We study the time evolution of the entangled kaon system by considering the Liouville - von Neumann equation with an additional term which allows for decoherence. We choose as generators of decoherence the projectors to the 2-particle eigenstates of the Hamiltonian. Then we compare this model with the data of the CPLEAR experiment and find in this way an upper bound on the strength $λ$ of the decoherence. We also relate $λ$ to an effective decoherence parameter $ζ$ considered previously in literature. Finally we discuss our model in the light of different measures of entanglement, i.e. the von Neumann entropy $S$, the entanglement of formation $E$ and the concurrence $C$, and we relate the decoherence parameter $ζ$ to the loss of entanglement: $1 - E$.
We consider departures from hamiltonian dynamics in the evolution of neutral kaons due to their interactions with environment that generate entanglement among them. We propose a phenomenological model of stochastic re-scattering and estimate the coefficients of the effective hamiltonian and decoherence terms. Finally we analyze the interplay between the weak interaction and matter effects and propose the observables suitable to measure the matter characteristics of CPT violation and decoherence.
Quantum interference effects between past and future events (neutral kaon transitions, including CP violating decays) are discussed for entangled kaon pairs produced through $ϕ\to K^0 \bar{K^0}$ in $ϕ$-factories. Contrasting with the exciting conclusions of other recent analyses, we predict the inexistence of such an observable effect.
We propose the use of entangled pairs of neutral kaons, considered as a promising tool to close the well known loopholes affecting generic Bell's inequality tests, in a specific Hardy-type experiment. Hardy's contradiction without inequalities between Local Realism and Quantum Mechanics can be translated into a feasible experiment by requiring ideal detection efficiencies for only one of the observables to be alternatively measured. Neutral kaons are near to fulfil this requirement and therefore to close the efficiency loophole.
For the entangled neutral kaon system we formulate a Bell inequality sensitive to CP violation in mixing. Via this Bell inequality we obtain a bound on the leptonic CP asymmetry which is violated by experimental data. Furthermore, we connect the Bell inequality with a decoherence approach and find a lower bound on the decoherence parameter which practically corresponds to Furry's hypothesis.
We extend the use of Bell-inequalities to $Φ\to K^0 \bar{K^0}$ decays by exploiting analogies and differences to the well-known and experimentally verified singlet-spin case. Contrasting with other analyses, our Bell-inequalities are violated by quantum mechanics and can strictly be derived from local realistic theories. In principle, quantum mechanics could then be tested using unstable, oscillating states governed by a CP-violating Hamiltonian.
We investigate Bell inequalities for neutral kaon systems from Phi resonance decay to test local realism versus quantum mechanics. We emphasize the unitary time evolution of the states, that means we also include all decay product states, in contrast to other authors. Only this guarantees the use of the complete Hilbert space. We develop a general formalism for Bell inequalities including both arbitrary "quasi spin" states and different times; finally we analyze Wigner-type inequalities. They contain an additional term, a correction function h, as compared to the spin 1/2 or photon case, which…
In the context of the entangled $B^0 \bar B^0$ state produced at the $Υ(4S)$ resonance, we consider a modification of the usual quantum-mechanical time evolution with a dissipative term, which contains only one parameter denoted by $λ$ and respects complete positivity. In this way a decoherence effect is introduced in the time evolution of the 2-particle $B^0 \bar B^0$ state, which becomes stronger with increasing distance between the two particles. While our model of time evolution has decoherence for the 2-particle system, we assume that, after the decay of one of the two B mesons, the resul…
This paper presents properties of the so-called quasi-Bell states: entangled states written as superpositions of nonorthogonal states. It is shown that a special class of those states, namely entangled coherent states, are more robust against decoherence due to photon absorption than the standard bi-photon Bell states.
