Quantum-state tomography for spin-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:math>systems

Hofmann, Holger F.; Takeuchi, Shigeki

doi:10.1103/physreva.69.042108

Cited by 31 publications

(24 citation statements)

References 16 publications

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“…Example 3.7 (Encoding: from spin-1/2 to spin-1). According to [40], there are five spatial directions    ¼ Î n n , The actual data to start with is the set of physical spin-1/2 observablesˆ( )…”

Section: Concrete Realization In Our Universementioning

confidence: 99%

An operational approach to spacetime symmetries: Lorentz transformations from quantum communication

Hoehn

Müller

2016

New J. Phys.

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In most approaches to fundamental physics, spacetime symmetries are postulated a priori and then explicitly implemented in the theory. This includes Lorentz covariance in quantum field theory and diffeomorphism invariance in quantum gravity, which are seen as fundamental principles to which the final theory has to be adjusted. In this paper, we suggest, within a much simpler setting, that this kind of reasoning can actually be reversed, by taking an operational approach inspired by quantum information theory. We consider observers in distinct laboratories, with local physics described by the laws of abstract quantum theory, and without presupposing a particular spacetime structure. We ask what information-theoretic effort the observers have to spend to synchronize their descriptions of local physics. If there are 'enough' observables that can be measured universally on several different quantum systems, we show that the observers' descriptions are related by an element of the orthochronous Lorentz group ( ) + O 3, 1 , together with a global scaling factor. Not only does this operational approach predict the Lorentz transformations, but it also accurately describes the behavior of relativistic Stern-Gerlach devices in the WKB approximation, and it correctly predicts that quantum systems carry Lorentz group representations of different spin. This result thus hints at a novel information-theoretic perspective on spacetime.

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Section: Concrete Realization In Our Universementioning

confidence: 99%

An operational approach to spacetime symmetries: Lorentz transformations from quantum communication

Hoehn

Müller

2016

New J. Phys.

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“…A similar reconstruction of qutrit states is proposed in [44]. Higher spins (S = 4) are reconstructed in [45].…”

Section: Examples: Qubits and Qutritsmentioning

confidence: 89%

“…The difference between mappings reduces to a particular choice of spin-s portraits implicitly used in these transforms; namely, [12,20] rely on spin-1/2 portraits, whereas [7,44] extensively employ spin-j portraits.…”

Section: Discussionmentioning

confidence: 99%

Inverse spin-s portrait and representation of qudit states by single probability vectors

Filippov

Man’ko

2010

J Russ Laser Res

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Using the tomographic probability representation of qudit states and the inverse spin-portrait method, we suggest a bijective map of the qudit density operator onto a single probability distribution. Within the framework of the approach proposed, any quantum spin-j state is associated with the (2j + 1)(4j + 1)-dimensional probability vector whose components are labeled by spin projections and points on the sphere S 2 . Such a vector has a clear physical meaning and can be relatively easily measured. Quantum states form a convex subset of the 2j(4j + 3) simplex, with the boundary being illustrated for qubits (j = 1/2) and qutrits (j = 1). A relation to the (2j + 1) 2 -and (2j + 1)(2j + 2)-dimensional probability vectors is established in terms of spin-s portraits. We also address an auxiliary problem of the optimum reconstruction of qudit states, where the optimality implies a minimum relative error of the density matrix due to the errors in measured probabilities.

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“…Quantum state tomography is a singularly useful tool for reconstructing the density matrices of quantum states [40,41], It allows the extraction of relevant quantum information quantities such as qubit fidelities and the degrees of entan glement. For one qubit with two levels, tomography requires measuring the three orthogonal components of the Bloch vector.…”

Section: B Quantum State Tomographymentioning

confidence: 99%

Qubit fidelity of a single atom transferred among the sites of a ring optical lattice

Shi

Liu

et al. 2014

Phys. Rev. A

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We demonstrate the transfer of a single atom in a ring optical lattice with the aid of an auxiliary moving tweezer and investigate the influences on fidelity of the qubit encoded in the atom. When the tweezer has deeper trap depth and moves across the lattice, it is observed that an atom in one site follows the movement. The transfer efficiency of one atom to the destination site reaches up to 95%. This scheme is suitable for scalable quantum registers because of no influence on the other sites. We obtain atomic qubit fidelity during the transfer process by using quantum state tomography. Extracted fidelity indicates that the eigenstate is well preserved, while the superposition state is influenced. In combination with spin-echo measurement, dephasing mechanisms in this process are analyzed and discussed in detail. Loss of qubit fidelity is found to result from heating effects induced by this process and pointing instabilities of the trap laser. Our results pave the way for quantum computation with single atoms trapped in a scalable optical lattice.

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Quantum-state tomography for spin-lsystems

Cited by 31 publications

References 16 publications

An operational approach to spacetime symmetries: Lorentz transformations from quantum communication

An operational approach to spacetime symmetries: Lorentz transformations from quantum communication

Inverse spin-s portrait and representation of qudit states by single probability vectors

Qubit fidelity of a single atom transferred among the sites of a ring optical lattice

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