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arXiv:1211.0133 · Physical Review A

Implementation schemes for unsharp measurements with trapped ions

Sujit K. Choudhary, Thomas Konrad, Hermann Uys

Published Jan 31, 2013• 19 citations
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Abstract

Unsharp positive operator-valued measurements allow a variety of measurement applications which minimally disrupt the state of the quantum system. Experimental schemes are proposed for implementing unsharp measurements on the qubit levels of a trapped ion. The schemes rely on introducing weak entanglement between the state of a target ion and that of an auxiliary ion, using standard ion-trap quantum logic operations, and then realizing an unsharp measurement through projective measurement on the auxiliary atom. We analyze common sources of error and their effect on different applications of unsharp measurements.

DOI
10.1103/physreva.87.012131

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Unsharp positive operator-valued measurements allow a variety of measurement applications which minimally disrupt the state of the quantum system. Experimental schemes are proposed for implementing unsharp measurements on the qubit levels of a trapped ion. The schemes rely on introducing weak entanglement between the state of a target ion and that of an auxiliary ion, using standard ion-trap quantum logic operations, and then realizing an unsharp measurement through projective measurement on the auxiliary atom. We analyze common sources of error and their effect on different applications of unsharp measurements.
Abstract Numerical simulations are used to study unsharp measurements in a system of trapped ytterbium ions to monitor resonantly driven Rabi oscillations of a target ion by weak coupling to an auxiliary ion. The simulation combines the positive operator-valued measure formalism and optical Bloch equations to model the state of the target ion during the implementation of the unsharp measurement protocol. State monitoring is done using an estimation scheme that is updated with the unsharp measurement results. The model expands on previous work by explicitly including spontaneous emission into the calculations. We propose a method to determine convergence of the estimation scheme, useful in an experimental setting, which does not rely on using the target state. The simulation results show the feasibility conditions for implementing unsharp measurements experimentally and demonstrate the robustness of the estimation scheme in the presence of experimental noise and when the qubit Rabi frequency is not precisely known. We find that the timescale of transitions that change the motional state is the main technical challenge for experimental implementation.
Although quantum mechanics has been able to explain a wide range of physical, chemical, and even biological events with unprecedented accuracy, fundamental problems remain. For instance, the problem of quantum measurement and quantum entanglement, which are the most perplexing problems that have persisted since the foundation of quantum mechanics. Both are crucial quantum resources with broad applications in quantum information science, quantum computing and quantum optics. For this reason, this thesis is devoted to research the quantum measurement from the weakest regime to the strongest one as well as the dynamics of entanglement of different quantum systems. In this work, we study the measurement transition for a coherent-squeezed pointer state through a transition factor Γ that involves a system-pointer coupling by using an arbitrary measured observable A. In addition, we show that the shift in the pointer’s position and momentum establishes a relationship with a new value defined as the transition value, which generalizes the weak value as well as the conditional expectation value. Furthermore, a new strategy is introduced to achieve different measurement regimes by just adjusting the r and ϕξ parameters of the coherent-squeezed pointer state, opening an interesting way to test quantum mechanics foundations. Our scheme has been theoretically applied in a trapped ion illuminated by a bichromatic laser beam, with a high potential to be implemented in future experimental setups. Besides, we propose a method to regulate the quantum entanglement in the system mentioned before as well as a dispersive-hybrid system where a qubit is directly coupled to a cavity and a mechanical resonator. Entanglement can be controlled by only tuning the squeezing parameters associated with the vibrational mode. As the squeezing amplitude becomes larger, the maximal entanglement abruptly falls to zero at specific squeezing phases. For the hybrid system, it is also possible to generate entanglement for bipartitions from the qubit-cavity-resonator system after applying this strategy. Entangled qubit-cavity states are created through squeezing, even though there is no direct interaction between them. We also analyze the effect of atomic, optical, and vibrational losses on the quantum entanglement. We finally discuss our schemes to be implemented in future experimental setups and promote further studies to generalize the concept of “monogamy of entanglement” in tripartite systems outside qubit-composite states, in particular, (2 ⊗ 2 ⊗ n)-dimensional systems.