Decoherence effects in entangled fermion pairs at colliders
Higgs Centre for Theoretical Physics, School of Physics and Astronomy, The University of Edinburgh（爱丁堡大学物理与天文学学院希格斯理论物理中心）；Dipartimento di Fisica e Astronomia, Università di Bologna（博洛尼亚大学物理与天文学系）；Centre for Cosmology, Particle Physics and Phenomenology (CP3), Université Catholique de Louvain（天主教鲁汶大学宇宙学、粒子物理与现象学中心）
Self-interactions and interaction with the environment tend to push quantum systems toward states of maximal entanglement. This is a definition of decoherence. We argue that these maximally entangled states fall into the well-defined classes that can be uniquely described by the values of certain entanglement invariants. After discussing these ideas we present examples of maximally entangled states for a number of generic systems, construct compact states in the most entangled classes for tripartite systems, and suggest how they may be constructed for other $n$-partite systems. We study random…
We investigate the decay of entanglement, due to decoherence, of multi-qubit systems that are initially prepared in highly (in some cases maximally) entangled states. We assume that during the decoherence processes each qubit of the system interacts with its own, independent environment. We determine, for systems with a small number of qubits and for various decoherence channels, the initial states exhibiting the most robust entanglement. We also consider a restricted version of this robustness optimization problem, only involving states equivalent under local unitary transformations to the |G…
When a superposition $(|α>-|-α>)$ of two coherent states with opposite phase falls upon a 50-50 beamsplitter, the resulting state is entangled. Remarkably, the amount of entanglement is exactly 1 ebit, irrespective of $α$, as was recently discovered by O. Hirota and M. Sasaki. Here we discuss decoherence properties of such states and give a simple protocol that teleports one qubit encoded in Schrödinger cat states
We demonstrate the relevance of entanglement, Bell inequalities and decoherence in particle physics. In particular, we study in detail the features of the ``strange'' $K^0 \bar K^0$ system as an example of entangled meson--antimeson systems. The analogies and differences to entangled spin--1/2 or photon systems are worked, the effects of a unitary time evolution of the meson system is demonstrated explicitly. After an introduction we present several types of Bell inequalities and show a remarkable connection to CP violation. We investigate the stability of entangled quantum systems pursuing th…
We propose the generation of entangled states with trapped calcium ions using a combination of an rf dressed state and a spin dependent force. Using this method, a decoherence-free entangled state of rf qubits can be directly generated and ideally its fidelity is close to unity. We demonstrate an rf entangled state with a fidelity of 0.68, which has a coherence time of more than 200 ms by virtue of the fact that it is an eigenstate with energy gaps between adjacent levels.Using the same technique, we also produce a qutrit-qutrit entangled state with a fidelity of 0.77, which exceeds the thresh…
By choosing H nucleus in Carbon-13 labelled trichloroethylene as one qubit environment, and two C nuclei as a two-qubit system, we have simulated quantum decoherence when the system lies in an entangled state using nuclear magnetic resonance (NMR). Decoupling technique is used to trace over the environment degrees of freedom. Experimental results show agreements with the theoretical predictions. Our experiment scheme can be generalized to the case that environment is composed of multiple qubits.
We study two different decoherence modes for entangled qubits by considering a Liouville - von Neumann master equation. Mode A is determined by projection operators onto the eigenstates of the Hamiltonian and mode B by projectors onto rotated states. We present solutions for general and for Bell diagonal states and calculate for the later the mixedness and the amount of entanglement given by the concurrence. We propose a realization of the decoherence modes within neutron interferometry by applying fluctuating magnetic fields. An experimental test of the Kraus operator decomposition describing…
Decoherence-free states protect quantum information from collective noise, the predominant cause of decoherence in current implementations of quantum communication and computation. Here we demonstrate that spontaneous parametric down-conversion can be used to generate four-photon states which enable the encoding of one qubit in a decoherence-free subspace. The immunity against noise is verified by quantum state tomography of the encoded qubit. We show that particular states of the encoded qubit can be distinguished by local measurements on the four photons only.
Distillability sudden death and sudden birth in a two-qutrit system under decoherence of finite temperature is studied in detail. By using of the negativity and realignment criterion, it is shown that certain initial prepared free entangled states may become bound entangled or separable states in a finite time. Moreover, initial prepared bound entangled or separable states also may become distillabile entangled states in a finite time.
