TY - JOUR

T1 - Phase-random states

T2 - ensembles of states with fixed amplitudes and uniformly distributed phases in a fixed basis

AU - Nakata, Yoshifumi

AU - Turner, Peter S.

AU - Murao, Mio

N1 - Revised, 12 pages, 4 figure

PY - 2012/7/3

Y1 - 2012/7/3

N2 - Motivated by studies of typical properties of quantum states in statistical mechanics, we introduce phase-random states, an ensemble of pure states with fixed amplitudes and uniformly distributed phases in a fixed basis. We first show that canonical states typically appear in subsystems of phase-random states. We then investigate the simulatability of phase-random states, which is directly related to that of time evolution in closed systems, by studying their entanglement properties. We find that starting from a separable state, time evolutions under Hamiltonians composed of only separable eigenstates generate extremely high entanglement and are difficult to simulate with matrix product states. We also show that random quantum circuits consisting of only two-qubit diagonal unitaries can generate an ensemble with the same average entanglement as phase-random states.

AB - Motivated by studies of typical properties of quantum states in statistical mechanics, we introduce phase-random states, an ensemble of pure states with fixed amplitudes and uniformly distributed phases in a fixed basis. We first show that canonical states typically appear in subsystems of phase-random states. We then investigate the simulatability of phase-random states, which is directly related to that of time evolution in closed systems, by studying their entanglement properties. We find that starting from a separable state, time evolutions under Hamiltonians composed of only separable eigenstates generate extremely high entanglement and are difficult to simulate with matrix product states. We also show that random quantum circuits consisting of only two-qubit diagonal unitaries can generate an ensemble with the same average entanglement as phase-random states.

KW - quant-ph

U2 - 10.1103/PhysRevA.86.012301

DO - 10.1103/PhysRevA.86.012301

M3 - Article (Academic Journal)

JO - Physical Review A: Atomic, Molecular and Optical Physics

JF - Physical Review A: Atomic, Molecular and Optical Physics

SN - 1050-2947

ER -