Duplicating classical bits with universal quantum cloning machine

It seems there is a large gap between quantum cloning and classical duplication since quantum mechanics forbid perfect copies of unknown quantum states. In this paper, we prove that a classical duplication process can be realized by using a universal quantum cloning machine(QCM). A classical bit is encoded not on a single quantum state, but on a large number of single identical quantum states. Errors are inevitable when copying these identical quantum states due to the quantum no-cloning theorem. When a small part of errors are ignored, i.e., errors as the minority are automatically corrected by the majority, the fidelity of duplicated copies of classical information will approach unity infinitely. In this way, the classical bits can be duplicated precisely with a universal QCM, which presents a natural transition from quantum cloning to classical duplication. The implement of classical duplication by using QCM shines new lights on the universality of quantum mechanics.     

Optimal filters for photon cloning with an optical amplifier

We study the performance of a practical quantum cloning scheme consisting of a continuously pumped broadband optical amplifier followed by optimal spectral and temporal filters for spontaneous emission suppression. Our simulation results demonstrate that the fidelity of this system is no better than a random cloning machine when the average input photon number is below one, but asymptotically approaches the quantum limit of an optimal quantum cloning machine as the input photon number increases. We also show that this system has a better fidelity than cloning based on state estimation, though for a large number of clones both cloning methods asymptotically approach the quantum limit.     

量子信息讲座 第五讲 量子克隆与量子复制

量子态不可克隆体现了量子力学的固有特性,它是量子信息科学的重要基础之一．文章简要介绍了量子不可克隆定理的物理内容以及量子复制机的基本原理,通过幺正坍缩过程我们构造了一种概率量子克隆机,并论证所有线性无关的量子态都可以被概率量子克隆机克隆     

量子比特的普适远程翻转和克隆

提出一种把量子隐形传态、最佳普适量子比特翻转和最佳普适量子克隆三者结合起来的量子比特普适远程翻转和克隆方案.当发送者和处于不同地点的三个接收者共享一个特定的四粒子纠缠态作为量子信道时,通过发送者的Bell基测量、经典通信和各个接收者的局域幺正变换,一个接收者能够以2/3的最佳保真度得到一份原未知量子比特的正交补态,另外两个接收者能够分别以5/6的最佳保真度得到原未知量子比特的一份拷贝.此方案用较少的量子纠缠资源同时完成了未知量子比特的普适远程翻转和克隆,且其保真度分别达到了最佳.实现此方案的关键在于构造出发送者和接收者共享的特定四粒子纠缠态作为量子信道,分析了此特殊四粒子态内在的纠缠结构.     

Applications of quantum cloning

Quantum Cloning Machines (QCMs) allow for the copying of information, within the limits imposed by quantum mechanics. These devices are particularly interesting in the high-gain regime, i.e., when one input qubit generates a state of many output qubits. In this regime, they allow for the study of certain aspects of the quantum to classical transition. The understanding of these aspects is the root of the two recent applications that we will review in this paper: the first one is the Quantum Cloning Radiometer, a device which is able to produce an absolute measure of spectral radiance. This device exploits the fact that in the quantum regime information can be copied with only finite fidelity, whereas when a state becomes macroscopic, this fidelity gradually increases to 1. Measuring the fidelity of the cloning operation then allows to precisely determine the absolute spectral radiance of the input optical source. We will then discuss whether a Quantum Cloning Machine could be used to produce a state visible by the naked human eye, and the possibility of a Bell Experiment with humans playing the role of detectors.     

Separating the classical and quantum information via quantum cloning

An application of quantum cloning to optimally interface a quantum system with a classical observer is presented; in particular, we describe a procedure to perform a minimal disturbance measurement on a single qubit by adopting a 1-->2 cloning machine followed by a generalized measurement on a single clone and the anticlone or on the two clones. Such a scheme can be applied to enhance the transmission fidelity over a lossy quantum channel.     

A remark on the optimal cloning of an N-level quantum system

We study quantum cloning machines (QCM) that act on an unknown N-level quantum state and make M copies. We give a formula for the maximum of the fidelity of cloning and exhibit the unitary transformations that realize this optimal fidelity. We also extend the results to treat the case of M copies from () identical N-level quantum systems. Received 21 September 1999     

Continuous-variable quantum state transfer with partially disembodied transport

We propose a new protocol of implementing continuous-variable quantum state transfer using partially disembodied transport. This protocol may improve the fidelity at the expense of the introduction of a semiquantum channel between the parties, in comparison with quantum teleportation using the same strength of entanglement. Depending on the amount of information destroyed in the measurement, this protocol may be regarded as a teleportation protocol (complete destruction of input state), or as a cloning protocol (partial destruction), or as a direct transmission (no destruction). This scheme can be straightforwardly implemented with a setup that is at present experimentally accessible.     

Implementing 2→<Emphasis Type="Italic">M</Emphasis> Phase-covariant Cloning in Spin Networks

We propose a scheme to implement 2→M phase-covariant quantum cloning machine by using a M+2 spin star network in which the two central spins interact with the M outer spins respectively. The effect of the magnetic field on the fidelity of the cloning is also investigated. By applying an external magnetic field on the spin system, the fidelity of the cloning machine can be largely improved.     

Quantum cloning with an optical fiber amplifier

It has been shown theoretically that a light amplifier working on the physical principle of stimulated emission should achieve optimal quantum cloning of the polarization state of light. We demonstrate close-to-optimal universal quantum cloning of polarization in a standard fiber amplifier for telecom wavelengths. For cloning 1-->2 we find a fidelity of 0.82, the optimal value being 5 / 6=0.83.     