We study the protective measurement of a qubit by a second qubit acting as a probe. Consideration of this model is motivated by the possibility of its experimental implementation in multiqubit systems such as trapped ions. In our scheme, information about the expectation value of an arbitrary observable of the system qubit is encoded in the rotation of the state of the probe qubit. We describe the structure of the Hamiltonian that gives rise to this measurement and analyze the resulting dynamics under a variety of realistic conditions, such as noninfinitesimal measurement strengths, repeated measurements, non-negligible intrinsic dynamics of the probe, and interactions of the system and probe qubits with an environment. We propose an experimental realization of our model in an ion trap. The experiment may be performed with existing technology and makes use of established experimental methods for the engineering and control of Hamiltonians for quantum gates and quantum simulations of spin systems.
We propose a protocol for extracting work from a coherent quantum battery state by exploiting measurement-assisted feedback mediated by a continuous-variable pointer. The scheme relies on the unitary operator U=exp⁡(−ikt H^⊗P^/ℏ)U = \exp(-i k t \, \hat{H} \otimes \hat{P}/\hbar)U=exp(−iktH^⊗P^/ℏ), which generates entanglement between the battery's energy eigenstates and the position of an auxiliary pointer. A subsequent projective measurement of the pointer's position conditionally prepares the battery in a pure state from which work can be extracted via a feedback unitary. We analyze the protocol for a two-level quantum battery and a Gaussian pointer, computing the conditional states and the corresponding daemonic ergotropy. For the pure initial state considered, we find that the daemonic ergotropy equals the standard ergotropy for all interaction strengths, demonstrating that the measurement-assisted feedback recovers the full extractable work that would otherwise become inaccessible due to entanglement with the pointer when its degrees of freedom are traced out. The protocol thus provides a physically transparent realization of a quantum Maxwell demon, where the pointer acts as a quantum measurement ancilla whose position becomes correlated with the battery's energy. The scheme is amenable to experimental implementation in trapped-ion systems, and it contributes to the ongoing efforts to understand the role of quantum coherence and measurement in thermodynamics.
We describe a scalable, high-speed, and robust architecture for measurement-based quantum computing with trapped ions. Measurement-based architectures offer a way to speed up operation of a quantum computer significantly by parallelizing the slow entangling operations and transferring the speed requirement to fast measurement of qubits. We show that a 3D cluster state suitable for fault-tolerant measurement-based quantum computing can be implemented on a 2D array of ion traps. We propose the projective measurement of ions via multiphoton photoionization for nanosecond operation and discuss the viability of such a scheme for Ca ions.
Experiments with individual trapped ions are ideally suited to investigate fundamental issues of quantum mechanics such as the measurement process. At the same time electrodynamically trapped ions have been used with great success to demonstrate quantum logic operations and are a candidate for scalable quantum computing. In this article a brief introduction is given to the basic steps that constitute a quantum measurement; in particular, measurements on single quantum systems are considered. Then experiments with single Yb+ are reviewed demonstrating the quantum Zeno paradox, as well as an experiment where an adaptive algorithm for quantum state estimation of qubits was implemented. In the last section of this article -- devoted to experiments and new ideas related to quantum information processing (QIP) with trapped ions -- the realization of various quantum channels using a hyperfine qubit of Yb+ is briefly discussed. Then a concept for QIP with trapped ions is reviewed where rf or microwave radiation is used instead of laser light for coherent manipulation of a collection of ions. In a suitably modified trap the ions form an artificial ion "molecule" to which the techniques developed in nuclear magnetic resonance and electron spin resonance experiments can be directly applied. Finally, coherent excitation of optical electric quadrupole transitions in Yb+ and Ba+ is reported. In addition, robust Raman cooling of a pair of Ba+ ions is reviewed.