Lin Zhang, Junde Wu
In the paper, the dynamical additivity of bi-stochastic quantum operations is characterized and the strong dynamical additivity is obtained under some restrictions.
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Inevitable Negativity: Additivity Commands Negative Quantum Channel Entropy
本文利用特定超信道提出构造性、公理化和操作性三种等价的信道优超方法，建立信道不确定性框架，并证明量子信道熵必然为负。
Additivity of Entangled Channel Capacity for Quantum Input States
介绍了统一量子信息理论的代数方法和量子纠缠作为广义编码的运算方法。在引入复合量子态和Araki-Umegaki（a型）和Belavkin-Staszewski（b型）量子相对熵信息发散的基础上，通过广义编码处理了两类量子互信息，并定义了两类相应的量子信道容量为上确界。证明了量子信道容量通过纠缠的可加性，从而将V. P. Belavkin的结果推广到任意量子信道对任意类型的量子相对熵的乘积.
Building upon work by Matsumoto, we show that the quantum relative entropy with full-rank second argument is determined by four simple axioms: i) Continuity in the first argument, ii) the validity of the data-processing inequality, iii) additivity under tensor products, and iv) super-additivity. This observation has immediate implications for quantum thermodynamics, which we discuss. Specifically, we demonstrate that, under reasonable restrictions, the free energy is singled out as a measure of athermality. In particular, we consider an extended class of Gibbs-preserving maps as free operation…
We investigate decoherence induced by a quantum channel in terms of minimal output entropy and of map entropy. The latter is the von Neumann entropy of the Jamiolkowski state of the channel. Both quantities admit q-Renyi versions. We prove additivity of the map entropy for all q. For the case q = 2, we show that the depolarizing channel has the smallest map entropy among all channels with a given minimal output Renyi entropy of order two. This allows us to characterize pairs of channels such that the output entropy of their tensor product acting on a maximally entangled input state is larger t…
On super additivity of Fisher information in fully Gaussian metrology
本研究证明在完全高斯计量中，当信息同时编码在位移和协方差矩阵时，Fisher信息可呈现超加性特性，并通过量子光学平台展示了其在参数估计中的应用。
Singularising preserving countable additivity quantum channels on quantum measurable cardinals
利用Pettis积分和Yosida-Hewitt分解，研究von Neumann代数上由算子群平均诱导的量子信道，给出信道保持σ-可加性并完全抑制正常分量的充分条件，结合Ulam实值可测基数理论揭示将正常态变为奇异但严格σ-可加态的新现象。
Quantum channels preserving sigma-additivity on diagonal von Neumann algebras and Ulam measurable cardinals
研究量子态在$\ell_2(κ)$上的性质与基数$κ$的集合论性质之间的相互作用，探讨σ-可加态的存在性及其结构动力学特性，证明对角代数上的σ-可加态可表示为皮蒂积分，构建量子通道将正常态映射到σ-可加态。
Additivity of quantum relative entropies as a single-copy criterion
研究量子信息中正则化是否必要的问题，提出单副本优化器满足特定性质时Umegaki相对熵等量可加，适用于假设检验和量子资源理论。
A microscopic definition of the thermodynamic entropy in an isolated quantum system must satisfy (i) additivity, (ii) extensivity and (iii) the second law of thermodynamics. We show that the diagonal entropy, which is the Shannon entropy in the energy eigenbasis at each instant of time, meets the first two requirements and that the third requirement is satisfied if an arbitrary external operation is performed at typical times. In terms of the diagonal entropy, thermodynamic irreversibility follows from the facts that the Hamiltonian dynamics restricts quantum trajectories under unitary evoluti…
We study the process of assisted work distillation. This scenario arises when two parties share a bipartite quantum state $ρ_{AB}$ and their task is to locally distil the optimal amount of work when one party is restricted to thermal operations whereas the other can perform general quantum operations and they are allowed to communicate classically. We demonstrate that this question is intimately related to the distillation of classical/quantum correlations. In particular, we show that the advantage of one party performing global measurements over many copies of $ρ_{AB}$ is related to the non-a…
Divisibility of dynamical maps is visualized by trajectories in the parameter space and analyzed within the framework of collision models. We introduce ultimate completely positive (CP) divisible processes, which lose CP divisibility under infinitesimal perturbations, and characterize Pauli dynamical semigroups exhibiting such a property. We construct collision models with factorized environment particles, which realize additivity and multiplicativity of generators of CP divisible maps. A mixture of dynamical maps is obtained with the help of correlated environment. Mixture of ultimate CP divi…
We propose an alternative framework for quantifying coherence. The framework is based on a natural property of coherence, the additivity of coherence for subspace-independent states, which is described by an operation-independent equality rather than operation-dependent inequalities and therefore applicable to various physical contexts. Our framework is compatible with all the known results on coherence measures but much more flexible and convenient for applications, and by using it many open questions can be resolved.
