| 1. |
- Anandan, Jeeva S., et al.
(författare)
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Reply to Comment on `Geometric phases for mixed states in interferometry'
- 2002
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Ingår i: Physical Review Letters. - 0031-9007 .- 1079-7114. ; 89, s. 268902-
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)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. |
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| 3. |
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| 4. |
- Ericsson, Marie, et al.
(författare)
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Generalization of the geometric phase to completely positive maps
- 2003
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Ingår i: Physical Review A. Atomic, Molecular, and Optical Physics. - 1050-2947 .- 1094-1622. ; 67:2, s. 020101(R)-
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Tidskriftsartikel (refereegranskat)abstract
- We generalize the notion of relative phase to completely positive maps with known unitary representation, based on interferometry. Parallel transport conditions that define the geometric phase for such maps are introduced. The interference effect is embodied in a set of interference patterns defined by flipping the environment state in one of the two paths. We show for the qubit that this structure gives rise to interesting additional information about the geometry of the evolution defined by the CP map.
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| 5. |
- Ericsson, Marie, et al.
(författare)
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Mixed state geometric phases, entangled systems, and local unitary transformations
- 2003
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Ingår i: Physical Review Letters. - 0031-9007 .- 1079-7114. ; 91:9, s. 090405-
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Tidskriftsartikel (refereegranskat)abstract
- The geometric phase for a pure quantal state undergoing an arbitrary evolution is a "memory'' of the geometry of the path in the projective Hilbert space of the system. We find that Uhlmann's geometric phase for a mixed quantal state undergoing unitary evolution not only depends on the geometry of the path of the system alone but also on a constrained bi-local unitary evolution of the purified entangled state. We analyze this in general, illustrate it for the qubit case, and propose an experiment to test this effect. We also show that the mixed state geometric phase proposed recently in the context of interferometry requires uni-local transformations and is therefore essentially a property of the system alone.
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| 6. |
- Ericsson, Marie, et al.
(författare)
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Quantum computation using the Aharonov-Casher set up
- 2002
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Ingår i: Physics Letters A. - 0375-9601 .- 1873-2429. ; 303:1, s. 7-10
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Tidskriftsartikel (refereegranskat)abstract
- It is argued that the Aharonov-Casher set up could be used as the basic building block for quantum computation. We demonstrate explicitly in this scenario one- and two-qubit phase shift gates that are fault tolerant to deformations of the path when encircling two sites of the computational system around each other.
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| 7. |
- Ericsson, Marie, et al.
(författare)
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Towards a quantum Hall effect for atoms using electric fields
- 2002
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Ingår i: Physical Review A. Atomic, Molecular, and Optical Physics. - 1050-2947 .- 1094-1622. ; 65:1, s. 013607-
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Tidskriftsartikel (refereegranskat)abstract
- An atomic analogue of Landau quantization based on the Aharonov-Casher (AC) interaction is developed. The effect provides a first step towards an atomic quantum Hall system using electric fields, which may be realized in a Bose-Einstein condensate.
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| 8. |
- Filipp, Stefan, et al.
(författare)
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Off-diagonal generalization of the mixed-state geometric phase
- 2003
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Ingår i: Physical Review A. Atomic, Molecular, and Optical Physics. - 1050-2947 .- 1094-1622. ; 68:4, s. 042112-
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Tidskriftsartikel (refereegranskat)abstract
- The concept of off-diagonal geometric phases for mixed quantal states in unitary evolution is developed. We show that these phases arise from three basic ideas: (1) fulfillment of quantum parallel transport of a complete basis, (2) a concept of mixed state orthogonality adapted to unitary evolution, and (3) a normalization condition. We provide a method for computing the off-diagonal mixed state phases to any order for unitarities that divide the parallel transported basis of Hilbert space into two parts: one part where each basis vector undergoes cyclic evolution and one part where all basis vectors are permuted among each other. We also demonstrate a purification based experimental procedure for the two lowest order mixed state phases and consider a physical scenario for a full characterization of the qubit mixed state geometric phases in terms of polarization-entangled photon pairs. An alternative second order off-diagonal mixed state geometric phase, which can be tested in single-particle experiments, is proposed.
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| 9. |
- Filipp, Stefan, et al.
(författare)
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Off-diagonal geometric phases for mixed states
- 2003
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Ingår i: Physical Review Letters. - 0031-9007 .- 1079-7114. ; 90:5, s. 050403-
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Tidskriftsartikel (refereegranskat)abstract
- We extend the off-diagonal geometric phase [Phys. Rev. Lett. 85, 3067 (2000)] to mixed quantal states. The nodal structure of this phase in the qubit (two-level) case is compared with that of the diagonal mixed state geometric phase [Phys. Rev. Lett. 85, 2845 (2000)]. Extension to higher dimensional Hilbert spaces is delineated. A physical scenario for the off-diagonal mixed state geometric phase in polarization-entangled two-photon interferometry is proposed.
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| 10. |
- Friedenauer, Axel, et al.
(författare)
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Noncyclic geometric quantum computation
- 2003
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Ingår i: Physical Review A. Atomic, Molecular, and Optical Physics. - 1050-2947 .- 1094-1622. ; 67:2, s. 024303-
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Tidskriftsartikel (refereegranskat)abstract
- Geometric quantum computation is extended to the noncyclic case. Adiabatic NMR implementations of geometric phase shift gates at any precession angle and their concomitant fault tolerance with respect to the amplitude of the oscillating field are analysed. Nonadiabatic one-qubit geometric quantum computation is considered from the noncyclic perspective, with particular emphasis on errors in precession angles.
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