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Register a new userQuantum information processing in phase space: A modular variables approach
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Binary quantum information can be fault tolerantly encoded in states defined in infinite dimensional Hilbert spaces. Such states define a computational basis, and permit a perfect equivalence between continuous and discrete universal operations. The drawback of this encoding is that the corresponding logical states are unphysical, meaning infinitely localized in phase space. We use the modular variables formalism to show that, in a number of protocols relevant for quantum information and for the realization of fundamental tests of quantum mechanics, it is possible to loosen the requirements on the logical subspace without jeopardizing their usefulness or their successful implementation. Such protocols involve measurements of appropriately chosen modular observables that permit the readout of the encoded discrete quantum information from the corresponding logical states. Finally, we demonstrate the experimental feasibility of our approach by applying it to the transverse degrees of freedom of single photons.
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We introduce a novel strategy, based on the use of modular variables, to encode and deterministically process quantum information using states described by continuous variables. Our formalism leads to a general recipe to adapt existing quantum information protocols, originally formulated for finite dimensional quantum systems, to infinite dimensional systems described by continuous variables. This is achieved by using non unitary and non-gaussian operators, obtained from the superposition of gaussian gates, together with adaptative manipulations in qubit systems defined in infinite dimensional Hilbert spaces. We describe in details the realization of single and two qubit gates and briefly discuss their implementation in a quantum optical set-up.
This dissertation serves as a general introduction to Wigner functions, phase space, and quantum metrology but also strives to be useful as a how-to guide for those who wish to delve into the realm of using continuous variables, to describe quantum states of light and optical interferometry. We discuss the advantages of Wigner functions and their use to describe many quantum states of light. Throughout our metrology discussions, we will also discuss various quantum limits and use quantum Fisher information to show optimal bounds. When applicable, we also discuss the use of quantum Gaussian information and how it relates to our Wigner function treatment. The remainder of our discussion focuses on investigating the effects of photon addition and subtraction to various states of light and analyze the nondeterministic nature of this process. We use examples of $m$ photon additions to a coherent state as well as discuss the properties of an $m$ photon subtracted thermal state. We also provide an argument that this process must always be a nondeterministic one, or the ability to violate quantum limits becomes apparent. We show that using phase measurement as ones metric is much more restrictive, which limits the usefulness of photon addition and subtraction. When we consider SNR however, we show improved SNR statistics, at the cost of increased measurement time. In this case of SNR, we also quantify the efficiency of the photon addition and subtraction process.
We give a dimension independent formulation of the quantum search algorithm introduced in [L. K. Grover, Phys. Rev. Lett. {bf 79}, 325 (1997)]. This algorithm provides a quadratic gain when compared to its classical counterpart by manipulating quantum two--level systems, qubits. We show that this gain, already known to be optimal, is preserved, irrespectively of the dimension of the system used to encode quantum information. This is shown by adapting the protocol to Hilbert spaces of any dimension using the same sequence of operations/logical gates as its original qubit formulation. Our results are detailed and illustrated for a system described by continuous variables, where qubits can be encoded in infinitely many distinct states using the modular variable formalism.
The optical fibre is an essential tool for our communication infrastructure since it is the main transmission channel for optical communications. The latest major advance in optical fibre technology is spatial division multiplexing (SDM), where new fibre designs and components establish multiple co-existing data channels based on light propagation over distinct transverse optical modes. Simultaneously, there have been many recent developments in the field of quantum information processing (QIP), with novel protocols and devices in areas such as computing, communication and metrology. Here, we review recent works implementing QIP protocols with SDM optical fibres, and discuss new possibilities for manipulating quantum systems based on this technology.
Quantum computing is an attractive and multidisciplinary field, which became a focus for experimental and theoretical research during last decade. Among other systems, like ions in traps or superconducting circuits, solid-states based qubits are considered to be promising candidates for first experimental tests of quantum hardware. Here we report recent progress in quantum information processing with point defect in diamond. Qubits are defined as single spin states (electron or nuclear). This allows exploring long coherence time (up to seconds for nuclear spins at cryogenic temperatures). In addition, the optical transition between ground and excited electronic states allows coupling of spin degrees of freedom to the state of the electromagnetic field. Such coupling gives access to the spin state readout via spin-selective scattering of photon. This also allows using of spin state as robust memory for flying qubits (photons).
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