# Iterative algorithm for reconstruction of entangled states

@article{ehek2001IterativeAF, title={Iterative algorithm for reconstruction of entangled states}, author={Jaroslav Řeh{\'a}{\vc}ek and Zdeněk Hradil and Miroslav Je{\vz}ek}, journal={Physical Review A}, year={2001}, volume={63}, pages={040303} }

An iterative algorithm for the reconstruction of an unknown quantum state from the results of incompatible measurements is proposed. It consists of Expectation-Maximization step followed by a unitary transformation of the eigenbasis of the density matrix. The procedure has been applied to the reconstruction of the entangled pair of photons.

## Tables from this paper

## 89 Citations

### Quantification of entanglement by means of convergent iterations.

- Computer SciencePhysical review letters
- 2003

The relative entropy of entanglement of a given bipartite quantum state is calculated by means of a convergent iterative algorithm. When this state turns out to be nonseparable, the algorithm also…

### Diluted maximum-likelihood algorithm for quantum tomography

- Mathematics
- 2007

We propose a refined iterative likelihood-maximization algorithm for reconstructing a quantum state from a set of tomographic measurements. The algorithm is characterized by a very high convergence…

### Quantum measurement and estimation

- PhysicsOFC 2001
- 2001

Information about quantum systems is inferred from a sequence of measurements made on it. The maximum likelihood (ML) estimation gives an arguably natural optimum approach in quantum theory. The…

### Quantum Statistical Inference

- Biology
- 2006

We studied state estimation for several quantum statistical models and for estimation of unitary evolution. We also researched the hypothesis testing and state discrimination for entangled states…

### Optimal detection device for unknown quantum channel

- PhysicsPolish-Slovak-Czech Optical Conference on Wave and Quantum Aspects of Contemporary Optics
- 2003

Discrimination task is treated in the case of only partial prior information from measurements of unknown quantum sources. The construction of the optimal discrimination device and estimation of…

### Quantum inference of states and processes

- Physics
- 2003

The maximum-likelihood principle unifies inference of quantum states and processes from experimental noisy data. Particularly, a generic quantum process may be estimated simultaneously with unknown…

### Iterative maximum-likelihood reconstruction in quantum homodyne tomography

- Mathematics
- 2004

I propose an iterative expectation maximization algorithm for reconstructing the density matrix of an optical ensemble from a set of balanced homodyne measurements. The algorithm applies directly to…

### Quantum state reconstruction: a comparison of maximum likelihood and tomographic schemes

- PhysicsQELS 2001
- 2001

Summary form only given. Experimental techniques for measurement of the quantum state of light have been the subject of intensive investigation for some time. Tomographic techniques have been applied…

### Triggered qutrits for quantum communication protocols.

- PhysicsPhysical review letters
- 2004

This Letter shows for the first time the experimental implementation of these three basic steps on a pure state in a three-dimensional space, by means of the orbital angular momentum of the photons, and demonstrates that any transformation in the three- dimensional space can be performed.

### Quantum state tomography with quantum shot noise

- Physics
- 2006

We propose a scheme for a complete reconstruction of one- and two-particle orbital quantum states in mesoscopic conductors. The conductor in the transport state continuously emits orbital quantum…

## References

SHOWING 1-6 OF 6 REFERENCES

### Phys

- Rev. A 55, R1561
- 1997

### Phys

- Lett. A 261, 20
- 1999

### Phys

- Rev. Lett. 78, 2275
- 1997

### Phys

- Rev. Lett. 62 2377 (1989); A. S. Lane, S. L. Braunstein, C. M. Caves, Phys. Rev. A 47 1667 (1993); J. Řeháček, Z. Hradil, M. Zawisky, S. Pascazio, H. Rauch, J. Peřina, Phys. Rev. A 60, 473 (1999); G. M. D’ Ariano, M. G. A. Paris, M. F. Sacchi, Phys. Rev. A 62, 023815
- 2000

### A: Math

- Gen. to be published
- 2000