Comment on “Quantum Entropy and Special Relativity”

Abstract

Peres, Scudo, and Terno (PST) point out in [1] that the entropy of relativistic qubits is not a relativistic scalar. The crucial element of the construction is the reduced density matrix of 'spin degrees of freedom' defined by a partial trace over momenta of a full 1-particle density matrix of a massive spin-1/2 particle. I understand that the Authors have in mind an experiment where detectors are blind to the particle momentum and distinguish only different polarizations. In this context I want to point out two elements that have led to some controversies concerning the physical meaning of the phenomenon.If the momentum operator has spectral representation P = dΓ(p)p|p p| then the helicity operator. A probability that the particle has helicity s is given by p s = ψ|Π s |ψ = dΓ(p)|ψ(p, s)| 2 . Elliptic polarizations correspond to observables U W 0 U † where U may be momentum dependent. If U is momentum independent then the probabilities associated with U Π s U

Physical interpretation of the Wigner rotations and its implications for relativistic quantum information

“…We are led to the conclusion that it is not possible to make a momentum-spin separation of the system and to define a reduced density matrix for spin, as was done in many previous papers on the subject [2, 4, 9, 10, 12, 15-21, 23, 24]. We also show that the use of the Pauli-Lubanski (or similar) spin operators to describe spin measurements, as in [1,5,8,11,13,14,16,22,23], depends on the coupling of the spin to a quantity that transforms as part of a four-vector under the Lorentz transformations in the measuring apparatus. However, we do not know if such a coupling exists in nature.…”

Radiative processes of two entangled atoms outside a Schwarzschild black hole

“…Among several investigations in the field, we would also like to mention the analysis regarding quantum teleportation between noninertial observers [69][70][71], relativistic approaches to the EinsteinPodolsky-Rosen framework and also to Bell's inequality [72][73][74][75]. References [76][77][78][79][80][81][82][83] provide more intriguing discussions on the subject of relativistic quantum entanglement for the interested reader. The point is that most of these studies were implemented in a framework of open quantum systems.…”

Three-particle Bell-like inequalities under Lorentz transformations

“…This situation is considered by many authors for both of the low-and high-energy particles, and some of these efforts can be found in refs. [29][30][31][32][33][34][43][44][45][46][47][48][49][50][51][64][65][66]. In the laboratory frame (S) for a system, including three spin-1 2 particles with the spin state |ψ and the momentum state | − → p 1 − → p 2 − → p 3 , the state of the system is written as…”

“…More debates on the results published by Peres and his colleagues can be found in refs. [31,32]. Additionally, it is useful to mention here that relativistic motions may induce some noises to the quantum cryptographic protocols [33,34].…”