Quantum channels, also called quantum operations, are linear, trace preserving and completely positive transformations in the space of quantum states. Such operations describe discrete time evolution of an open quantum system interacting with an environment. The thesis contains an analysis of properties of quantum channels and different entropies used to quantify the decoherence introduced into the system by a given operation. Part I of the thesis provides a general introduction to the subject. In Part II, the action of a quantum channel is treated as a process of preparation of a quantum ense…
In this note, we survey some elementary theorems and proofs concerning dynamical matrices theory. Some mathematical concepts and results involved in quantum information theory are reviewed. A little new result on the matrix representation of quantum operation are obtained. And best separable approximation for quantum operations is presented.
We characterize the operational task of environment-assisted distillation of quantum coherence under different sets of free operations when only a finite supply of copies of a given state is available. We first evaluate the one-shot assisted distillable coherence exactly, and introduce a semidefinite programming bound on it in terms of a smooth entropic quantity. We prove the bound to be tight for all systems in dimensions 2 and 3, which allows us to obtain computable expressions for the one-shot rate of distillation, establish an analytical expression for the best achievable fidelity of assis…
Completely positive and trace-preserving maps characterize physically implementable quantum operations. On the other hand, general linear maps, such as positive but not completely positive maps, which can not be physically implemented, are fundamental ingredients in quantum information, both in theoretical and practical perspectives. This raises the question of how well one can simulate or approximate the action of a general linear map by physically implementable operations. In this work, we introduce a systematic framework to resolve this task using the quasiprobability decomposition techniqu…
We consider properties of quantum channels with use of unified entropies. Extremal unravelings of quantum channel with respect to these entropies are examined. The concept of map entropy is extended in terms of the unified entropies. The map $(q,s)$-entropy is naturally defined as the unified $(q,s)$-entropy of rescaled dynamical matrix of given quantum channel. Inequalities of Fannes type are obtained for introduced entropies in terms of both the trace and Frobenius norms of difference between corresponding dynamical matrices. Additivity properties of introduced map entropies are discussed. T…
Dynamical decoupling is a key method to mitigate errors in a quantum mechanical system, and we studied it in a series of papers dealing in particular with the problems arising from unbounded Hamiltonians. The standard bangbang model of dynamical decoupling, which we also used in those papers, requires decoupling operations with infinite amplitude, which is strictly speaking unrealistic from a physical point of view. In this paper we look at decoupling operations of finite amplitude, discuss under what assumptions dynamical decoupling works with such finite amplitude operations, and show how th…
Erasing, Converting, and Communicating: The Power of Resource-Nongenerating Operations
本文研究静态和动态量子资源理论中的资源非生成操作，推导了状态转换的充分条件，构建了动态资源理论并提出公理化量化方法，分析了动态资源的擦除，并应用于状态转换率和经典通信容量界限。
Coherent superposition and entanglement are two fundamental aspects of non-classicality. Here we provide a quantitative connection between the two on the level of operations by showing that the dynamical coherence of an operation upper bounds the dynamical entanglement that can be generated from it with the help of additional incoherent operations. In case a particular choice of monotones based on the relative entropy is used for the quantification of these dynamical resources, this bound can be achieved. In addition, we show that an analog to the entanglement potential exists on the level of …
Implementing precise operations on quantum systems is one of the biggest challenges for building quantum devices in a noisy environment. Dynamical decoupling (DD) attenuates the destructive effect of the environmental noise, but so far it has been used primarily in the context of quantum memories. Here, we present a general scheme for combining DD with quantum logical gate operations and demonstrate its performance on the example of an electron spin qubit of a single nitrogen-vacancy center in diamond. We achieve process fidelities >98% for gate times that are 2 orders of magnitude longer than…
Divisibility of dynamical maps turns out to be a fundamental notion in characterising Markovianity of quantum evolution, although the decision problem for divisibility itself is computationally intractable. In this work, we propose the operational characterisation of divisibility of dynamical maps by exploiting distinguishability of quantum channels. We prove that distinguishability for any pair of quantum channels does not increase under divisible maps, and then, in terms of channel distinguishability with entanglement between system and $k$-dimensional ancillas, provide the operational chara…
This paper establishes single-letter formulas for the exact entanglement cost of simulating quantum channels under free quantum operations that completely preserve positivity of the partial transpose (PPT). First, we introduce the $κ$-entanglement measure for point-to-point quantum channels, based on the idea of the $κ$-entanglement of bipartite states, and we establish several fundamental properties for it, including amortization collapse, monotonicity under PPT superchannels, additivity, normalization, faithfulness, and non-convexity. Second, we introduce and solve the exact entanglement cos…
Quantum discord in a bipartite system can be dynamically revealed and quantified through purely local operations on one of the two subsystems. To achieve this, the local detection method harnesses the influence of initial correlations on the reduced dynamics of an interacting bipartite system. This article's aim is to provide an accessible introduction to this method and to review recent theoretical and experimental progress.
