Entanglement entropy and determination of an unknown quantum state
Abstract
An initial unknown quantum state can be determined with a single measurement apparatus by letting it interact with an auxiliary, ancilla, system as proposed by Allahverdyan, Balian, and Nieuwenhuizen [Phys. Rev. Lett. 92, 120402 (2004)]. In the case of two qubits, this procedure allows one to reconstruct the initial state of the qubit of interest, S , by measuring three commuting observables and therefore by means of a single apparatus, for the total system S+A at a later time. The determinant of the matrix of the linear transformation connecting the measurements of three commuting observables at time t>0 to the components of the polarization vector of S at time t=0 is used as an indicator of the reconstructability of the initial state of the system S . We show that a connection between the entanglement entropy of the total system S+A and such a determinant exists, and that for a pure state a vanishing entanglement individuates, without a need for any measurement, those intervals of time for which the reconstruction procedure is least efficient. This property remains valid for a generic dimension of S . In the case of a mixed state, this connection is lost.
- Publication:
-
Physical Review A
- Pub Date:
- December 2008
- DOI:
- 10.1103/PhysRevA.78.062115
- arXiv:
- arXiv:0811.4679
- Bibcode:
- 2008PhRvA..78f2115A
- Keywords:
-
- 03.65.Wj;
- 03.65.Ud;
- 05.30.-d;
- 05.70.Ln;
- State reconstruction quantum tomography;
- Entanglement and quantum nonlocality;
- Quantum statistical mechanics;
- Nonequilibrium and irreversible thermodynamics;
- Quantum Physics
- E-Print:
- 5 pages 2 figures, accepted for publication on Physical Review A