| 1. |
- Anandan, Jeeva S., et al.
(author)
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Reply to Comment on `Geometric phases for mixed states in interferometry'
- 2002
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In: Physical Review Letters. - 0031-9007 .- 1079-7114. ; 89, s. 268902-
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Journal article (other academic/artistic)abstract
- The only difference between Bhandari's viewpoint and ours [Phys. Rev. Lett. 85, 2845 (2000)] is that our phase is defined modulo 2π, whereas Bhandari argues that two phases that differ by 2π n, n integer, may be distinguished experimentally in a history-dependent manner. (Reply to the Comment in Phys. Rev. Lett. 89, 268901 (2001) by R. Bhandari.)
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| 2. |
- Ekert, Artur, et al.
(author)
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Geometric quantum computation
- 2000
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In: Journal of Modern Optics. - : Informa UK Limited. ; 47:14-15, s. 2501-2513
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Journal article (peer-reviewed)abstract
- We describe in detail a general strategy for implementing a conditional geometric phase between two spins. Combined with single-spin operations, this simple operation is a universal gate for quantum computation, in that any unitary transformation can be implemented with arbitrary precision using only single-spin operations and conditional phase shifts. Thus quantum geometrical phases can form the basis of any quantum computation. Moreover, as the induced conditional phase depends only on the geometry of the paths executed by the spins it is resilient to certain types of errors and offers the potential of a naturally fault-tolerant way of performing quantum computation.
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| 3. |
- Kaltenbaek, Rainer, et al.
(author)
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Macroscopic Quantum Resonators (MAQRO) : 2015 update
- 2016
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In: EPJ Quantum Technology. - : Springer Berlin/Heidelberg. - 2196-0763. ; 3:1
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Research review (peer-reviewed)abstract
- Do the laws of quantum physics still hold for macroscopic objects - this is at the heart of Schrodinger's cat paradox - or do gravitation or yet unknown effects set a limit for massive particles? What is the fundamental relation between quantum physics and gravity? Ground-based experiments addressing these questions may soon face limitations due to limited free-fall times and the quality of vacuum and microgravity. The proposed mission Macroscopic Quantum Resonators (MAQRO) may overcome these limitations and allow addressing such fundamental questions. MAQRO harnesses recent developments in quantum optomechanics, high-mass matter-wave interferometry as well as state-of-the-art space technology to push macroscopic quantum experiments towards their ultimate performance limits and to open new horizons for applying quantum technology in space. The main scientific goal is to probe the vastly unexplored 'quantum-classical' transition for increasingly massive objects, testing the predictions of quantum theory for objects in a size and mass regime unachievable in ground-based experiments. The hardware will largely be based on available space technology. Here, we present the MAQRO proposal submitted in response to the 4th Cosmic Vision call for a medium-sized mission (M4) in 2014 of the European Space Agency (ESA) with a possible launch in 2025, and we review the progress with respect to the original MAQRO proposal for the 3rd Cosmic Vision call for a medium-sized mission (M3) in 2010. In particular, the updated proposal overcomes several critical issues of the original proposal by relying on established experimental techniques from high-mass matter-wave interferometry and by introducing novel ideas for particle loading and manipulation. Moreover, the mission design was improved to better fulfill the stringent environmental requirements for macroscopic quantum experiments.
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| 4. |
- Sjöqvist, Erik, et al.
(author)
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Geometric phases for mixed states in interferometry
- 2000
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In: Physical Review Letters. - 0031-9007 .- 1079-7114. ; 85:14, s. 2845-2849
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Journal article (peer-reviewed)abstract
- We provide a physical prescription based on interferometry for introducing the total phase of a mixed state undergoing unitary evolution, which has been an elusive concept in the past. We define the parallel transport condition that provides a connection form for obtaining the geometric phase for mixed states. The expression for the geometric phase for mixed state reduces to well known formulas in the pure state case when a system undergoes noncyclic and unitary quantum evolution.
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| 5. |
- Williamson, Mark S., et al.