We experimentally demonstrate coherence recovery of singlet-triplet superpositions by interlacing qubit rotations between Carr-Purcell (CP) echo sequences. We then compare performance of Hahn, CP, concatenated dynamical decoupling (CDD) and Uhrig dynamical decoupling (UDD) for singlet recovery. In the present case, where gate noise and drift combined with spatially varying hyperfine coupling contribute significantly to dephasing, and pulses have limited bandwidth, CP and CDD yield comparable results, with T2 ~ 80 microseconds.
A simple formula for the average gate fidelity of a quantum dynamical operation
本文提出了一个简单的公式，用于计算酉量子门和量子点上的一般量子操作之间的平均保真度，推广了Bowman等人[Phys. Lett. A 294，258（2002）]。该公式可用于实验测定平均门保真度。我们还给出了Horodecki等人[Phys. Rev. A 60，1888（1999）]的一个公式的简化证明，该公式将平均门保真度与纠缠保真度联系起来。
Quantum Dynamical Resource Theory under Resource Non-increasing Framework
本文提出资源非增框架研究动力学资源理论，给出多种自由操作下的量化候选方案，并具体量化了有无后选择测量场景中的动力学相干性，同时为度量赋予量子判别任务的操作意义。
Universality from Quadratic Angular-Momentum Operations: Exact Dynamical Lie Algebras and the Role of the Casimir Obstruction
本文研究二次角动量运算的普适性，证明在固定粒子数子空间上实现普适控制，但抽象动力学李代数受Casimir障碍限制，并精确刻画了相应代数结构。
Spectral properties of an arbitrary matrix can be characterized by the entropy of its rescaled singular values. Any quantum operation can be described by the associated dynamical matrix or by the corresponding superoperator. The entropy of the dynamical matrix describes the degree of decoherence introduced by the map, while the entropy of the superoperator characterizes the a priori knowledge of the receiver of the outcome of a quantum channel Phi. We prove that for any map acting on a N--dimensional quantum system the sum of both entropies is not smaller than ln N. For any bistochastic map th…
We prove the quantum Zeno effect in open quantum systems whose evolution, governed by quantum dynamical semigroups, is repeatedly and frequently interrupted by the action of a quantum operation. For the case of a quantum dynamical semigroup with a bounded generator, our analysis leads to a refinement of existing results and extends them to a larger class of quantum operations. We also prove the existence of a novel strong quantum Zeno limit for quantum operations for which a certain spectral gap assumption, which all previous results relied on, is lifted. The quantum operations are instead req…
Dynamically corrected gates were recently introduced [Khodjasteh and Viola, Phys. Rev. Lett. 102, 080501 (2009)] as a tool to achieve decoherence-protected quantum gates based on open-loop Hamiltonian engineering. Here, we further expand the framework of dynamical quantum error correction, with emphasis on elucidating under what conditions decoherence suppression can be ensured while performing a generic target quantum gate, using only available bounded-strength control resources. Explicit constructions for physically relevant error models are detailed, including arbitrary linear decoherence a…
In this paper, we extend the resource theory of magic to the channel case by considering completely stabilizer preserving operations (CSPOs) as free. We introduce and characterize the set of CSPO preserving and completely CSPO preserving superchannels. We quantify the magic of quantum channels by extending the generalized robustness and the min relative entropy of magic from the state to the channel domain and show that they bound the single-shot dynamical magic cost and distillation. We also provide analytical conditions for qubit interconversion under CSPOs and show that it is a linear progr…
In spite of their outstanding experimental relevance, Gaussian operations in continuous-variable quantum systems are subjected to fundamental limitations, as it is known that general resources cannot be distilled within the Gaussian paradigm. We show that these limitations can be overcome by considering a collaborative setting where one party increases the amount of local resource with the aid of another party, whose operations are assumed to be Gaussian but are otherwise unrestricted; the two parties can only communicate classically. We show that in single-shot scenarios, unlike in the well-k…
We study the occurrence of errors in a continuously decoupled two-qubit state during a $\sqrt{SWAP}$ quantum operation under decoherence. We consider a realization of this quantum gate based on the Heisenberg exchange interaction, which alone suffices for achieving universal quantum computation. Furthermore, we introduce a continuous-dynamical-decoupling scheme that commutes with the Heisenberg Hamiltonian to protect it from the amplitude damping and dephasing errors caused by the system-environment interaction. We consider two error-protection settings. One protects the qubits from both ampli…
We consider the evolution of an arbitrary quantum dynamical semigroup of a finite-dimensional quantum system under frequent kicks, where each kick is a generic quantum operation. We develop a generalization of the Baker-Campbell-Hausdorff formula allowing to reformulate such pulsed dynamics as a continuous one. This reveals an adiabatic evolution. We obtain a general type of quantum Zeno dynamics, which unifies all known manifestations in the literature as well as describing new types.
