Hans Aschauer, Hans J. Briegel
In this contribution we will give a brief overview on the methods used to overcome decoherence in quantum communication protocols. We give an introduction to quantum error correction, entanglement purification and quantum cryptography. It is shown that entanglement purification can be used to create ``private entanglement'', which makes it a useful tool for cryptographic protocols.
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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 …
Quantum technologies have shown immeasurable potential to effectively solve several information processing tasks such as prime number factorization, unstructured database search or complex macromolecule simulation. As a result of such capability to solve certain problems that are not classically tractable, quantum machines have the potential revolutionize the modern world via applications such as drug design, process optimization, unbreakable communications or machine learning. However, quantum information is prone to suffer from errors caused by the so-called decoherence, which describes the …
We define a time continuous version of the concept of "local operations and classical communication" (LOCC), ubiquitous in quantum information theory. It allows us to construct GKLS master equations for particle systems that have (1) an arbitrary pair potential, and (2) local decoherence terms, but that do not entangle the constituents. The local decoherence terms take a particularly simple form if a principle of least decoherence is applied.
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 propose a scheme for long-distance distribution of quantum entanglement in which the entanglement between qubits at intermediate stations of the channel is established by using bright light pulses in squeezed states coupled to the qubits in cavities with a weak dispersive interaction. The fidelity of the entanglement between qubits at the neighbor stations (10 km apart from each other) obtained by postselection through the balanced homodyne detection of 7 dB squeezed pulses can reach F=0.99 without using entanglement purification, at same time, the probability of successful generation of en…
The central issue in this article is to transmit a quantum state in such a way that after some decoherence occurs, most of the information can be restored by a suitable decoding operation. For this purpose, we incorporate redundancy by mapping a given initial quantum state to a messenger state on a larger-dimensional Hilbert space via a $C^*$-algebra embedding. Our noise model for the transmission is a phase damping channel which admits a noiseless or decoherence-free subspace or subsystem. More precisely, the transmission channel is obtained from convex combinations of a set of lowest rank ye…
Entanglement Swapping Scheduling for Quantum Repeater Chains under Decoherence during Classical Communications
本研究开发分析模型，揭示量子中继链中中继器数量增加与退相干影响间的权衡，发现存在最优中继器数量，为未来量子网络设计提供指导。
Channel nonlocality under decoherence
本文量化双向量子信道的非局域性，识别抵抗退相位噪声的成分，并证明其在量子协议及噪声通信中的关键作用，同时揭示退相干下量子模拟随机过程的通信优势。
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…
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 …
By considering distance-regular graphs as spin networks, we investigate the state transfer fidelity in this class of networks. The effect of environment on the dynamics of state transfer is modeled using Milburn's intrinsic decoherence [G. J. Milburn, Phys. Rev. A 44, 5401 (1991)]. We consider a particular type of spin Hamiltonians which are extended version of those of Christandl et al [Phys. Rev. A 71, 032312 (2005)]. It is shown that decoherence destroys perfect communication channels. Using optimal coupling strengths derived by Jafarizadeh and Sufiani [Phys. Rev. A 77, 022315 (2008)], we s…
We show that private shared reference frames can be used to perform private quantum and private classical communication over a public quantum channel. Such frames constitute a novel type of private shared correlation (distinct from private classical keys or shared entanglement) useful for cryptography. We present optimally efficient schemes for private quantum and classical communication given a finite number of qubits transmitted over an insecure channel and given a private shared Cartesian frame and/or a private shared reference ordering of the qubits. We show that in this context, it is use…
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.
In this paper we consider decoherence-free communication over multiple access and $k$-user quantum channels. First, we concentrate on a hermitian unitary noise model $U$ for a two-access bi-unitary channel and show that in this case a decoherence-free code exists if the space of Schmidt matrices of an eigensubspace of $U$ exhibits certain properties of decomposability. Then, we show that our technique is also applicable for generic random unitary two-access channels. Finally, we consider the applicability of the result to the case of a larger number of senders and general Kraus operators.
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…
Examining a Quantum System Subject to Energy Decoherence
本文针对相互作用量子系统的能量退相干问题，通过解析与数值方法研究振荡器-自旋系统的动态退相干效应并对比无退相干情况，还探索其与热力学的联系。
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.
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.
We propose and analyze a multiphoton-state coherent transport protocol in a coupled-resonator quantum network. A multiphoton swap gate between two antipodes can be achieved with neither external modulation nor coupling strength engineering. Moreover, we extend this result to a coupled-resonator chain of arbitrary length with different coupling strengths. Effects of decoherence via quantum nondemolition interaction are studied with sources including vacuum quantum fluctuation and bath thermal excitations when the bath is in the thermal equilibrium state. These observations are helpful to unders…
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.
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.
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.
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.
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.