Cloning of continuous quantum variables

The cloning of quantum variables with continuous spectra is analyzed. A Gaussian quantum cloning machine is exhibited that copies equally well the states of two conjugate variables such as position and momentum. It also duplicates all coherent states with a fidelity of 2/3. More generally, the copies are shown to obey a no-cloning Heisenberg-like uncertainty relation.     

Quantum Switchboard with Coupled-Cavity Array

The ability to control the flow of quantum information is deterministically useful for scaling up quantum computation. In this paper, we demonstrate a controllable quantum switchboard which directs the teleportation protocol to one of two targets, fully dependent on the sender’s choice. Importantly, the quantum switchboard also acts as a optimal quantum cloning machine, which allows the receivers to recover the unknown quantum state with a maximal fidelity of 56. This protects the system from the complete loss of quantum information in the event that the teleportation protocol fails. We also provide an experimentally feasible physical implementation of the proposal using a coupled-cavity array. The proposed switchboard can be utilized for the efficient routing of quantum information in a large quantum network.     

Optimal asymmetric economical state-dependent cloners

We present the optimal asymmetric economical 1-3 phase-covariant and real state cloning in two-dimensions. The fidelity distributions of copies of two state-dependent cloners are the same, and higher than that of the optimal asymmetric universal quantum cloning. Using a quantum network, we calculate the single-qubit rotation angles to implement two symmetric economical state-dependent cloners. We also propose an experimentally feasible scheme to implement the optimal asymmetric economical 1-3 phase-covariant cloner. The scheme can be realized with the success probability of 100%.     

Entanglement Preserving in Quantum Copying of Three-Qubit Entangled State

We study the degree to which quantum entanglement survives when a three-qubit entangled state iscopied by using local and non-local processes, respectively, and investigate iterating quantum copyingfor the three-qubitsystem. There may exist inter-three-qubit entanglement and inter-two-qubit entanglement for the three-qubit system.We show that both local and non-local copying processes degrade quantum entanglement in the three-particle systemdue to a residual correlation between the copied output and the copying machine. We also show that the inter-two-qubitentanglement is preserved better than the inter-three-qubit entanglement in the local cloning process. We find thatnon-local cloning is much more efficient than the local copying for broadcasting entanglement, and output state vianon-local cloning exhibits the fidelity better than local cloning.     

On universal quantum cloning and state estimation

Both perfect cloning and perfect state estimation of an unknown pure quantum state are impossible, due to principles of quantum mechanics. Nevertheless, they can be performed imperfectly. A link between these two scenarios allows us to derive an upper bound for the fidelity in one of them, given an upper bound is known in the other. Furthermore, it is shown that also a lower bound on cloning is related to an upper bound on state estimation. Received: 15 June 1999 / Revised version: 23 September 1999 / Published online: 10 November 1999     

Proposal for inverting the quantum cloning of photons

We propose an experiment where a photon is first cloned by stimulated parametric down-conversion, making many (imperfect) copies, and then the cloning transformation is inverted, regenerating the original photon while destroying the copies. Focusing on the case where the initial photon is entangled with another photon, we study the conditions under which entanglement can be proven in the final state. The proposed experiment would provide a clear demonstration that quantum information is preserved in quantum cloning. It would furthermore allow a definitive experimental proof for micro-macro entanglement in the intermediate multiphoton state, which is still an outstanding challenge. Finally, it might provide a quantum detection technique for small differences in transmission (e.g., in biological samples), whose sensitivity scales better with the number of photons used than a classical transmission measurement.     

Non-Gaussian cloning of quantum coherent states is optimal

We consider the optimal cloning of quantum coherent states with single-clone and joint fidelity as figures of merit. While the latter is maximized by a Gaussian cloner, the former is not: the optimal single-clone fidelity for a symmetric 1-to-2 cloner is 0.6826, compared to 2/3 in a Gaussian setting. This cloner can be realized with an optical parametric amplifier and certain non-Gaussian bimodal states. Finally, we show that the single-clone fidelity of the optimal 1-to-infinity cloner is 1/2. It is achieved by a Gaussian scheme and cannot be surpassed even with supplemental bound entangled states.     

Fidelity of quantum information for V-type three-level atom interacting with a number state light field in Kerr medium

In this paper the evolution characteristics of the fidelity of quantum information for the V-type three-level atom interacting with number state light field in Kerr meddium are investigated. It shows that the periodicity of the evolutions of fidelity of quantum information is influenced by the Kerr coefficient, the photon number of the initial field and intensity of light. The evolutions of the fidelity of quantum information are modulated by the initial number state field. The Rabi oscillation frequency and the modulation frequency of fidelity for the field and the system vary with the value of the Kerr coefficient. The evolutions of fidelity of quantum information obviously show the quantum collapse and revival behaviours in the system of atom interacting with light field.     

Fidelity between Gaussian mixed states with quantum state quadrature variances

In this paper, from the original definition of fidelity in a pure state, we first give a well-defined expansion fidelity between two Gaussian mixed states. It is related to the variances of output and input states in quantum information processing. It is convenient to quantify the quantum teleportation(quantum clone) experiment since the variances of the input(output) state are measurable. Furthermore, we also give a conclusion that the fidelity of a pure input state is smaller than the fidelity of a mixed input state in the same quantum information processing.