We develop a procedure of generalized continuous dynamical decoupling (GCDD) for an ensemble of $d$-level systems (qudits), allowing one to protect the action of an arbitrary multi-qudit gate from general noise. We first present our GCDD procedure for the case of an arbitrary qudit and apply it to the case of a Hadamard gate acting on a qutrit. This is done using a model that, in principle, could be implemented using the three magnetic hyperfine states of the ground energy level of $^{87}\mathrm{Rb}$ and laser beams whose intensities and phases are modulated according to our prescription. We s…
Effects of dynamical phases in Shor's factoring algorithm with operational delays
理想量子算法通常假设量子计算是通过一系列幺正变换连续进行的。然而，在实际的量子计算过程中，连续操作之间总是存在空闲的有限时间间隔。在这些延迟期间，相干“误差”将从叠加的波函数的动态相位累积。在这里，我们将探讨肖尔的量子因子分解算法的敏感性，这样的错误。我们的研究结果清楚地表明了严重的敏感性Shor的因式分解算法之间的连续酉变换的延迟时间的存在。具体地，在存在这些{ \it相干“错误”}的情况下，获得正确答案的概率随着工作寄存器的量子位的数量呈指数下降。本文提出了一种特别简单的相位匹配方法，以{ \it避免}或抑制这些{ \it相干错误}时，使用Shor的算法因式分解整数。这个相位匹配条件的鲁棒性进行评估分析或数值分解的几个整数：$4, 15, 21$，和33。
Time-dependent Rabi frequencies to protect quantum operations on an atomic qutrit by continuous dynamical decoupling
本文研究利用时间依赖拉比频率和连续动力学解耦保护原子三能级系统量子门操作免受环境噪声影响，并通过模拟验证其可行性，最终应用于保护区分三元素排列奇偶性的量子算法。
A class of unitary operations generated by idealized, semiclassical fields is studied. The operations implemented by sharp potential kicks are revisited and the possibility of performing them by softly varying external fields is examined. The possibility of using the ion traps as 'operation factories' transforming quantum states is discussed. The non-perturbative algorithms indicate that the results of abstract $δ$-pulses of oscillator potentials can become real. Some of them, if empirically achieved, could be essential to examine certain atypical quantum ideas. In particular, simple dynamical…
Quantum phase estimation algorithms with delays: effects of dynamical phases
执行实际量子计算所需的顺序操作之间不可避免的有限时间间隔会降低量子计算机的性能。在这些延迟期间，由于量子比特的叠加波函数的自由演化，产生了不想要的相对动力学相位。一般来说，这些相干的“误差”修改了所需的量子干涉，从而破坏了正确的结果，相比之下，理想的标准量子计算不考虑连续酉操作之间的延迟的影响。在这里，我们表明，在量子相位估计算法的框架中，这些相干相位的“错误”，所产生的时间延迟之间的顺序操作，可以避免通过设置的延迟时间，以满足一定的匹配条件。
Quantum information technologies demand highly accurate control over quantum systems. Achieving this requires control techniques that perform well despite the presence of decohering noise and other adverse effects. Here, we review a general technique for designing control fields that dynamically correct errors while performing operations using a close relationship between quantum evolution and geometric space curves. This approach provides access to the global solution space of control fields that accomplish a given task, facilitating the design of experimentally feasible gate operations for a…
As is well-known in the context of topological insulators and superconductors, short-range-correlated fermionic pure Gaussian states with fundamental symmetries are systematically classified by the periodic table. We revisit this topic from a quantum-information-inspired operational perspective without referring to any Hamiltonians, and apply the formalism to bosonic Gaussian states as well as (both fermionic and bosonic) locality-preserving unitary Gaussian operations. We find that while bosonic Gaussian states are all trivial, there exist nontrivial bosonic Gaussian operations that cannot be…
Quantum coherence, like entanglement, is a fundamental resource in quantum information. In recent years, remarkable progress has been made in formulating resource theory of coherence from a broader perspective. The notions of block-coherence and POVM-based coherence have been established. Certain challenges, however, remain to be addressed. It is difficult to define incoherent operations directly, without requiring incoherent states, which proves a major obstacle in establishing the resource theory of dynamical coherence. In this paper, we overcome this limitation by introducing an alternate d…
Hierarchy of Qubit Dynamical Maps in the Presence of Symmetry and Coherence
