基于腔QED及连续变量的量子信息处理
摘要
量子信息学是量子物理学与信息科学相结合的产物,是一门新兴的交叉学科,它是一种通过量子系统的各种相干特性,进行计算、编码和信息传输的全新信息方式。量子信息包括量子密码、量子计算以及量子通信等。其中量子计算可以利用各种量子算法去降低特定运算的复杂度,这就要求我们在实际的物理系统中实现各种的逻辑门操作,从而对目标量子比特进行控制。此外,量子信息处理还涉及量子态制备以及对量子态的克隆等各个方面,其中前者可以为量子信息处理提供所需的纠缠态,而对后者的讨论可以加深对量子力学的不可克隆定理的认识。
目前,量子信息处理在光学系统、离子阱、腔QED、核磁共振、量子点等各种的量子系统中都有很大的发展。其中,腔QED为实现量子信息处理提供了一个良好的平台。迄今为止,在光学腔和微波腔的实验中已经实现了量子的非破坏测量、量子态制备、量子逻辑门以及单光子源的制备等,但是仍然存在一些技术上的困难必须克服,因而各种基于腔QED技术实现量子信息处理的方案是很多实验组所关注的焦点。此外,随着实验技术的发展,特别是利用线性器件和前馈控制完成的非线性相互作用技术的成熟,在光学系统中的连续变量领域,多体纠缠的制备以及相干态克隆、隐形传态等一系列实验已经相继完成。基于腔QED以及连续变量这两个领域,我们的工作集中在实现相位门操作,以及讨论已知相位相干态克隆、配对相干态的制备。
1.在腔QED中实现原子编码和光子编码的受控相位门
量子计算机比经典计算机能更有效地解决诸如大数因子分解等一些计算难题,而通过利用两量子比特的受控相位门以及任意的单比特逻辑门可以构造任意的多比特逻辑门,从而实现普适量子计算。基于腔QED系统,我们分别利用原子和光子编码,实现了两比特受控相位门操作,其中前者还可以直接推广到N量子比特的情况,而且操作时间不随着量子比特的增多而变化;而后者则有效地克服原子自发辐射对门操作的影响。同时,我们还对系统的消相干对这两个方案的影响进行了讨论,给出门操作的保真度随自发辐射以及腔衰减率变化的数值解。
2.在连续变量中实现已知相位的相干态克隆
量子信息最早起源于研究单粒子的离散变量系统,随后逐渐拓展到具有无限Hilbert空间的连续变量系统。目前在量子信息中利用的连续变量光场主要是相干态光场和压缩态光场,这两者在量子通讯中皆有着广泛的应用。由于量子不可克隆定理,我们不能精确地克隆一个未知的量子态,这是量子密码的重要前提,它确保了量子密码的安全性。但是人们可以尽可能精确地复制所有输入态,我们在这里给出一种已知相位的相干态克隆方案,与以前的方案相比较,通过减少辅助模以及利用压缩真空态,可以极大地提高克隆的保真度。随后,为了简化实验难度,我们提出一个实验可行的方案,利用线性器件,零拍测量以及前馈操作,完成局域的已知相位相干态克隆。更进一步,通过引入一个额外的EPR纠缠态,实现非局域的克隆过程。
3.利用弱cross-Kerr介质制备配对相干态
在量子通讯、量子计算和量子密码中,量子态是信息的载体,量子信息处理归根到底是一种量子态的操纵过程。因此,人们期望按照自己的意愿实现对量子态的制备和操纵,以达到特定的目标。其中,配对相干态是一种拥有优异的非经典性质的量子态,而且,基于高效的零拍测量,特定的配对相干态可以违背Clauser-Horne-Bell不等式,从而验证局域隐变量理论和量子力学之间谁孰谁非。我们利用弱cross-Kerr介质、on/off探测器以及相干态,实现配对相干态的制备,该方案可以克服现有光子探测器效率低下的问题。我们还讨论了该方案的可行性,并且以保真度逼近1地生成可以最大违背CH-Bell不等式的配对相干态。最后,当输入态用其他量子态取代相干态时,可以分别得到双模猫态以及有限维的任意双模光子数关联态。
Quantum information science is the new related areas of quantum mechanics andclassical information science. By using various coherent properties of quantum sys-tems, quantum information science manifests a novel type of information processing incomputation, encoding and information transmission. Quantum information process-ing is mainly composed of quantum cryptography, quantum computation and quan-tum communication. In quantum computation, one can obviously decrease the com-putational complexity by using quantum algorithm. Besides the quantum gate design,quantum information processing also includes quantum state engineering and quantumstate cloning, the former can provide the entanglement state which we need in quantuminformation processing, and the latter can go further insight in the quantum no-cloningtheorem.
