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Journal ArticleDOI

Classical and quantum control of a simple quantum system

01 Dec 2007-International Journal of Quantum Information (World Scientific Publishing Company)-Vol. 05, Iss: 06, pp 857-884
TL;DR: In this article, a qubit which is prepared in one of two non-orthogonal states and subjected to bit-flipping noise is considered, and the objective is to use measurement and feedback control to correct the state of the qubit.
Abstract: A qubit which is prepared in one of two non-orthogonal states and subjected to bit-flipping noise is considered. The objective is to use measurement and feedback control to correct the state of the qubit. Three classical schemes using projective measurements, i.e. discrimination and re-preparation, do nothing and random preparation, have been discussed, and are not optimal with respect to a performance which is quantified by the average fidelity of the corrected state compared to the initial state. In addition, one quantum scheme using a non-projective measurement with an optimum measurement strength achieves the best trade-off between gaining information about the system and disturbing it through measurement back-action. The performance of a quantum control scheme outperforms the classical schemes. Furthermore, no universal corrected scheme is discussed.
Citations
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Journal ArticleDOI
TL;DR: In this paper, a general bipartite anisotropic Ising model including an inhomogeneous magnetic field is analyzed in a non-local basis, and the evolution is expressed in the Bell basis, it shows a regular block structure suggesting a SU(2) decomposition.
Abstract: Entanglement is considered a basic physical resource for modern quantum applications as Quantum Information and Quantum Computation. Interactions based on specific physical systems able to generate and sustain entanglement are subject to deep research to get understanding and control on it. Atoms, ions or quantum dots are considered key pieces in quantum applications because they are elements in the development toward a scalable spin-based quantum computer through universal and basic quantum operations. Ising model is a type of interaction generating entanglement in quantum systems based on matter. In this work, a general bipartite anisotropic Ising model including an inhomogeneous magnetic field is analyzed in a non-local basis. This model summarizes several particular models presented in literature. When evolution is expressed in the Bell basis, it shows a regular block structure suggesting a SU(2) decomposition. Then, their algebraic properties are analyzed in terms of a set of physical parameters which define their group structure. In particular, finite products of pulses in this interaction are analyzed in terms of SU(4) covering. Thus, evolution denotes remarkable properties, in particular those related potentially with entanglement and control, which give a fruitful arena for further quantum developments and generalization.

19 citations

Journal ArticleDOI
TL;DR: In this paper, a general anisotropic three dimensional Ising model including an inhomogeneous magnetic field is analyzed to obtain their evolution and then, their algebraic properties which are controlled through a set of physical parameters.
Abstract: Entanglement is considered as a basic physical resource for modern quantum applications in Quantum Information and Quantum Computation theories. Interactions able to generate and sustain entanglement are subject to deep research in order to have understanding and control on it, based on specific physical systems. Atoms, ions or quantum dots are considered a key piece in quantum applications because is a basic piece of developments towards a scalable spin-based quantum computer through universal and basic quantum operations. Ising model is a type of interaction which generates and modifies entanglement properties of quantum systems based on matter. In this work, a general anisotropic three dimensional Ising model including an inhomogeneous magnetic field is analyzed to obtain their evolution and then, their algebraic properties which are controlled through a set of physical parameters. Evolution denote remarkable group properties when is analyzed in a non local basis, in particular those related with entanglement. These properties give a fruitful arena for further quantum applications and their control.

15 citations

Journal ArticleDOI
TL;DR: The development and progress that have been made in all these aspects in China, including control theory, automation, agriculture, defense, and other social sectors are reviewed.
Abstract: Automation is the utilization of control techniques together with other information technology to control industrial processes, reducing the need for human intervention. It plays a highly important role in social and economy as well as in daily life. Control theory is the theory of automation, and is an interdisciplinary branch of engineering and mathematics, examining the behavior of dynamical systems. China has a long history of manufacturing automatic devices. In recent years, some rapid progresses in control theory have been made in China. Many new theories and new methodologies have been developed to meet the increasing demands in industry, agriculture, defense, and other social sectors. Contemporary sciences such as complexity, systems biology, quantum technologies, have also found their close links to control theories and technologies. On the other hand, control theory itself has many unsolved fundamental problems requiring further studies and investigation. This paper is to review the development and progress that have been made in all these aspects in China. Some remarks on the future development of control theory are also presented.