We show how to use decoherence-free subspaces over collective-noise quantum channels to convey classical information in perfect secrecy. We argue that codes defined over decoherence-free subspaces are codes for quantum wiretap channels in which the gain of information by a non-authorized receiver is zero. We also show that if some symmetry conditions are guaranteed, the maximum rate on which these secret communications take place is equal to the Holevo-Schumacher-Westmoreland capacity of the quantum channel.
Decoherence to quantum theory from a causally-indefinite post-quantum theory
本文提出通过超退相干过程从高阶量子理论产生标准量子理论，并探讨其对因果性与纯度公理的潜在影响。
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.
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…
The problem investigated in this paper is einselection, i. e. the selection of mutually exclusive quantum states with definite probabilities through decoherence. Its study is based on a theory of decoherence resulting from the projection method in the quantum theory of irreversible processes, which is general enough for giving reliable predictions. This approach leads to a definition (or redefinition) of the coupling with the environment involving only fluctuations. The range of application of perturbation calculus is then wide, resulting in a rather general master equation. Two distinct cases…
Quantum decoherence has been studied using nuclear magnetic resonance(NMR). By choosing one qubit to simulate environment, we examine the decoherence behavior of two quantum systems: a one qubit system and a two qubit system. The experimental results show agreements with the theoretical predictions. Our experiment schemes can be generalized to the case that the environment is composed of multiple qubits.
A scheme to implement a quantum computer subjected to decoherence and governed by an untunable qubit-qubit interaction is presented. By concatenating dynamical decoupling through bang-bang (BB) pulse with decoherence-free subspaces (DFSs) encoding, we protect the quantum computer from environment-induced decoherence that results in quantum information dissipating into the environment. For the inherent qubit-qubit interaction that is untunable in the quantum system, BB control plus DFSs encoding will eliminate its undesired effect which spoils quantum information in qubits. We show how this qua…
Liquid-state NMR quantum computer has demonstrated the possibility of quantum computation and supported its development. Using NMR quantum computer techniques, we observed phase decoherence under two kinds of artificial noise fields; one a noise with a long period, and the other with shorter random period. The first one models decoherence in a quantum channel while the second one models transverse relaxation. We demonstrated that the bang-bang control suppresses decoherence in both cases.
We give an elementary account of quantum measurement and related topics from the modern perspective of decoherence. The discussion should be comprehensible to students who have completed a basic course in quantum mechanics with exposure to concepts such as Hilbert space, density matrices, and von Neumann projection (``wavefunction collapse'').
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…
The second order quantum decoherence (SOQDC)is proposed as a novel description for the loss of quantum coherence only reflected by second order quantum correlations. By calculating the two-time correlation function, the phenomenon of SOQDC is studied in details for a simple model, a two boson system interacting with a reservoir composed of one or many bosons. The second order quantum decoherence effects can be observed in the sketched cavity QED experiment.
We analyze the long time behavior of a discrete time quantum walk subject to decoherence with a strong spatial dependence, acting on one half of the lattice. We show that, except for limiting cases on the decoherence parameter, the quantum walk at late times behaves sub-ballistically, meaning that the characteristic features of the quantum walk are not completely spoiled. Contrarily to expectations, the asymptotic behavior is non Markovian, and depends on the amount of decoherence. This feature can be clearly shown on the long time value of the Generalized Chiral Distribution (GCD).
Decoherence is the major stumbling block in the realization of a large-scale quantum computer. Ingenious methods have been devised to overcome decoherence, but their success has been proven only for over-simplified models of system-environment interaction. Whether such methods will be reliable in the face of more realistic models is a fundamental open question. In this partly pedagogical article, we study two toy models of quantum information processing, using the language of \emph{quantum walks}. Decoherence is incorporated in 3 ways - by coupling to a noisy `projective measurement' system, a…
We show how to realize, by means of non-abelian quantum holonomies, a set of universal quantum gates acting on decoherence-free subspaces and subsystems. In this manner we bring together the quantum coherence stabilization virtues of decoherence-free subspaces and the fault-tolerance of all-geometric holonomic control. We discuss the implementation of this scheme in the context of quantum information processing using trapped ions and quantum dots.
In this thesis we describe methods for avoiding the detrimental effects of decoherence while at the same time still allowing for computation of the quantum information. The philosophy of the method discussed in the first part of this thesis is to use a symmetry of the decoherence mechanism to find robust encodings of the quantum information. Stability, control, and methods for using decoherence-free information in a quantum computer are presented with a specific emphasis on decoherence due to a collective coupling between the system and its environment. Universal quantum computation on such co…
For a wide set of quantum systems it is demonstrated that the quantum regime can be considered as the transient phase while the final classical statistical regime is a permanent state. A basis where exact matrix decoherence appears for these final states is found. The relation with the decoherence of histories formalism is studied. A set of final intrinsically consistent histories is found.
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