So far, quantum information processing has been wonderfully developed in severalsystems, such as optical system, trapped iron, cavity QED, nuclear magnetic resonance(NMR), quantum dots and so on. Among them, cavity QED offers an excellent stagefor quantum information processing. Up to now, quantum non-demolition measure-ment, quantum state preparations, quantum gates and single-photon sources have beenrealized in the experiments with cavity QED. However, there still lots of technologicalproblems to be overcome, so the efficient schemes in the context of cavity QED attracta lot of attentions. Besides the field of cavity QED, the optical technology recently hasbeen rapidly developed by using linear optical devices, homodyne measurement andfeedforward operations. In the continuous variables domain of optical systems, many-body entanglement state preparations, coherent state cloning and quantum teleportationhave been realized in the experiment. In this thesis, we focus on several proposals forquantum information processing in these two fields.
1. Quantum controlled-phase gate for atomic and photonic qubits based on cavityQED
It has been shown that some intractable problems for classical computers can besolved efficiently by quantum computer. For example, using qubits and quantum op-erations, Shor’s algorithm can give an exponential speedup for factoring big numbersand Grover’s algorithm can provide a quadratic speedup for unordered database search.It is known that two-qubit controlled-phase gates and one-qubit gates are universal for constructing quantum computer. Based on cavity QED, we proposed the two-qubitquantum controlled phase gate for atomic and photonic qubits, respectively. The for-mer can be generalized to N-qubit case with the same interaction time, and the latteris insensitive to the in?uence of atomic spontaneous emission. Meanwhile, we alsodiscussed the in?uence of the system decoherence and showed the gate fidelity versussuch in?uences in these two schemes.
2. The cloning of coherent state with known phases
Quantum information science originally investigated discrete variables system.Subsequently, it was extended to the continuous variables systems with infinite dimen-sional Hilbert space. The mainly continuous variables of light in the lab are coherentstate and squeezed state, both of them are widely used in quantum communication. Itis well known that we can not clone an arbitrary quantum state based on quantum no-cloning theorem, which is the foundation of quantum cryptography security. However,we can clone the quantum state as close as possible. We proposed a scheme to achievethe cloning of coherent state with known phases. Compared with the previous proposal,this scheme obviously improves the cloning fidelity by reducing an auxiliary state andusing squeezed vacuum states. Next, in order to simplify the difficulties of experiment,we gave a method to realize the local cloning of coherent state with known phases byusing linear optical devices, homodyne measurement and feedforward operations. Fur-thermore, by employing an additional EPR state, a nonlocal cloning process can berealized.
3. Preparation of the pair coherent state with weak cross-Kerr media
In quantum communication, quantum computation and quantum cryptography,quantum state is the information carrier, so quantum information processing can bebrie?y seen as a process of manipulating quantum state. We need to prepare and controlquantum state to achieve a certain goal. The pair coherent state is a quantum state withprominent nonclassical properties. It can also violate the Clauser-Horne-Bell inequal-ity based on homodyne measurement. So the experimental realization of pair coherentstate is very practically important. We gave a nonlocal method for generating such statewith two traveling wave fields in distinct districts by using weak cross-Kerr media andon/off detection. When the input states are coherent states, we can probabilisticallygenerate the pair coherent state. This scheme is robust against the low quantum effi-ciency of photon detectors. Moreover, we revealed that two-mode Schro¨dinger cat stateand generalized two-mode correlated photon number state can be obtained by replacingthe input states.