(author)
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Geometric local invariants and pure three-qubit states
- 2011
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In: Physical Review A. Atomic, Molecular, and Optical Physics. - 1050-2947 .- 1094-1622. ; 83:6
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Journal article (peer-reviewed)abstract
- We explore a geometric approach to generating local SU(2) and SL(2,C) invariants for a collection of qubits inspired by lattice gauge theory. Each local invariant or 'gauge' invariant is associated to a distinct closed path (or plaquette) joining some or all of the qubits. In lattice gauge theory, the lattice points are the discrete space-time points, the transformations between the points of the lattice are defined by parallel transporters and the gauge invariant observable associated to a particular closed path is given by the Wilson loop. In our approach the points of the lattice are qubits, the link-transformations between the qubits are defined by the correlations between them and the gauge invariant observable, the local invariants associated to a particular closed path are also given by a Wilson loop-like construction. The link transformations share many of the properties of parallel transporters although they are not undone when one retraces one's steps through the lattice. This feature is used to generate many of the invariants. We consider a pure three qubit state as a test case and find we can generate a complete set of algebraically independent local invariants in this way, however the framework given here is applicable to mixed states composed of any number of d level quantum systems. We give an operational interpretation of these invariants in terms of observables.
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| 6. |
- Williamson, Mark S., et al.
(author)
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Global asymmetry of many-qubit correlations : A lattice-gauge-theory approach
- 2011
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In: Physical Review A. Atomic, Molecular, and Optical Physics. - 1050-2947 .- 1094-1622. ; 84:3, s. 032302-
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Journal article (peer-reviewed)abstract
- We introduce a novel bridge between the familiar gauge field theory approaches used in many areas of modern physics such as quantum field theory and the SLOCC protocols familiar in quantum information. Although the mathematical methods are the same the meaning of the gauge group will be different. The measure we introduce, `twist', is constructed as a Wilson loop from a correlation induced holonomy. The measure can be understood as the global asymmetry of the bipartite correlations in a loop of three or more qubits; if the holonomy is trivial (the identity matrix), the bipartite correlations can be globally untwisted using general local qubit operations, the gauge group of our theory, which turns out to be the group of Lorentz transformations familiar from special relativity. If it is not possible to globally untwist the bipartite correlations in a state globally using local operations, the twistedness is given by a non-trivial element of the Lorentz group, the correlation induced holonomy. We provide several analytical examples of twisted and untwisted states for three qubits, the most elementary non-trivial loop one can imagine.
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| 7. |
- Åberg, Johan, 1974-
(author)
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Open Quantum Systems : Effects in Interferometry, Quantum Computation, and Adiabatic Evolution
- 2005
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Doctoral thesis (other academic/artistic)abstract
- The effects of open system evolution on single particle interferometry, quantum computation, and the adiabatic approximation are investigated.Single particle interferometry: Three concepts concerning completely positive maps (CPMs) and trace preserving CPMs (channels), named subspace preserving (SP) CPMs, subspace local channels, and gluing of CPMs, are introduced. SP channels preserve probability weights on given orthogonal sum decompositions of the Hilbert space of a quantum system. Subspace locality determines what channels act locally with respect to such decompositions. Gluings are the possible total channels obtainable if two evolution devices, characterized by channels, act jointly on a superposition of a particle in their inputs. It is shown that gluings are not uniquely determined by the two channels. We determine all possible interference patterns in single particle interferometry for given channels acting in the interferometer paths. It is shown that the standard interferometric setup cannot distinguish all gluings, but a generalized setup can.Quantum computing: The robustness of local and global adiabatic quantum search subject to decoherence in the instantaneous eigenbasis of the search Hamiltonian, is examined. In both the global and local search case the asymptotic time-complexity of the ideal closed case is preserved, as long as the Hamiltonian dynamics is present. In the case of pure decoherence, where the environment monitors the search Hamiltonian, it is shown that the local adiabatic quantum search performs as the classical search with scaling N, and that the global search scales like N3/2 , where N is the list length. We consider success probabilities p<1 and prove bounds on the run-time with the same scaling as in the conditions for the p → 1 limit.Adiabatic evolution: We generalize the adiabatic approximation to the case of open quantum systems in the joint limit of slow change and weak open system disturbances.
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