We microscopically model the decoherence dynamics of entangled coherent states under the influence of vacuum fluctuation. We derive an exact master equation with time-dependent coefficients reflecting the memory effect of the environment, by using the Feynman-Vernon influence functional theory in the coherent-state representation. Under the Markovian approximation, our master equation recovers the widely used Lindblad equation in quantum optics. We then investigate the non-Markovian entanglement dynamics of the quantum channel in terms of the entangled coherent states under noise. Compared wit…
We study the exact decoherence dynamics of the entangled squeezed state of two single-mode optical fields interacting with two independent and uncorrelated environments. We analyze in detail the non-Markovian effects on the entanglement evolution of the initially entangled squeezed state for different environmental correlation time scales. We find that the environments have dual actions on the system: backaction and dissipation. In mparticular, when the environmental correlation time scale is comparable to the time scale for significant change in the system, the backaction would counteract the…
In a $ϕ$ factory, neutral kaons are produced in Einstein-Podolsky-Rosen (EPR) states, furthermore, a $K_S$ is tagged if its entangled partner is detected as $K_L$, and vice versa. Here we point out that upon its detection as $K_L$, one of the EPR-entangled particles is projected into one of the orthogonal basis states, consequently the other particle should be projected to the state orthogonal to $K_L$, denoted as $K_{\perp L}$, rather than $K_S$, because $K_S$ is not orthogonal to $K_L$. Therefore the semileptonic charge asymmetry of what was previously regarded as $K_S$ is really that of $K_…
The Lindblad generators of the master equation define which kind of decoherence happens in an open quantum system. We are working with a two qubit system and choose the generators to be projection operators on the eigenstates of the system and unitary bilocal rotations of them. The resulting decoherence modes are studied in detail. Besides the general solutions we investigate the special case of maximally entangled states - the Bell singlet states. The results are depicted in the so-called spin geometry picture which allows to illustrate the evolution of the (nonlocal) correlations stored in a…
Every entangled state can be perturbed, for instance by decoherence, and stay entangled. For a large class of pure entangled states, we show how large the perturbation can be. Our class includes all pure bipartite and all maximally entangled states. For an entangled state, E, the constucted neighborhood of entangled states is the region outside two parallel hyperplanes, which sandwich the set of all separable states. The states for which these neighborhoods are largest are the maximally entangled ones. As the number of particles, or the dimensions of the Hilbert spaces for two of the particles…
We analyse decoherence properties of entangled coherent states (ECSs) due to channel losses, and compare to the performance of bi-photon Bell states. By employing the concept of "entanglement of formation" (EOF), the degradation of fidelity and degree of entanglement are calculated. Two situations are considered: (1) asymmetric and (2) symmetric noise channel. In the first case, only the lower bound of EOF is given. However, in the latter case, we have obtained an explicit expression of concurrence (and then EOF) and found surprisingly our result is just incompatible with that of [Phys. Rev. A…
In a recent work (Borras et al., Phys. Rev. A {\bf 79}, 022108 (2009)), we have determined, for various decoherence channels, four-qubit initial states exhibiting the most robust possible entanglement. Here we explore some geometrical features of the trajectories in state space generated by the decoherence process, connecting the initially robust pure state with the completely decohered mixed state obtained at the end of the evolution. We characterize these trajectories by recourse to the distance between the concomitant time dependent mixed state and different reference states.
We report on exciton-acoustic-phonon coupling effects on the generation of exciton maximally entangled states in N=2 and 3 quantum dot systems. In particular, we address the question of the combined effect of laser pulses, appropriate for generating Bell and Greenberger-Horne-Zeilinger entangled states, together with decoherence mechanisms as provided by a phonon reservoir. By solving numerically the master equation for the optically driven exciton-phonon kinetics, we show that the generation of maximally entangled exciton states is preserved over a reasonable parameter window.
Using Lindblad approach to study decoherence of quantum systems, we study the decoherence and decay of entangled states, formed by two basic states of a chain of thee qubits. We look on these states for a possible regular dependence on their decay as a function of their energy separation between the basic states under different type of environments. We found not regular or significant dependence on this energy separation for the type of environment considered .
Quantum properties are soon subject to decoherence once the quantum system interacts with the classical environment. In this paper we experimentally test how propagation losses, in a Gaussian channel, affect the bi-partite Gaussian entangled state generated by a sub-threshold type-II optical parametric oscillator (OPO). Experimental results are discussed in terms of different quantum markers, as teleportation fidelity, quantum discord and mutual information, and continuous variables (CV) entanglement criteria. To analyse state properties we have retrieved the composite system covariance matrix…
Entangled K0 anti-K0 pairs are shown to be suitable to discuss extensions and tests of Bohr's complementarity principle through the quantum marking and quantum erasure techniques suggested by M. O. Scully and K. Druehl [Phys. Rev. A 25, 2208 (1982)]. Strangeness oscillations play the role of the traditional interference pattern linked to wave-like behaviour, whereas the distinct propagation in free space of the K_S and K_L components mimics the two possible interferometric paths taken by particle-like objects.
We investigate the influence of environmental noise on polarization entangled light generated by parametric emission in a cavity. By adopting a recently developed separability criterion, we show that: i) self-stimulation may suppress the detrimental influence of noise on entanglement; ii) when self-stimulation becomes effective, a classical model of parametric emission incorporating noise provides the same results of quantum theory for the expectation values involved in the separability criterion. Moreover we show that, in the macroscopic limit, it is impossible to observe violations of local …
We derive a first order differential equation for the decoherence of an orbital angular momentum entangled biphoton state propagating through a turbulent atmosphere. The derivation is based on the distortion that orbital angular momentum states experience due to propagation through a thin sheet of turbulent atmosphere. This distortion is treated as an infinitesimal transformation leading to a first order differential equation, which we call an infinitesimal propagation equation. The equation is applied to a simple qubit case to show how the entanglement decays.
