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arXiv:1605.08287 · Physical Review A

Quantum-polarization state tomography

Ömer Bayraktar, Marcin Świłło, Carlota Canalias, Gunnar G. Bjork

Published Aug 30, 2016• 28 citations
arXivHTMLPDF

Abstract

We propose and demonstrate a method for quantum-state tomography of qudits encoded in the quantum polarization of $N$-photon states. This is achieved by distributing $N$ photons nondeterministically into three paths and their subsequent projection, which for $N=1$ is equivalent to measuring the Stokes (or Pauli) operators. The statistics of the recorded $N$-fold coincidences determines the unknown $N$-photon polarization state uniquely. The proposed, fixed setup manifestly rules out any systematic measurement errors due to moving components and allows for simple switching between tomography of different states, which makes it ideal for adaptive tomography schemes.

DOI
10.1103/physreva.94.020105

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Quantum state tomography (QST), the process through which the density matrix of a quantum system is characterized from measurements of specific observables, is a fundamental pillar in the fields of quantum information and computation. In this work, we propose a simple QST method to reconstruct the density matrix of two qubits encoded in the polarization and path degrees of freedom of a single photon, which can be realized with a single linear-optical setup. We demonstrate that the density matrix can be fully described in terms of the Stokes parameters related to the two possible paths of the photon, together with a quantum version of the two-point Stokes parameters introduced here. Our findings put forward photonic circuits for the investigation of the dynamics of open quantum systems.
Quantum state tomography (QST), the process through which the density matrix of a quantum system is characterized from measurements of specific observables, is a fundamental pillar in the fields of quantum information and computation. In this work, we propose a simple QST method to reconstruct the density matrix of two qubits encoded in the polarization and path degrees of freedom of a single photon, which can be realized with a single linear-optical setup. We demonstrate that the density matrix can be fully described in terms of the Stokes parameters related to the two possibles paths of the photon, together with a quantum version of the two-point Stokes parameters introduced here. Our findings put forward photonic circuits for the investigation of the dynamics of open quantum systems.
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A scheme for quantum-state tomography is presented that can be performed for polarized light with an arbitrary photon-number distribution. The proposed method fills the gap between existing polarization-tomography schemes for single-photon states and for optical fields with very large photon numbers. It consists of an optical homodyne setup triggered by the outcome of a single-photon counting module. The configuration space of polarization is parametrized by Euler angles and by an additional interference parameter, whose assessment requires conditional homodyne measurements.
We consider the task of performing quantum state tomography on a ddd-level spin qudit, using only measurements of spin projection onto different quantization axes. After introducing a basis of operators closely related to the spherical harmonics, which obey the rotational symmetries of spin qudits, we map our quantum tomography task onto the classical problem of signal recovery on the sphere. We then provide algorithms with O(rd3)O(r{d}^{3})O(rd3) serial runtime, parallelizable down to O(rd2)O(r{d}^{2})O(rd2) for: (i) computing a priori upper bounds on the expected error with which spin projection measurements along rrr given axes can reconstruct an unknown qudit state, and (ii) estimating a posteriori the statistical error in a reconstructed state. Our algorithms motivate a simple randomized tomography protocol for which we find that using more measurement axes can yield substantial benefits that plateau after $r\ensuremath{\approx}3d$.