In this final chapter, we focus more on quantum information and quantum computing applications of atomic ensembles. We first examine ways of implementing continuous variables in quantum information processing using atomic ensembles, based on the Holstein--Primakoff approximation. Methods to perform quantum teleportation using this method, and some seminal experiments using this approach are introduced. We then introduce other approaches not based on the Holstein--Primakoff approximation to represent quantum information, namely the spinor quantum computing scheme. After showing a simple example of how such a scheme works with Deutsch's algorithm, we describe how adiabatic quantum computing can be performed, which displays the key feature of quantum error suppression.
In this final chapter, we focus more on quantum information and quantum computing applications of atomic ensembles. We first examine ways of implementing continuous variables in quantum information processing using atomic ensembles, based on the Holstein--Primakoff approximation. Methods to perform quantum teleportation using this method, and some seminal experiments using this approach are introduced. We then introduce other approaches not based on the Holstein--Primakoff approximation to represent quantum information, namely the spinor quantum computing scheme. After showing a simple example of how such a scheme works with Deutsch's algorithm, we describe how adiabatic quantum computing can be performed, which displays the key feature of quantum error suppression.
This thesis presents three different results in quantum information theory. The first result addresses the theoretical foundations of quantum metrology. The Heisenberg limit considered as the ultimate limit in quantum metrology sets a lower bound on how precisely a physical quantity can be measured given a certain amount of resources in any possible measurement. Recently, however, several measurement procedures have been proposed in which the Heisenberg limit seemed to be surpassed. This led to an extensive debate over the question how the sensitivity scales with the physical resources and the computational resources that are used in estimation procedures. Here, we reconcile the physical definition of the relevant resources with the information-theoretical scaling in terms of the query complexity of a quantum network. This leads to a novel and ultimate Heisenberg limit that applies to all conceivable measurement procedures. The second result reveals a close relationship between quantum metrology and the Deutsch-Jozsa algorithm over continuous-variable quantum systems. Here, we develop a general procedure, characterized by two parameters, that unifies parameter estimation and the Deutsch-Jozsa algorithm. The procedure estimates a value of an unknown parameter with Heisenberg-limited precision or solves the Deutsch-Jozsa problem in a single run without the use of any entanglement. The third result illustrates how physical principles that govern interaction of light and matter can be efficiently employed to create a computational resource for a (one-way) quantum computer. More specifically, we demonstrate theoretically a scheme based on atomic ensembles and the dipole blockade mechanism for generation of the so-called cluster states in a single step. This procedure is significantly more efficient than any known robust probabilistic entangling operation.
In general, all forms of information processing can be considered in a quantum mechanical context, including for example communication, channel capacities, and the quantum limits to information extraction. In this chapter we introduce the basic features of quantum information processing. We first present qubits as abstractions of two-level addressable quantum systems, before generalizing this concept to higher-dimensional qudit systems, and continuous variables. We introduce the stabilizer formalism towards the beginning of our discussion as a convenient way to track quantum information. In Section 2.2 we derive the no-cloning theorem, which leads us to cryptography, teleportation, and quantum repeaters. Section 2.3 describes quantum computing with qubits. We start with a brief description of the circuit model, and use it to define cluster states and the one-way model. We study the properties of cluster states and discuss error correction. In the last section we introduce quantum computing over continuous variables. Quantum information Classically, information is carried by ‘bits’, which are physical systems that have two (macroscopic) states denoted by 0 and 1. These bits are described classically, which immediately raises the question of how we should extend this information-theoretic description to the quantum mechanical case. This will lead to the quantum unit of information, the quantum bit or ‘qubit’. 2.1.1 Classical and quantum bits We can define the qubit as a two-dimensional quantum system, which means that the state space of the system is a two-dimensional complex Hilbert space ℋ.
Quantum information processing offers fundamental improvements over classical information processing, such as computing power, secure communication, and high-precision measurements. However, the best way to create practical devices is not yet known. This textbook describes the techniques that are likely to be used in implementing optical quantum information processors. After developing the fundamental concepts in quantum optics and quantum information theory, the book shows how optical systems can be used to build quantum computers according to the most recent ideas. It discusses implementations based on single photons and linear optics, optically controlled atoms and solid-state systems, atomic ensembles, and optical continuous variables. This book is ideal for graduate students beginning research in optical quantum information processing. It presents the most important techniques of the field using worked examples and over 120 exercises.
In the standard approach to adiabatic quantum computing (AQC), quantum information stored on qubits are adia- batically evolved to find the lowest energy state of a problem Hamiltonian. Here we investigate a variation of AQC where spin ensembles are used in place of qubits. The use of ensembles duplicates the quantum information, and allows errors to be suppressed during the adiabatic evolution. We show that there are two distinct types of problem Hamiltonians under this mapping, where the first excited state is a single particle perturbation on the ground state (Type I); or a macroscopically distinct fully polarized state (Type II). For Type I problems, we find that the minimum gap for large ensembles is well predicted by mean-field theory and the AQC performance improves with ensemble size, realizing error-suppression. For Type II problems, the performance of the AQC is mixed, and the gap can increase or decrease with ensemble size depending on the problem instance. The incidences of the Type II problems are greatly suppressed with ensemble size, and consequently for randomly chosen problem instances the success probability of the scheme improves with the ensemble size. Our approach shows that it is possible to perform AQC without the necessity of controlling individual qubits, which allows for an alternative route towards implementing AQC.
Quantum information has been witnessing great science value and latent application since 1980's. The research work presented here consist of mainly two important parts: manipulations of multiphoton entanglement and atomic ensembles based quantum memory. In first part, the experimental technique multi-photon entanglement is further developed to study fundamental issues in quantum mechanics, remarkable applications to quantum communication and quantum computation. Specifically, we have demonstrated a bit-flip error-free transfer of quantum information, violation of Bell's inequality beyond Tsirelson's bound, teleportation of a two-qubit composite system, as well as the one-way computing by two-photon-four-qubit cluster state. To overcome un-scalability problem due to probabilistic feature in linear optical quantum information processing, we investigated in the second part the physics of atomic ensembles based quantum memory. We show that theoretically, entanglement between distant locations can be deterministically generated. The experimental work has thoroughly developed the necessary techniques and we have achieved deterministic single photon source, and interference of the photons from independent atomic ensembles, teleportation between photonic and atomic qubits, a novel way to create a robust entanglement between an atomic and a photonic qubit, and memory based entanglement swapping. We believe, the developed techniques here would dramatically facilitate progresses in many fields including global quantum communication, linear optical quantum computation and the foundations of quantum mechanics etc.
Quantum error correction is essential for fault-tolerant quantum computation, yet most existing codes rely on local control and stabilizer measurements that are difficult to implement in systems dominated by collective interactions. Inspired by spin-GKP codes in PhysRevA.108.022428, we develop a general framework for Holstein-Primakoff spin codes, which maps continuous-variable bosonic codes onto permutation-symmetric spin ensembles via the Holstein-Primakoff approximation. We show that HP codes are robust to both collective and local-spin noise and propose an explicit measurement-free local error recovery procedure to map local noise into correctable collective-spin errors.