We present an efficient algorithm that solves the quantum state tomography problem from an arbitrary number of projective measurements in any finite dimension $d$ . The algorithm is flexible enough to allow us to impose any desired rank $r$ to the state to be reconstructed, ranging from pure ( $r=1$ ) to full rank $(r=d)$ quantum states. The method exhibits successful and fast convergence under the presence of realistic errors in both state preparation and measurement stages, and also when considering overcomplete sets of observables. We demonstrate that the method outperforms semidefinite programming quantum state tomography for some sets of physically relevant quantum measurements in every finite dimension.We present an efficient algorithm that solves the quantum state tomography problem from an arbitrary number of projective measurements in any finite dimension $d$. The algorithm is flexible enough to allow us to impose any desired rank $r$ to the state to be reconstructed, ranging from pure ($r=1$) to full rank $(r=d)$ quantum states. The method exhibits successful and fast convergence under the presence of realistic errors in both state preparation and measurement stages, and also when considering overcomplete sets of observables. We demonstrate that the method outperforms semidefinite programming quantum state tomography for some sets of physically relevant quantum measurements in every finite dimension.

Dec 12, 20190 citations

Computer Simulation for Quantum Tomography

Bohdan Yavorskyy

Advances in intelligent systems and computingDec 22, 20200 citations

Semidefinite programming from optimization to quantum chemistry

光浩福田, Mituhiro Fukuda

Jul 1, 20090 citations

Quantum Tomography

Martin Ringbauer

Springer thesesJan 1, 20171 citation

Correcting for finite statistics effects in a quantum steering experiment

Sophie Engineer, Ana C. S. Costa, Alexandre C. Orthey +7 more

Verifying entanglement between parties is essential for creating secure quantum communication. However, finite statistics can lead to false positive outcomes in any tests for entanglement. Here, we introduce a one-sided device-independent protocol that corrects for apparent signaling effects in experimental probability distributions, caused by statistical fluctuations and experimental imperfections. We use semidefinite programming to identify the optimal inequality, for our experimental probability distribution, without resource-intensive tomography. Our protocol is numerically and experimentally analyzed in the context of random, misaligned measurements, correcting apparent signaling where necessary. Our results show a significantly higher probability of violation than existing state-of-the-art inequalities. This study demonstrates the power of semidefinite programming for entanglement verification and brings quantum networks closer to practical applications.Verifying entanglement between parties is essential for creating secure quantum communication. However, finite statistics can lead to false positive outcomes in any tests for entanglement. Here, we introduce a one-sided device-independent protocol that corrects for apparent signaling effects in experimental probability distributions, caused by statistical fluctuations and experimental imperfections. We use semidefinite programming to identify the optimal inequality, for our experimental probability distribution, without resource-intensive tomography. Our protocol is numerically and experimentally analyzed in the context of random, misaligned measurements, correcting apparent signaling where necessary. Our results show a significantly higher probability of violation than existing state-of-the-art inequalities. This study demonstrates the power of semidefinite programming for entanglement verification and brings quantum networks closer to practical applications.

arXiv:2305.14116Physical Review ResearchMay 16, 20250 citations

We present an efficient algorithm that solves the quantum state tomography problem from an arbitrary number of projective measurements in any finite dimension

d

. The algorithm is flexible enough to allow us to impose any desired rank

r

to the state to be reconstructed, ranging from pure (

r=1

) to full rank

(r=d)

quantum states. The method exhibits successful and fast convergence under the presence of realistic errors in both state preparation and measurement stages, and also when considering overcomplete sets of observables. We demonstrate that the method outperforms semidefinite programming quantum state tomography for some sets of physically relevant quantum measurements in every finite dimension.