-
1
-
-
12444320554
-
-
For a historical introduction, see Springer, New York
-
For a historical introduction, see J. Gemmer, M. Michel, and G. Mahler, Quantum Thermodynamics (Springer, New York, 2004), and references therein.
-
(2004)
Quantum Thermodynamics
-
-
Gemmer, J.1
Michel, M.2
Mahler, G.3
-
2
-
-
4244156556
-
-
10.1103/PhysRevLett.80.1373
-
H. Tasaki, Phys. Rev. Lett. 80, 1373 (1998). 10.1103/PhysRevLett.80.1373
-
(1998)
Phys. Rev. Lett.
, vol.80
, pp. 1373
-
-
Tasaki, H.1
-
6
-
-
33144456594
-
-
10.1103/PhysRevLett.96.050403
-
S. Goldstein, J. L. Lebowitz, R. Tumulka, and N. Zanghi, Phys. Rev. Lett. 96, 050403 (2006). 10.1103/PhysRevLett.96.050403
-
(2006)
Phys. Rev. Lett.
, vol.96
, pp. 050403
-
-
Goldstein, S.1
Lebowitz, J.L.2
Tumulka, R.3
Zanghi, N.4
-
9
-
-
33646759564
-
-
10.1080/00107510600581136
-
M. Hartmann, Contemp. Phys. 47, 89 (2006). 10.1080/00107510600581136
-
(2006)
Contemp. Phys.
, vol.47
, pp. 89
-
-
Hartmann, M.1
-
11
-
-
33947276703
-
-
10.1103/PhysRevA.75.032109
-
P. Zanardi, H. T. Quan, X. Wang, and C. P. Sun, Phys. Rev. A 75, 032109 (2007). 10.1103/PhysRevA.75.032109
-
(2007)
Phys. Rev. A
, vol.75
, pp. 032109
-
-
Zanardi, P.1
Quan, H.T.2
Wang, X.3
Sun, C.P.4
-
12
-
-
33749345011
-
-
10.1103/PhysRevE.74.031123
-
P. Zanardi and N. Paunkovic, Phys. Rev. E 74, 031123 (2006). 10.1103/PhysRevE.74.031123
-
(2006)
Phys. Rev. e
, vol.74
, pp. 031123
-
-
Zanardi, P.1
Paunkovic, N.2
-
13
-
-
33846134423
-
-
10.1209/epl/i2006-10388-9
-
S. O. Skrovseth, Europhys. Lett. 76, 1179 (2006). 10.1209/epl/i2006- 10388-9
-
(2006)
Europhys. Lett.
, vol.76
, pp. 1179
-
-
Skrovseth, S.O.1
-
16
-
-
66349135211
-
-
In this paper, we take as measure of distance between two quantum states the Uhlmann fidelity, defined as FU (ρ1, ρ2) =Tr (ρ1 ρ2 ρ1) 1/2. We stress that other measurements of proximity between states, such as the fidelity functions derived from the trace distance, FTr (ρ1, ρ2) =1- 1 2 Tr [| ρ1 - ρ2 |], or the Hilbert-Schmidt distance FHS (ρ1, ρ2) =1- 1 2 Tr [(ρ1 - ρ2) 2], or the relative entropy S (ρ1 ρ2) =Tr [ρ1 (log ρ1 -log ρ2)], lead to the same main results.
-
In this paper, we take as measure of distance between two quantum states the Uhlmann fidelity, defined as FU (ρ1, ρ2) =Tr (ρ1 ρ2 ρ1) 1/2. We stress that other measurements of proximity between states, such as the fidelity functions derived from the trace distance, FTr (ρ1, ρ2) =1- 1 2 Tr [| ρ1 - ρ2 |], or the Hilbert-Schmidt distance FHS (ρ1, ρ2) =1- 1 2 Tr [(ρ1 - ρ2) 2], or the relative entropy S (ρ1 ρ2) =Tr [ρ1 (log ρ1 -log ρ2)], lead to the same main results.
