# Measuring relational information between quantum states, and applications

@inproceedings{Oszmaniec2021MeasuringRI, title={Measuring relational information between quantum states, and applications}, author={Michał Oszmaniec and Daniel Jost Brod and Ernesto F. Galv{\~a}o}, year={2021} }

The geometrical arrangement of a set of quantum states can be completely characterized using relational information only. This information is encoded in the pairwise state overlaps, as well as in Bargmann invariants of higher degree written as traces of products of density matrices. We describe how to measure Bargmann invariants using suitable generalizations of the SWAP test. This allows for a complete and robust characterization of the projective-unitary invariant properties of any set of…

#### One Citation

Negative quasiprobabilities enhance phase estimation in quantum-optics experiment

- Physics
- 2021

Noah Lupu-Gladstein, ∗ Y. Batuhan Yilmaz, † David R. M. Arvidsson-Shukur, 3, ‡ Aharon Brodutch, § Arthur O. T. Pang, ¶ Aephraim M. Steinberg, ∗∗ and Nicole Yunger Halpern 5, 6, 7 CQIQC and Department…

#### References

SHOWING 1-10 OF 32 REFERENCES

Measuring polynomial invariants of multiparty quantum states

- Physics
- 2004

We present networks for directly estimating the polynomial invariants of multiparty quantum states under local transformations. The structure of these networks is closely related to the structure of…

Direct estimations of linear and nonlinear functionals of a quantum state.

- Physics, MedicinePhysical review letters
- 2002

We present a simple quantum network, based on the controlled-SWAP gate, that can extract certain properties of quantum states without recourse to quantum tomography. It can be used as a basic…

Self-testing quantum states and measurements in the prepare-and-measure scenario

- Physics, MathematicsPhysical Review A
- 2018

The goal of self-testing is to characterize an a priori unknown quantum system based solely on measurement statistics, i.e. using an uncharacterized measurement device. Here we develop self-testing…

Simulating quantum systems using real Hilbert spaces.

- Physics, MedicinePhysical review letters
- 2009

We develop a means of simulating the evolution and measurement of a multipartite quantum state under discrete or continuous evolution using another quantum system with states and operators lying in a…

Optimal unambiguous discrimination of pure quantum states.

- Mathematics, MedicinePhysical review letters
- 2012

A complete geometric view is presented for the optimal unambiguous discrimination among N > 2 pure states and a graphic method for finding and classifying the optimal solutions is illustrated on the example of three states.

A Characterization of Projective Unitary Equivalence of Finite Frames and Applications

- Mathematics, Computer ScienceSIAM J. Discret. Math.
- 2016

This work gives an algorithm to recover the sequence of vectors (up to projective unitary equivalence) from a small subset of these projective invariants and applies it to SICs, MUBs, and harmonic frames and extends the results to the projective similarity of vectors.

Multiparticle Interference of Pairwise Distinguishable Photons.

- Medicine, PhysicsPhysical review letters
- 2020

Here, an interference signal is experimentally measured that depends only on the multiparticle interference of four photons in a four-port interferometer despite pairs of them occupying distinguishable states.

Efficient Quantum Algorithms for GHZ and
W
States, and Implementation on the IBM Quantum Computer

- Computer Science, MathematicsAdvanced Quantum Technologies
- 2019

Efficient algorithms with logarithmic step complexities for the generation of entangled GHZ and W states useful for quantum networks are proposed and an implementation on the IBM quantum computer up to N=16 is demonstrated.

General setting for Berry's phase.

- Physics, MedicinePhysical review letters
- 1988

It is shown that Berry's phase appears in a more general context than realized so far, using some ideas introduced by Pancharatnam in his study of the interference of polarized light to allow a meaningful comparison of the phase between any two nonorthogonal vectors in Hilbert space.

Distinguishability and Many-Particle Interference.

- Physics, MedicinePhysical review letters
- 2017

It is shown that the distinguishability between pairs of photons is not sufficient to fully describe the photons' behavior in a scattering process, but that a collective phase, the triad phase, plays a role.