Perfect quantum state mirroring in a chain of N spins is defined as the condition in which the state 丨i 丨of the chain is swapped into the state 丨N - i丨 within a time evolution interval r. Such a phenomenon is an i...Perfect quantum state mirroring in a chain of N spins is defined as the condition in which the state 丨i 丨of the chain is swapped into the state 丨N - i丨 within a time evolution interval r. Such a phenomenon is an interesting way of transfering entanglement. An expressions for the perfect mirroring of a single qubit contained in a spin chain were proposed in the past. We exploit such an expressions for calculating the evolution times in chains of both two and three spins. In the case of a chain of two qubits, we derive conditions under which the associated four Bell states diagonalize the Hamiltonian. It is found that for the two Bell states 丨Ф＋） and 丨Ф-）, perfect mirroring does not occur （i.e. entanglement is not preserved under swapping）. On the other hand, perfect single qubit mirror effect （entanglement preservation） indeed occurs for the other two Bell states 丨ψ＋） and 丨ψ-） which are mapped into 丨Ф＋） and 丨Ф-） respectively. For the case of a chain of three qubits, the effects of a perfect single qubit mirroring on a set of four maximally entangled three qubit states ψl, ψ2, X1, and X2are studied. Due to the fact that quantum mirroring preserves maximal entanglement, the states ψ1 and ψ2 are not altered. However, quantum mirroring changes the states X1 and X2 only if we apply perfect quantum state mirroring in the site a = 1 of the three qubits spin chain. The above constrains the preservation of maximal entanglement under qubit mirroring of such a state. Due to the fact that swapping has already been experimentally tested, a posible, experimental implementations of single qubit mirroring is possible.展开更多
We study the Bell's inequality and multipartite entanglement generation for initially maximally entangled states of free Dirac field in a non inertial frame and asymptotically flat Robertson–Walker space-time.For...We study the Bell's inequality and multipartite entanglement generation for initially maximally entangled states of free Dirac field in a non inertial frame and asymptotically flat Robertson–Walker space-time.For two qubit case,we show that the Bell's inequality always is violated as measured by the accelerated observers which are in the causally connected regions.On the other hand,for those observers in the causally disconnected regions inequality is not violated for any values of acceleration.The generated three qubit state from two qubit state due to acceleration of one parties has a zero 3-tangle.For a three qubit state,the inequality violated for measurements done by both causally connected and disconnected observers.Initially GHZ state with non zero 3-tangle,in accelerated frame,transformed to a four qubit state with vanishing 4-tangle value.On the other hand,for a W-state with zero 3-tangle,in non inertial frame,transformed to a four qubit state with a non-zero 4-tangle acceleration dependent.In an expanding space-time with asymptotically flat regions,for an initially maximally entangled state,the maximum value of violation of Bell's inequality in the far past decreased in the far future due to cosmological particle creation.For some initially maximally entangled states,the generated four qubit state due to expansion of space-time,has non vanishing 4-tangle.展开更多
文摘Perfect quantum state mirroring in a chain of N spins is defined as the condition in which the state 丨i 丨of the chain is swapped into the state 丨N - i丨 within a time evolution interval r. Such a phenomenon is an interesting way of transfering entanglement. An expressions for the perfect mirroring of a single qubit contained in a spin chain were proposed in the past. We exploit such an expressions for calculating the evolution times in chains of both two and three spins. In the case of a chain of two qubits, we derive conditions under which the associated four Bell states diagonalize the Hamiltonian. It is found that for the two Bell states 丨Ф＋） and 丨Ф-）, perfect mirroring does not occur （i.e. entanglement is not preserved under swapping）. On the other hand, perfect single qubit mirror effect （entanglement preservation） indeed occurs for the other two Bell states 丨ψ＋） and 丨ψ-） which are mapped into 丨Ф＋） and 丨Ф-） respectively. For the case of a chain of three qubits, the effects of a perfect single qubit mirroring on a set of four maximally entangled three qubit states ψl, ψ2, X1, and X2are studied. Due to the fact that quantum mirroring preserves maximal entanglement, the states ψ1 and ψ2 are not altered. However, quantum mirroring changes the states X1 and X2 only if we apply perfect quantum state mirroring in the site a = 1 of the three qubits spin chain. The above constrains the preservation of maximal entanglement under qubit mirroring of such a state. Due to the fact that swapping has already been experimentally tested, a posible, experimental implementations of single qubit mirroring is possible.
基金Islamic Azad University,Khorram Branch,for Financial support
文摘We study the Bell's inequality and multipartite entanglement generation for initially maximally entangled states of free Dirac field in a non inertial frame and asymptotically flat Robertson–Walker space-time.For two qubit case,we show that the Bell's inequality always is violated as measured by the accelerated observers which are in the causally connected regions.On the other hand,for those observers in the causally disconnected regions inequality is not violated for any values of acceleration.The generated three qubit state from two qubit state due to acceleration of one parties has a zero 3-tangle.For a three qubit state,the inequality violated for measurements done by both causally connected and disconnected observers.Initially GHZ state with non zero 3-tangle,in accelerated frame,transformed to a four qubit state with vanishing 4-tangle value.On the other hand,for a W-state with zero 3-tangle,in non inertial frame,transformed to a four qubit state with a non-zero 4-tangle acceleration dependent.In an expanding space-time with asymptotically flat regions,for an initially maximally entangled state,the maximum value of violation of Bell's inequality in the far past decreased in the far future due to cosmological particle creation.For some initially maximally entangled states,the generated four qubit state due to expansion of space-time,has non vanishing 4-tangle.