-
-
-
-
17
-
-
84924581223
-
-
Cambridge University Press, Cambridge, England
-
S. Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, England, 1999).
-
(1999)
Quantum Phase Transitions
-
-
Sachdev, S.1
-
19
-
-
8644277736
-
-
10.1103/PhysRevA.3.786
-
E. Barouch and B. McCoy, Phys. Rev. A 3, 786 (1971). 10.1103/PhysRevA.3. 786
-
(1971)
Phys. Rev. A
, vol.3
, pp. 786
-
-
Barouch, E.1
McCoy, B.2
-
20
-
-
0036757880
-
-
10.1103/PhysRevA.66.032110
-
T. J. Osborne and M. A. Nielsen, Phys. Rev. A 66, 032110 (2002). 10.1103/PhysRevA.66.032110
-
(2002)
Phys. Rev. A
, vol.66
, pp. 032110
-
-
Osborne, T.J.1
Nielsen, M.A.2
-
21
-
-
34547653542
-
-
We are omitting the local terms since we focus on possible corrections due to interactions at the boundary of the considered block. In this case (i.e., h=0) the model presented in Eq. 12 gives the classical limit of the quantum model. The classical limit of the full quantum Hamiltonian H n can be found in 10.1103/PhysRevB.76.064405
-
We are omitting the local terms since we focus on possible corrections due to interactions at the boundary of the considered block. In this case (i.e., h=0) the model presented in Eq. 12 gives the classical limit of the quantum model. The classical limit of the full quantum Hamiltonian H n can be found in A. Cuccoli, A. Taiti, R. Vaia, and P. Verrucchi, Phys. Rev. B 76, 064405 (2007). However, the analysis of the latter goes beyond the scope of the present paper. 10.1103/PhysRevB.76.064405
-
(2007)
Phys. Rev. B
, vol.76
, pp. 064405
-
-
Cuccoli, A.1
Taiti, A.2
Vaia, R.3
Verrucchi, P.4
-
22
-
-
66349119162
-
-
Here we are not considering systems for which an exchange of particles is possible between subparts of them or between the system and its environment.
-
Here we are not considering systems for which an exchange of particles is possible between subparts of them or between the system and its environment.
-
-
-
-
23
-
-
66349105193
-
-
Clearly, such an improvement is of relevance only in those cases where the fidelity F [Ω2 (β), ρ 2 (β)] is significantly smaller than 1. In particular, our calculations show an improvement in the fidelity also for h 1. However, in these cases, F [Ω2 (β), ρ 2 (β)] is already almost indistinguishable from 1. The improvement obtained optimizing the local temperature is then insignificant.
-
Clearly, such an improvement is of relevance only in those cases where the fidelity F [Ω2 (β), ρ 2 (β)] is significantly smaller than 1. In particular, our calculations show an improvement in the fidelity also for h 1. However, in these cases, F [Ω2 (β), ρ 2 (β)] is already almost indistinguishable from 1. The improvement obtained optimizing the local temperature is then insignificant.
-
-
-
-
26
-
-
19744365684
-
-
10.1103/PhysRevLett.93.207205
-
M. Zwolak and G. Vidal, Phys. Rev. Lett. 93, 207205 (2004). 10.1103/PhysRevLett.93.207205
-
(2004)
Phys. Rev. Lett.
, vol.93
, pp. 207205
-
-
Zwolak, M.1
Vidal, G.2
-
27
-
-
0037061511
-
-
10.1038/416608a
-
A. Osterloh, L. Amico, G. Falci, and R. Fazio, Nature (London) 416, 608 (2002). 10.1038/416608a
-
(2002)
Nature (London)
, vol.416
, pp. 608
-
-
Osterloh, A.1
Amico, L.2
Falci, G.3
Fazio, R.4
|