目前,量子信息处理在光学系统、离子阱、腔QED、核磁共振、量子点等各种的量子系统中都有很大的发展。其中,腔QED为实现量子信息处理提供了一个良好的平台。迄今为止,在光学腔和微波腔的实验中已经实现了量子的非破坏测量、量子态制备、量子逻辑门以及单光子源的制备等,但是仍然存在一些技术上的困难必须克服,因而各种基于腔QED技术实现量子信息处理的方案是很多实验组所关注的焦点。此外,随着实验技术的发展,特别是利用线性器件和前馈控制完成的非线性相互作用技术的成熟,在光学系统中的连续变量领域,多体纠缠的制备以及相干态克隆、隐形传态等一系列实验已经相继完成。基于腔QED以及连续变量这两个领域,我们的工作集中在实现相位门操作,以及讨论已知相位相干态克隆、配对相干态的制备。
1.在腔QED中实现原子编码和光子编码的受控相位门
量子计算机比经典计算机能更有效地解决诸如大数因子分解等一些计算难题,而通过利用两量子比特的受控相位门以及任意的单比特逻辑门可以构造任意的多比特逻辑门,从而实现普适量子计算。基于腔QED系统,我们分别利用原子和光子编码,实现了两比特受控相位门操作,其中前者还可以直接推广到N量子比特的情况,而且操作时间不随着量子比特的增多而变化;而后者则有效地克服原子自发辐射对门操作的影响。同时,我们还对系统的消相干对这两个方案的影响进行了讨论,给出门操作的保真度随自发辐射以及腔衰减率变化的数值解。
2.在连续变量中实现已知相位的相干态克隆
量子信息最早起源于研究单粒子的离散变量系统,随后逐渐拓展到具有无限Hilbert空间的连续变量系统。目前在量子信息中利用的连续变量光场主要是相干态光场和压缩态光场,这两者在量子通讯中皆有着广泛的应用。由于量子不可克隆定理,我们不能精确地克隆一个未知的量子态,这是量子密码的重要前提,它确保了量子密码的安全性。但是人们可以尽可能精确地复制所有输入态,我们在这里给出一种已知相位的相干态克隆方案,与以前的方案相比较,通过减少辅助模以及利用压缩真空态,可以极大地提高克隆的保真度。随后,为了简化实验难度,我们提出一个实验可行的方案,利用线性器件,零拍测量以及前馈操作,完成局域的已知相位相干态克隆。更进一步,通过引入一个额外的EPR纠缠态,实现非局域的克隆过程。
3.利用弱cross-Kerr介质制备配对相干态
在量子通讯、量子计算和量子密码中,量子态是信息的载体,量子信息处理归根到底是一种量子态的操纵过程。因此,人们期望按照自己的意愿实现对量子态的制备和操纵,以达到特定的目标。其中,配对相干态是一种拥有优异的非经典性质的量子态,而且,基于高效的零拍测量,特定的配对相干态可以违背Clauser-Horne-Bell不等式,从而验证局域隐变量理论和量子力学之间谁孰谁非。我们利用弱cross-Kerr介质、on/off探测器以及相干态,实现配对相干态的制备,该方案可以克服现有光子探测器效率低下的问题。我们还讨论了该方案的可行性,并且以保真度逼近1地生成可以最大违背CH-Bell不等式的配对相干态。最后,当输入态用其他量子态取代相干态时,可以分别得到双模猫态以及有限维的任意双模光子数关联态。
Quantum information science is the new related areas of quantum mechanics andclassical information science. By using various coherent properties of quantum sys-tems, quantum information science manifests a novel type of information processing incomputation, encoding and information transmission. Quantum information process-ing is mainly composed of quantum cryptography, quantum computation and quan-tum communication. In quantum computation, one can obviously decrease the com-putational complexity by using quantum algorithm. Besides the quantum gate design,quantum information processing also includes quantum state engineering and quantumstate cloning, the former can provide the entanglement state which we need in quantuminformation processing, and the latter can go further insight in the quantum no-cloningtheorem.
