-classical (QC) differences in its average angular momentum scale as hbar^{2/3} for ch…
We study the effect of small decoherence in continuous-time quantum walks on long-range interacting cycles, which are constructed by connecting all the two nodes of distance m on the cycle graph. In our investigation, each node is continuously monitored by an individual point contact, which induces the decoherence process. We obtain the analytical probability distribution and the mixing time upper bound. Our results show that, for small rates of decoherence, themixing time upper bound is independent of distance parameter m and is proportional to inverse of decoherence rate.
Decoherence effects associated to the damping of a tunneling two-level system are shown to dominate the tunneling probability at short times in strong coupling regimes in the context of a soluble model. A general decomposition of tunneling rates in dissipative and unitary parts is implemented. Master equation treatments fail to describe the model system correctly when more than a single relaxation time is involved.
We investigate the non-dissipative decoherence of three qubit system obtained by manipulating the state of a trapped two-level ion coupled to an optical cavity. Modelling the environment as a set of noninteracting harmonic oscillators, analytical expressions for the state operator of tripartite composite system, the probability of generating maximally entangled GHZ state, and the population inversion have been obtained. The pointer observable is the energy of the isolated quantum system. Coupling to environment results in exponential decay of off diagonal matrix elements of the state operator …
This paper is a natural continuation of our previous paper arXiv:1011.4173 . We illustrated earlier that in classical Hamilton mechanics, for overwhelming majority of real chaotic macroscopic systems, alignment of their thermodynamic time arrows occurs because of their low interaction. This fact and impossibility to observe entropy decrease at introspection explain the second law of thermodynamics. The situation in quantum mechanics is even a little bit easier: all closed systems of finite volume are periodic or nearly periodic. The proof in quantum mechanics is in many respects similar to the…
We consider the effects of decoherence on Landau-Zener crossings encountered in a large-scale adiabatic-quantum-computing setup. We analyze the dependence of the success probability, i.e. the probability for the system to end up in its new ground state, on the noise amplitude and correlation time. We determine the optimal sweep rate that is required to maximize the success probability. We then discuss the scaling of decoherence effects with increasing system size. We find that those effects can be important for large systems, even if they are small for each of the small building blocks.
Quantum random walk in a two-dimensional lattice with randomly distributed traps is investigated. Distributions of quantum walkers are evaluated dynamically for the cases of Hadamard, Fourier, and Grover coins, and quantum to classical transition is examined as a function of the density of the traps. It is shown that traps act as a serious and additional source of quantum decoherence. Furthermore, non-trivial temporal dependence of the standard deviation of the probability distribution of the walker is found when the trapping imperfections are introduced.
We prove analytical results showing that decoherence can be useful for mixing time in a continuous-time quantum walk on finite cycles. This complements the numerical observations by Kendon and Tregenna (Physical Review A 67 (2003), 042315) of a similar phenomenon for discrete-time quantum walks. Our analytical treatment of continuous-time quantum walks includes a continuous monitoring of all vertices that induces the decoherence process. We identify the dynamics of the probability distribution and observe how mixing times undergo the transition from quantum to classical behavior as our decoher…
Bell's seminal paper shows that some correlations in quantum theory are not reconcilable with hidden variables and the classical notion of locality. Yet, a weaker notion of locality, known as no-signalling, survives the no-go-result. Here, we study its restrictiveness by considering the full set of local quantum observables. This leads to a much larger set of no-signalling constraints than usually considered, which is enough to exclude PR-boxes and other types of super-quantum correlations. We emphasise the close connection with contextuality, in particular, we show how no-signalling arises na…
In this paper, we study mixing and large decoherence in continuous-time quantum walks on one dimensional regular networks, which are constructed by connecting each node to its $2l$ nearest neighbors($l$ on either side). In our investigation, the nodes of network are represented by a set of identical tunnel-coupled quantum dots in which decoherence is induced by continuous monitoring of each quantum dot with nearby point contact detector. To formulate the decoherent CTQWs, we use Gurvitz model and then calculate probability distribution and the bounds of instantaneous and average mixing times. …
We study the influence of errors and decoherence on both the performance of Shor's factoring algorithm and Grover's search algorithm, and on the amount of interference in these algorithms using a recently proposed interference measure. We consider systematic unitary errors, random unitary errors, and decoherence processes. We show that unitary errors which destroy the interference destroy the efficiency of the algorithm, too. However, unitary errors may also create useless additional interference. In such a case the total amount of interference can increase, while the efficiency of the quantum…