该研究探究对称性与量子热力学变换的关系，证明U(1)守恒约束热操作的层级，提出借助奇宇称环境相干性打破层级的双量子比特方案，验证了量子相干性在功提取等场景的热力学增益。
Logical operations with a dynamical qubit in Floquet-Bacon-Shor code
该研究在超导量子处理器上实现了Floquet-Bacon-Shor码，展示了动态逻辑量子比特的逻辑运算和高保真度的纠缠态生成。
Single-Operation Rydberg Phase Gates via Dynamic Population Suppression
该研究提出了一种基于动态人口抑制的Rydberg相门技术，实现了任意阻塞强度下的高保真纠缠相门，为量子计算提供了新的实现路径。
In many quantum technologies adiabatic processes are used for coherent quantum state operations, offering inherent robustness to errors in the control parameters. The main limitation is the long operation time resulting from the requirement of adiabaticity. The superadiabatic method allows for faster operation, by applying counterdiabatic driving that corrects for excitations resulting from the violation of the adiabatic condition. In this article we show how to construct the counterdiabatic Hamiltonian in a system with forbidden transitions by using two-photon processes and how to correct for…
Environmentally induced Quantum Dynamical Phase Transition in the spin swapping operation
量子信息处理依赖于相干量子动力学来精确控制其基本操作。双自旋系统中的交换门交换简并态|+，->和|-,+>.在NMR中，这是通过打开和关闭自旋-自旋相互作用b=ΔE来实现的，该相互作用使能级分裂并引起具有固有频率ΔE/ \hbar的振荡。强度\hbar /τ_{SE}与相邻自旋的环境的相互作用在退相干时间尺度τ_n内降低了这种振荡。虽然实验频率ω和退相干时间τ_ε分别与b/ \hbar和τ_{SE}成正比，但我们给出的实验表明ω和τ_ε都有很大的偏差。通过求解多自旋动力学方程，证明了交换区限制在ΔE τ_{SE} > \hbar .超过与环境的临界相互作用，交换冻结，退相干速率下降为1/τ_PDMATHABMN（b/ \hbar）^2 τ_{SE}。当ω \propto \sqrt{(b/\hbar)^{2}-(k/τ_{SE})^2}变为虚的，类似于过阻尼的经典振子时，量子动力学相位之间的跃迁发生。在这里，0<k^2<1仅取决于系统-环境相互作用的各向异性，对于各向同性为0，对于XY相互作用为1。这种由量子芝诺效应主导的阶段的关键开始为控制量子动力学提供了新的机会。
Characterizing quantum phase transitions by single qubit operations
我们引入可观测量，借用量子信息理论的概念，在自旋系统的量子相变的表征。这些观测量是唯一定义的单自旋幺正操作。我们定义了基态和由单量子比特局域门作用产生的态之间的能隙。我们表明，这个静态量只涉及单网站的期望和两点关联函数的基态。然后我们讨论了一种动力学局域可观测量，定义为对基态进行瞬时单比特微扰后量子态演化的加速度。这个量也涉及三点相关性。我们证明了在一类自旋系统中，静态和动态观测量都能完全检测和表征量子临界点。
In this paper, we propose a scheme to eliminate the influence of noises on system dynamics, by means of a sequential unsharp measurements and unitary feedback operations. The unsharp measurements are carried out periodically during system evolution, while the feedback operations are well designed based on the eigenstates of the density matrices of the exact (noiseless) dynamical states and its corresponding post-measurement states. For illustrative examples, we show that the dynamical trajectory errors caused by both static and non-static noises are successfully eliminated in typical two-level…
For finite-dimensional quantum systems, such as qubits, a well established strategy to protect such systems from decoherence is dynamical decoupling. However many promising quantum devices, such as oscillators, are infinite dimensional, for which the question if dynamical decoupling could be applied remained open. Here we first show that not every infinite-dimensional system can be protected from decoherence through dynamical decoupling. Then we develop dynamical decoupling for continuous variable systems which are described by quadratic Hamiltonians. We identify a condition and a set of opera…
We consider a qubit coupled to another system (its environment), and discuss the relationship between the effects of subjecting the qubit to either a dynamical decoupling sequence of unitary operations, or a sequence of projective measurements. We give a formal statement concerning equivalence of a sequence of coherent operations on a qubit, precisely operations from a minimal set $\left\{\mathbf{I}_Q,\hatσ_x\right\}$, and a sequence of projective measurements of $\hatσ_x$ observable. Using it we show that when the qubit is subjected to $n$ such successive projective measurements at certain ti…
Protecting quantum states from the decohering effects of the environment is of great importance for the development of quantum computation devices and quantum simulators. Here, we introduce a continuous dynamical decoupling protocol that enables us to protect the entangling gate operation between two qubits from the environmental noise. We present a simple model that involves two qubits which interact with each other with a strength that depends on their mutual distance and generates the entanglement among them, as well as in contact with an environment. The nature of the environment, that is,…