So far, quantum information processing has been wonderfully developed in severalsystems, such as optical system, trapped iron, cavity QED, nuclear magnetic resonance(NMR), quantum dots and so on. Among them, cavity QED offers an excellent stagefor quantum information processing. Up to now, quantum non-demolition measure-ment, quantum state preparations, quantum gates and single-photon sources have beenrealized in the experiments with cavity QED. However, there still lots of technologicalproblems to be overcome, so the efficient schemes in the context of cavity QED attracta lot of attentions. Besides the field of cavity QED, the optical technology recently hasbeen rapidly developed by using linear optical devices, homodyne measurement andfeedforward operations. In the continuous variables domain of optical systems, many-body entanglement state preparations, coherent state cloning and quantum teleportationhave been realized in the experiment. In this thesis, we focus on several proposals forquantum information processing in these two fields.
1. Quantum controlled-phase gate for atomic and photonic qubits based on cavityQED
It has been shown that some intractable problems for classical computers can besolved efficiently by quantum computer. For example, using qubits and quantum op-erations, Shor’s algorithm can give an exponential speedup for factoring big numbersand Grover’s algorithm can provide a quadratic speedup for unordered database search.It is known that two-qubit controlled-phase gates and one-qubit gates are universal for constructing quantum computer. Based on cavity QED, we proposed the two-qubitquantum controlled phase gate for atomic and photonic qubits, respectively. The for-mer can be generalized to N-qubit case with the same interaction time, and the latteris insensitive to the in?uence of atomic spontaneous emission. Meanwhile, we alsodiscussed the in?uence of the system decoherence and showed the gate fidelity versussuch in?uences in these two schemes.
2. The cloning of coherent state with known phases
Quantum information science originally investigated discrete variables system.Subsequently, it was extended to the continuous variables systems with infinite dimen-sional Hilbert space. The mainly continuous variables of light in the lab are coherentstate and squeezed state, both of them are widely used in quantum communication. Itis well known that we can not clone an arbitrary quantum state based on quantum no-cloning theorem, which is the foundation of quantum cryptography security. However,we can clone the quantum state as close as possible. We proposed a scheme to achievethe cloning of coherent state with known phases. Compared with the previous proposal,this scheme obviously improves the cloning fidelity by reducing an auxiliary state andusing squeezed vacuum states. Next, in order to simplify the difficulties of experiment,we gave a method to realize the local cloning of coherent state with known phases byusing linear optical devices, homodyne measurement and feedforward operations. Fur-thermore, by employing an additional EPR state, a nonlocal cloning process can berealized.
3. Preparation of the pair coherent state with weak cross-Kerr media
In quantum communication, quantum computation and quantum cryptography,quantum state is the information carrier, so quantum information processing can bebrie?y seen as a process of manipulating quantum state. We need to prepare and controlquantum state to achieve a certain goal. The pair coherent state is a quantum state withprominent nonclassical properties. It can also violate the Clauser-Horne-Bell inequal-ity based on homodyne measurement. So the experimental realization of pair coherentstate is very practically important. We gave a nonlocal method for generating such statewith two traveling wave fields in distinct districts by using weak cross-Kerr media andon/off detection. When the input states are coherent states, we can probabilisticallygenerate the pair coherent state. This scheme is robust against the low quantum effi-ciency of photon detectors. Moreover, we revealed that two-mode Schro¨dinger cat stateand generalized two-mode correlated photon number state can be obtained by replacingthe input states.
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