Consider a discrete-time quantum walk on the $N$-cycle governed by the following condition: at every time step of the walk, the option persists, with probability $p$, of exercising a projective measurement on the coin degree of freedom. For a bipartite quantum system of this kind, we prove that the von Neumann entropy of the total density operator converges to its maximum value. Thus, when influenced by decoherence, the mutual information between the two subsystems, corresponding respectively to the space of the coin and the space of the walker, eventually must diminish to zero. To put it plai…
The possibility to observe quantum Zeno and anti-Zeno scenarios for atom-diatom reactive collisions is investigated for two diferent processes (F+HD and H+O_2) by means of time-dependent wave packet propagations. A novel approach is proposed in which the survival probabilities investigated are those obtained when the initial state is redefined after time intervals tau at which measurements are performed on the system. The comparison with the actual probability for the unperturbed system reveals the existence of a regime in which the decay from the initial state appears to be inhibited (the qua…
Much of the discussion of decoherence has been in terms of a particle moving in one dimension that is placed in an initial superposition state (a Schrödinger "cat" state) corresponding to two widely separated wave packets. Decoherence refers to the destruction of the interference term in the quantum probability function. Here, we stress that a quantitative measure of decoherence depends not only on the specific system being studied but also on whether one is considering coordinate, momentum or phase space. We show that this is best illustrated by considering Wigner phase space where the measur…
The mixing time of a discrete-time quantum walk on the hypercube is considered. The mean probability distribution of a Markov chain on a hypercube is known to mix to a uniform distribution in time O(n log n). We show that the mean probability distribution of a discrete-time quantum walk on a hypercube mixes to a (generally non-uniform) distribution pi(x) in time O(n) and the stationary distribution is determined by the initial state of the walk. An explicit expression for pi(x) is derived for the particular case of a symmetric walk. These results are consistent with those obtained previously f…
In this paper, we consider decoherence in continuous-time quantum walks on long-range interacting cycles (LRICs), which are the extensions of the cycle graphs. For this purpose, we use Gurvitz's model and assume that every node is monitored by the corresponding point contact induced the decoherence process. Then, we focus on large rates of decoherence and calculate the probability distribution analytically and obtain the lower and upper bounds of the mixing time. Our results prove that the mixing time is proportional to the rate of decoherence and the inverse of the distance parameter ($\emph{…
Decoherence is studied in an attractive proposal for an actual implementation of a quantum computer based on trapped ions. Emphasis is placed on the decoherence arising from the vibrational motion of the ions, which is compared with that due to spontaneous emission from excited states of the ions. The calculation is made tractable by exploiting the vast difference in time scales between the vibrational excitations and the intra-ionic electronic excitations. Since the latter are several orders of magnitude faster, an adiabatic approximation is used to integrate them out and find the inclusive p…
Universal quantum cloning machines (UQCMs), sometimes called quantum cloners, generate many outputs with identical density matrices, with as close a resemblance to the input state as is allowed by the basic principles of quantum mechanics. Any experimental realization of a quantum cloner has to cope with the effects of decoherence which terminate the coherent evolution demanded by a UQCM. We examine how many clones can be generated within a decoherence time. We compare the time that a quantum cloner implemented with trapped ions requires to produce $M$ copies from $N$ identical pure state inpu…
We study distribution schemes for a polarization entangled photon pair based on a decoherence-free subspace over lossy quantum channels and propose an efficient scheme that is robust against not only collective phase noises but also general collective noises for two qubits. While the proposed scheme employs two photons to build the decoherence-free subspace, the success probability is proportional to the channel transmittance of a single photon with the aid of a counter-propagating weak coherent light pulse. The key ingredient in the scheme is found to be the reciprocity of the channel. The pr…
We analyze qubit decoherence in the framework of geometric quantum mechanics. In this framework the qubit density operators are represented by probability distributions which are also the Kähler functions on the Bloch sphere. Interestingly, the complete positivity of the quantum evolution is recovered as ellipticity of the second order differential operator (deformed Laplacian) which governs the evolution of the probability distribution.