Towards the ultimate limits of quantum channel discrimination and quantum communication
本研究推进了量子信道判别及其基本极限的理解，开发了量子散度新工具，建立无记忆信道判别的量子Stein引理，证明相干与顺序策略下指数强逆性质等价，并揭示信道容量与信道散度数学结构的深刻联系。
We investigate the entangling capacity of dynamical operations when provided with local ancilla. A comparison is made between the entangling capacity with and without the assistance of prior entanglement. An analytic solution is found for the log-negativity entangling capacity of two-qubit gates, which equals the entanglement of the Choi matrix isomorphic to the unitary operator. Surprisingly, the availability of prior entanglement does not affect this result; a property we call resource independence of the entangling capacity. We prove several useful upper-bounds on the entangling capacity th…
Geometric phase is a promising element to induce high-fidelity and robust quantum operations due to its built-in noise-resilience feature. Unfortunately, its practical applications are usually circumscribed by requiring complex interactions among multiple levels/qubits and the longer gate-time than the corresponding dynamical ones. Here, we propose a general framework of geometric quantum computation with the integration of the time-optimal control technique, where the shortest smooth geometric path is found to realize accelerated geometric quantum gates, and thus greatly decreases the gate er…
The fidelity of applications on near-term quantum computers is limited by hardware errors. In addition to errors that occur during gate and measurement operations, a qubit is susceptible to idling errors, which occur when the qubit is idle and not actively undergoing any operations. To mitigate idling errors, prior works in the quantum devices community have proposed Dynamical Decoupling (DD), that reduces stray noise on idle qubits by continuously executing a specific sequence of single-qubit operations that effectively behave as an identity gate. Unfortunately, existing DD protocols have bee…
We develop a unified framework to characterize one-shot transformations of dynamical quantum resources in terms of resource quantifiers, establishing universal conditions for exact and approximate transformations in general resource theories. Our framework encompasses all dynamical resources represented as quantum channels, including those with a specific structure --- such as boxes, assemblages, and measurements --- thus immediately applying in a vast range of physical settings. For the particularly important manipulation tasks of distillation and dilution, we show that our conditions become …
The present thesis deals with various methods of quantum error correction. It is divided into two parts. In the first part, dynamical decoupling methods are considered which have the task of suppressing the influence of residual imperfections in a quantum memory. The suppression is achieved by altering the dynamics of an imperfect quantum memory with the help of a sequence of local unitary operations applied to the qudits. Whereas up to now the operations of such decoupling sequences have been constructed in a deterministic fashion, strategies are developed in this thesis which construct the o…
For adiabatic controls of quantum systems, the non-adiabatic transitions are reduced by increasing the operation time of processes. Perfect quantum adiabaticity usually requires the infinitely slow variation of control parameters. In this paper, we propose the dynamical quantum geometric tensor, as a metric in the control parameter space, to speed up quantum adiabatic processes and reach quantum adiabaticity in relatively short time. The optimal protocol to reach quantum adiabaticity is to vary the control parameter with a constant velocity along the geodesic path according to the metric. For …
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