PACS number s : 03.67.Mn, 89.70. c, 03.65. w, 02.50. r, 99.10.CdErratum: Connection between entanglement and the speed of quantum evolution
[Phys. Rev. A 72, 032337 (2005)]Peer reviewe

Batle, Josep

Casas, Montserrat

Plastino, A.

Plastino, Ángel R.

Digital.CSIC

Erratum: Connection between entanglement and the speed of quantum evolution[Phys. Rev. A 72, 032337 (2005)]J. Batle, M. Casas, A. Plastino, and A. R. PlastinoReceived 16 February 2006; published 17 April 2006DOI: 10.1103/PhysRevA.73.049904 PACS numbers: 03.67.Mn, 89.70.c, 03.65.w, 02.50.r, 99.10.CdIn Sec. II, Fig. 1 should be replaced by a new Fig. 1. This, in turn, originates small changes in the comments placed belowEq. 14. The specific origin of the errors in the previous wrong version of Fig. 1 was equation = C2/2, 1appearing in the second line after Eq. 14. This equation, corresponding to the upper curve in the previous Fig. 1, is wrongbecause it was wrongly derived from Eq. 13 which is indeed correct. A similar mistake led to Eq. 26 which must also bedeleted. It affects the old Fig. 2.According to the new Fig. 1, for all values of the concurrence C 0,1 the largest possible evolution time is given by /Tmin=2. This maximum value corresponds to = and =1/4 see Eq. 14. On the other hand, the minimum possiblevalue of  /Tmin is a monotonically decreasing function of C. Consequently, the difference between the maximum and theminimum evolution times augments as the concurrence grows.In Sec. III, Fig. 2 must be replaced by a new Fig. 2 as well, without changes in the caption. Furthermore, Eq. 23 must nowbe changed toTmin =4. 2As in the previously mentioned case of two distinguishable particles qubits, when we have two identical bosons themaximum evolution time is again for all values of C 0,1 given by  /Tmin=2. As a consequence, Eq. 26 must now bedeleted.Summing up, the amendments that have to be made in the paper are as follows: Figs. 1 and 2 have to be replaced by thecorresponding new ones; equation =C2 /2 in the second line after Eq. 14 has to be deleted; Eq. 23 has to be modified;and Eq. 26 has to be deleted.The main conclusions of the paper remain unchanged. Indeed, for systems of either two qubits or two identical bosons, thelower bound for the evolution time to an orthogonal state is a monotonically decreasing function of the concurrence. Allseparable states C=0 that evolve to an orthogonal state do so in the slowest “worst” possible way, associated with /Tmin=2. In order to achieve faster “better” evolution speeds associated with smaller values of  /Tmin one necessarilyneeds to increase the concurrence C that is, the amount of entanglement of the state. To achieve the fastest kind of possibleevolution  /Tmin=1, states of maximum entanglement C=1 are required.FIG. 1. Curves in the C ,T /TminC , /Tmin plane corre-sponding, for each value of C, to the states of two distinguishablequbits with maximum and minimum  /Tmin. The points representrandomly generated individual states that evolve to an orthogonalstate. All depicted quantities are dimensionless.FIG. 2. Curves in the C ,T /TminC , /Tmin plane corre-sponding, for each value of C, to the states of two bosons withmaximum and minimum  /Tmin. The points represent randomlygenerated individual states that evolve to an orthogonal state. Alldepicted quantities are dimensionless.PHYSICAL REVIEW A 73, 049904E 20061050-2947/2006/734/0499041/$23.00 ©2006 The American Physical Society049904-1

Erratum: Connection between entanglement and the speed of quantum evolution

Abstract

Similar works

Full text

Available Versions

Digital.CSIC