Lukas Knips

Systematic errors in current quantum state tomography tools.

Common tools for obtaining physical density matrices in experimental quantum state tomography are shown here to cause systematic errors. For example, using maximum likelihood or least squares optimization to obtain physical estimates for the quantum state, we observe a systematic underestimation of the fidelity and an overestimation of entanglement. Such strongly biased estimates can be avoided using linear evaluation of the data or by linearizing measurement operators yielding reliable and computational simple error bounds.

Weak value beyond conditional expectation value of the pointer readings

It is argued that a weak value of an observable is a robust property of a single pre- and postselected quantum system rather than a statistical property. During an infinitesimal time a system with a given weak value affected other systems as if it had been in an eigenstate with eigenvalue equal to the weak value. This differs significantly from the action of a system preselected only and possessing a numerically equal expectation value. The weak value has a physical meaning beyond a conditional average of a pointer in the weak measurement procedure. The difference between the weak value and the expectation value has been demonstrated on the example of photon polarization. In addition, the weak values for systems pre- and postselected in mixed states are considered.

An Improved Experiment to Determine the 'Past of a Particle' in the Nested Mach–Zehnder Interferometer

We argue that the modification proposed by Li et al. [Chin. Phys. Lett. 32 (2015) 050303] to the experiment of Danan et al. [Phys. Rev. Lett. 111 (2013) 240402] does not test the past of the photon as characterized by local weak traces. Instead of answering the questions: (i) were the photons in A? (ii) were the photons in B? and (iii) were the photons in C? the proposed experiment measures a degenerate operator answering the questions: (i) were the photons in A? and (ii) were the photons in B and C together? A negative answer to the last question does not tell us if photons were present in B or C. On the other hand, a simple variation of the proposal by Li et al. does provide conceptually better evidence for the past of the pre- and post-selected photon, but this evidence will be in agreement with the results of Danan et al.

Multipartite Entanglement Detection with Minimal Effort

Certifying entanglement of a multipartite state is generally considered a demanding task. Since an N qubit state is parametrized by 4^{N}-1 real numbers, one might naively expect that the measurement effort of generic entanglement detection also scales exponentially with N. Here, we introduce a general scheme to construct efficient witnesses requiring a constant number of measurements independent of the number of qubits for states like, e.g., Greenberger-Horne-Zeilinger states, cluster states, and Dicke states. For four qubits, we apply this novel method to experimental realizations of the aforementioned states and prove genuine four-partite entanglement with two measurement settings only.

Genuine Multipartite Entanglement without Multipartite Correlations

Nonclassical correlations between measurement results make entanglement the essence of quantum physics and the main resource for quantum information applications. Surprisingly, there are n-particle states which do not exhibit n-partite correlations at all but still are genuinely n-partite entangled. We introduce a general construction principle for such states, implement them in a multiphoton experiment and analyze their properties in detail. Remarkably, even without multipartite correlations, these states do violate Bell inequalities showing that there is no classical, i.e., local realistic model describing their properties.

Optimized state-independent entanglement detection based on a geometrical threshold criterion

Experimental procedures are presented for the rapid detection of entanglement of unknown arbitrary quantum states. The methods are based on the entanglement criterion using accessible correlations and the principle of correlation complementarity. Our first scheme essentially establishes the Schmidt decomposition for pure states, with few measurements only and without the need for shared reference frames. The second scheme employs a decision tree to speed up entanglement detection. We analyze the performance of the methods using numerical simulations and verify them experimentally for various states of two, three, and four qubits.

Multiqubit state tomography from a physical perspective

The statistical nature of measurements alone easily causes unphysical estimates in quantum state tomography (QST). Multinomial or Poissonian noise results in eigenvalue distributions converging to the Wigner semicircle distribution for already a modest number of qubits [1], see Fig. 1a). This enables one to estimate the influence of finite statistics to QST as well as the number of measurements necessary to avoid unphysical solutions. Knowing the impact of statistical noise on the eigenvalue distribution also directly leads to a physical state estimate with minimal numerical effort. Combining ideas from random matrix theory with pertubation theory, one can even obtain confidence regions for the state as well as for figures of merit like the fidelity.

Noise-powered entanglement detection

Entangled particles exhibit quantum correlations over arbitrary long distances in time and space which cannot be mimicked by local realistic models. In order to detect and utilize these correlations for quantum information tasks, measurements in different bases are necessary. A variety of schemes for experimentally characterizing quantum states have been devised. However, these are often experimentally demanding in terms of stability and insensitivity against noise. Standard methods such as state tomography and Bell tests [1, 2] will fail to reliably detect quantum correlations in the presence of unknown local perturbations to the measuring apparatus, as consecutive measurements must be co-ordinated via a shared choice of measurement basis (a shared reference frame). So called reference frame independent schemes overcome this difficulty [3, 4], however, even these schemes fail when the choice of local measurement setting is not repeatable, i.e. when there is drift.

Publisher’s Note: Multipartite Entanglement Detection with Minimal Effort [Phys. Rev. Lett. 117 , 210504 (2016)]

This corrects the article DOI: 10.1103/PhysRevLett.117.210504.