6 citations

Proceedings ArticleDOI
01 Dec 2009
TL;DR: The state convergence problem for closed quantum systems under degenerate cases is investigated by the LaSalle invariance principle and an implicit Lyapunov-based control strategy is proposed for the convergence analysis of finite dimensional bilinear Schrödinger equations.
Abstract: In this paper, we investigate the state convergence problem for closed quantum systems under degenerate cases. An implicit Lyapunov-based control strategy is proposed for the convergence analysis of finite dimensional bilinear Schrodinger equations. The degenerate cases that the systems do not satisfy the strong regular condition [17] and the condition 〈φ i |H 1 |φ j 〉 ≠= 0, i, j ≠= k for eigenstates φ i , φ j of H 0 different from target state φ k , are considered. First the Lyapunov function is defined by the implicit function and the existence is guaranteed by a fixed point theorem. Then the convergence analysis is investigated by the LaSalle invariance principle. Finally, an example is provided to show the effectiveness of proposed results.

5 citations

Journal ArticleDOI
TL;DR: In this article, a general anisotropic three dimensional Ising model including an inhomogeneous magnetic field is considered to obtain some general quantum control effects for their sustainability, programmed evolution or transformation: Evolution loops and Exchange operations.
Abstract: Control of quantum entanglement has been considered as elemental physical resource for quantum applications in Quantum Information and Quantum Computation. Control of entangled states on a couple of atoms, ions or quantum dots are milestones in almost all quantum applications towards a scalable spin-based quantum computers or quantum devices. For magnetic systems, Ising model is an interaction which generates and modifies entanglement properties of quantum systems based on matter. In addition, when this interaction includes driven magnetic fields, it can be controlled to sustain, characterize or modify entanglement and other quantum properties. In this work, recent results about evolution in a general anisotropic three dimensional Ising model including an inhomogeneous magnetic field is considered to obtain some general quantum control effects for their sustainability, programmed evolution or transformation: Evolution loops and Exchange operations. This control is achievable through a set of physical parameters, whose prescriptions are reported. The use of a non local basis in the model to express time evolution lets take advantage to describe and control the system, in particular with those issues associated with entanglement and operations mentioned before. Finally, some analysis about equivalent gates based on our development is made including an example with teleportation, using one of the gates constructed.

4 citations

References
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Journal ArticleDOI
TL;DR: The set of states accessible from an initial EPR state by one-particle operations are characterized and it is shown that in a sense they allow two bits to be encoded reliably in one spin-1/2 particle.
Abstract: As is well known, operations on one particle of an Einstein-Podolsky-Rosen (EPR) pair cannot influence the marginal statistics of measurements on the other particle. We characterize the set of states accessible from an initial EPR state by one-particle operations and show that in a sense they allow two bits to be encoded reliably in one spin-1/2 particle: One party, ``Alice,'' prepares an EPR pair and sends one of the particles to another party, ``Bob,'' who applies one of four unitary operators to the particle, and then returns it to Alice. By measuring the two particles jointly, Alice can now reliably learn which operator Bob used.

4,780 citations

Journal ArticleDOI
TL;DR: In this article, necessary and sufficient conditions for the separability of mixed states were provided for 2 × 2 and 2 × 3 systems, where the positivity of the partial transposition of a state is sufficient and necessary for its separability.

2,854 citations

Journal ArticleDOI
TL;DR: The results, reinterpreted from an invariant-theoretic viewpoint, provide a novel representation of a class of nonnegative symmetric polynomials, termed “sum of squares matrices.”

400 citations

Journal ArticleDOI
TL;DR: The trade-off between the information gain and that disturbance in the act of observation is investigated, and the optimal detection method is explicitly found in the case of two equiprobable nonorthogonal pure states.
Abstract: When an observer wants to identify a quantum state, which is known to be one of a given set of nonorthogonal states, the act of observation causes a disturbance to that state. We investigate the trade-off between the information gain and that disturbance. This issue has important applications in quantum cryptography. The optimal detection method, for a given tolerated disturbance, is explicitly found in the case of two equiprobable nonorthogonal pure states. \textcopyright{} 1996 The American Physical Society.

307 citations

Journal ArticleDOI
TL;DR: In this article, the authors present and analyze a proposal to demonstrate fundamental limits on quantum control of a single qubit arising from these properties of quantum measurements, and study the performance of a quantum control scheme that makes use of weak measurement followed by feedback control, and demonstrate that it realizes the optimal recovery from noise for this system.
Abstract: Measurements in quantum mechanics cannot perfectly distinguish all states and necessarily disturb the measured system. We present and analyze a proposal to demonstrate fundamental limits on quantum control of a single qubit arising from these properties of quantum measurements. We consider a qubit prepared in one of two nonorthogonal states and subsequently subjected to dephasing noise. The task is to use measurement and feedback control to attempt to correct the state of the qubit. We demonstrate that projective measurements are not optimal for this task, and that there exists a nonprojective measurement with an optimum measurement strength which achieves the best trade-off between gaining information about the system and disturbing it through measurement backaction. We study the performance of a quantum control scheme that makes use of this weak measurement followed by feedback control, and demonstrate that it realizes the optimal recovery from noise for this system. We contrast this approach with various classically inspired control schemes.

71 citations