We present a theoretical model for the dynamics of an electron that gets trapped by means of decoherence and quantum interference in the central quantum dot (QD) of a semiconductor nanoring (NR) made of five QDs, between 100 K and 300 K. The electron's dynamics is described by a master equation with a Hamiltonian based on the tight-binding model, taking into account electron-LO phonon interaction (ELOPI). Based on this configuration, the probability to trap an electron with no decoherence is almost 27%. In contrast, the probability to trap an electron with decoherence is 70% at 100 K, 63% at 2…
Recent experimental studies have shown that the relaxation time, $T_1$, and the dephasing time, $T_2$, of superconducting qubits fluctuate considerably over time. Time-varying quantum channel (TVQC) models have been proposed in order to consider the time varying nature of the parameters that define qubit decoherence. This dynamic nature of quantum channels causes a degradation of the performance of quantum error correction codes (QECC) that is portrayed as a flattening of their error rate curves. In this article, we introduce the concepts of quantum outage probability and quantum hashing outag…
Slow-roll inflation can become eternal if the quantum variance of the inflaton field around its slowly rolling classical trajectory is converted into a distribution of classical spacetimes inflating at different rates, and if the variance is large enough compared to the rate of classical rolling that the probability of an increased rate of expansion is sufficiently high. Both of these criteria depend sensitively on whether and how perturbation modes of the inflaton interact and decohere. Decoherence is inevitable as a result of gravitationally-sourced interactions whose strength are proportion…
We investigate the quantum walk on the line when decoherences are introduced either through simultaneous measurements of the chirality and particle position, or as a result of broken links. Both mechanisms drive the system to a classical diffusive behavior. In the case of measurements, we show that the diffusion coefficient is proportional to the variance of the initially localized quantum random walker just before the first measurement. When links between neighboring sites are randomly broken with probability $p$ per unit time, the evolution becomes decoherent after a characteristic time that…
We propose a novel approach to intrinsic decoherence without adding new assumptions to standard quantum mechanics. We generalize the Liouville equation just by requiring the dynamical semigroup property of time evolution and dropping the unitarity requirement. With no approximations and statistical assumptions we find a generalized Liouville equation which depends on two characteristic time t1 and t2 and reduces to the usual equation in the limit t1 = t2 -> 0. However, for t1 and t2 arbitrarily small but finite, our equation can be written as a finite difference equation which predicts state r…
Electron decoherence in cylindrical holes and circular apertures
ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology（光子科学研究所，巴塞罗那科技与科学研究所）；ICREA-Institució Catalana de Recerca i Estudis Avançats（加泰罗尼亚研究与高级研究学院）
It is one of the most important and long-standing issues of physics to derive the irreversibility out of a time-reversal symmetric equation of motion. The present paper considers the breaking of the time-reversal symmetry in open quantum systems and the emergence of an arrow of time. We claim that the time-reversal symmetric Schrödinger equation can have eigenstates that break the time-reversal symmetry if the system is open in the sense that it has at least a countably infinite number of states. Such eigenstates, namely the resonant and anti-resonant states, have complex eigenvalues. We show …
We determine the interqubit crosstalk- and charge-noise-induced decoherence time $T_2^\ast$ for a system of $L$ exchange-coupled electronic spin qubits in arrays of size $L=3$--$14$ for a number of different multiqubit geometries by directly calculating the return probability. We compare the behavior of the return probability to other quantities, namely, the average spin, the Hamming distance, and the entanglement entropy. In all cases, we use a starting state with alternating spins, $\left |Ψ_0\right >=\left |\downarrow\uparrow\downarrow\cdots\right >$. We show that a power law behavior, $T_2…
We study the intrinsic, disorder-induced decoherence of an isolated quantum system under its own dynamics. Specifically, we investigate the characteristic time scale (i.e., the decoherence time) associated with an interacting many-body system losing the memory of its initial state. To characterize the erasure of the initial state memory, we define a time scale, the intrinsic decoherence time, by thresholding the gradual decay of the disorder-averaged return probability. We demonstrate the system-size independence of the intrinsic decoherence time in different models, and we study its dependenc…