We present a proposal for realizing local decoherence-free evolution of given entangled states of two two-level (TL) ions. For two TL ions coupled to a single heavily damped cavity, we can use engineering reservoir scheme to obtain a decoherence-free subspace which can be nonadiabatically controlled by the system and reservoir parameters. Then the local decoherence-free evolution of the entangled states are achieved. And we also discuss the relation between the geometric phases and the entanglement of the two ions under the nonadiabatic coherent evolution.
We report on the coherence of Greenberger-Horne-Zeilinger (GHZ) states comprised of up to 8 qubits in the IBM ibmqx5 16-qubit quantum processor. In particular, we evaluate the coherence of GHZ states with $N=1,\ldots,8$ qubits, as a function of a delay time between state creation and measurement. We find that the decay in coherence occurs at a rate that is linear in the number of qubits. This is consistent with a model in which the dominant noise affecting the system is uncorrelated across qubits.
Decoherence effect on quantum entanglement of two optical qubits in a lossy cavity interacting with a nonlinear medium (Kerr nonlinearity) is analyzed. The qubits are assumed to be initially in the maximally entangled states (Bell or Bell-like states) or the maximally entangled mixed states, on the example of Werner and Werner-like states. Two kinds of measures of the entanglement are considered: the concurrence to describe a decay of the entanglement of formation of the qubits, and the negativity to determine a decay of the entanglement cost under positive-partial-transpose-preserving operati…
We investigate the dynamics of global entanglement, the Meyer-Wallach measure, under decoherence, analytically. We study two important class of multi-partite entangled states, the Greenberger-Horne-Zeilinger and the W state. We obtain exact results for various models of system-environment interactions (decoherence). Our results shows distinctly different scaling behavior for these initially entangled states indicating a relative robustness of the W state, consistent with previous studies.
Maintaining coherence of a qubit is of vital importance for realizing a large-scale quantum computer in practice. In this work, we study the central spin decoherence problem in the $XXX$ central spin model (CSM) and focus on the quantum states with different initial entanglement, namely intra-bath entanglement or system-bath entanglement. We analytically obtain their evolutions of fidelity, entanglement, and quantum coherence. When the initial bath spins constitute an $N$-particle entangled state (the Greenberger-Horne-Zeilinger-bath or the $W$-bath), the leading amplitudes of their fidelity e…
We experimentally demonstrate room-temperature storage of quantum entanglement using two nuclear spins weakly coupled to the electronic spin carried by a single nitrogen-vacancy center in diamond. We realize universal quantum gate control over the three-qubit spin system and produce entangled states encoded within the decoherence-free subspace of the two nuclear spins. By injecting arbitrary collective noise, we demonstrate that the decoherence-free entangled state has coherence time longer than that of other entangled states by an order of magnitude in our experiment.
We address the degradation of continuous variable (CV) entanglement in a noisy channel focusing on the set of photon-number entangled states. We exploit several separability criteria and compare the resulting separation times with the value of non-Gaussianity at any time, thus showing that in the low-temperature regime: i) non-Gaussianity is a bound for the relative entropy of entanglement and ii) Simon' criterion provides a reliable estimate of the separation time also for nonGaussian states. We provide several evidences supporting the conjecture that Gaussian entanglement is the most robust …
For entangled states of light both the amount of entanglement and the sensitivity to noise generally increase with the number of photons in the state. The entanglement-sensitivity tradeoff is investigated for a particular set of states, multi-dimensional entangled coherent states. Those states possess an arbitrarily large amount of entanglement $E$ provided the number of photons is at least of order $2^{2E}$. We calculate how fast that entanglement decays due to photon absorption losses and how much entanglement is left. We find that for very small losses the amount of entanglement lost is equ…
The ultimate stability of atomic clocks is limited by the quantum noise of the atoms. To reduce this noise it has been suggested to use entangled atomic ensembles with reduced atomic noise. Potentially this can push the stability all the way to the limit allowed by the Heisenberg uncertainty relation, which is denoted the Heisenberg limit. In practice, however, entangled states are often more prone to decoherence, which may prevent reaching this performance. Here we present an adaptive measurement protocol that in the presence of a realistic source of decoherence enables us to get near Heisenb…
We study the entanglement of entangled coherent states in vacuum environment by employing the entanglement of formation and propose a scheme to probabilistically teleport a coherent superposition state via entangled coherent states, in which the amount of classical information sent by Alice is restricted to one bit. The influence of decoherence due to photon absorpation is considered. It is shown that decoherence can improve the mean fidelity of probabilistic teleportation in some situations.
Entangled neutral K-mesons allow the study of their correlated dynamics at interference and decoherence times not accessible in any other system. We find novel quantum phenomena associated to a correlation-in-time between the two partners: the past state of the first decayed kaon, when it was entangled before its decay, is post-tagged by the result and the time of the future observation of the second decay channel. This surprising "from future to past" effect is fully observable and leads to the unique experimental tag of the KS-state, an unsolved problem since the discovery of CP violation.
A pure state decoheres into a mixed state as it entangles with an environment. When an entangled two-mode system is embedded in a thermal environment, however, each mode may not be entangled with its environment by their simple linear interaction. We consider an exactly solvable model to study the dynamics of a total system, which is composed of an entangled two-mode system and a thermal environment, and also an array of infinite beam splitters. It is shown that many-body entanglement of the system and the environment plays a crucial role in the process of disentangling the system.
We give an introduction to an entangled massive system, specifically the neutral kaon system, which has similarities to the entangled two photon system, but, however, also challenging differences.
The possibility of detracting the decoherence due to the acceleration process of the two-qutrit system is investigated, where we examined the behaviour of the relative entropy and the non-local information. For this purpose, the accelerated subsystems are allowed to pass through local or global noisy channels. It is shown that, the detraction potential depends on the type of the used noisy channel, local or global, and the initial settings of the accelerated qutrit systems, whether it is prepared in free or bound entangled intervals. The improving rate that depicted for systems prepared in the…
Efficient and faithful implementation of quantum information tasks, e.g., quantum computing, quantum communication and quantum metrology, requires robust and state-independent decoherence-suppressing measures to protect quantum information carriers. Here we present an experimental demonstration of a robust distribution scheme in which one photon of an entangled photon pair is successfully encoded into and decoded from a decoherence-free subspace (DFS) by a state-independent scheme. We achieved a high-fidelity distribution of the entangled state over fibre communication channel, and also demons…
The decoherence of two initially entangled qubits in anisotropic band gap photonic crystal has been studied analytically without Born or Markovian approximation. It is shown that the decoherence dynamics of two qubits in photonic crystal is greatly different from that of two qubits in vacuum or subjected to usual non-Markovian reservoir. The results also show that the finite time decoherence invoked by spontaneous emission could be suppressed efficiently and the entanglement of the Bell state possesses odd parity is more easily preserved in photonic crystal than that of the Bell state possesse…
In this paper we investigate a open two-qubit model whose dynamics is not exactly solvable. When the initial state is the maximum entangled state, as the exactly solvable open two-qubit model [D. Tolkunov and V. Privman, Phys. Rev. A 71, 060308(R) (2005)], the decay of entanglement of formation of the model, expressed by concurrence is also governed by the product of suppression factors describing decoherence of the subsystems (qubits). However, if the initial state is not the maximum entangled state, its concurrence will decrease faster than the product of the suppression factors describing d…
The decoherence of two initially entangled qubits in a non-Markovian reservoir has been investigated exactly without Born Markovian approximation and rotating-wave approximation(RWA). The non-perturbative quantum master equation is derived and its exact solution is obtained. The decoherence behaviors of two qubits, initially entangled in Bell states, has been investigated in three different cases of parameters. The results show that the counter-rotating wave terms have great influence on the decoherence behavior, and there are differences between the exact solution of the Hamiltonian with RWA …
It is known that maximally entangled Bell state and three-qubit W-type states are very useful in various quantum information processing task. Thus the problem of preparation of these type of states is very important in quantum information theory. But the factor which prohibit the generation of the above mentioned pure states shared between two and three distant partners is decoherence. When we send one qubit, from a two qubit state, through decoherence channel like amplitude damping channel, the purity of the qubit is lost and it ends up with a mixed state. Therefore it is very difficult to ke…
Single-photon entanglement may be the simplest type of entanglement but it is of vice importance in quantum communication. Here we present a practical protocol for distilling the single-photon entanglement from both photon loss and decoherence. With the help of some local single photons, the probability of single photon loss can be decreased and the less-entangled state can also be recovered to maximally entangled state simultaneously. It only requires some linear optical elements which makes it feasible in current experiment condition. This protocol might find applications in current quantum …
