Entanglement negativity is a measure of mixed-state entanglement increasingly used to investigate and characterize emerging quantum many-body phenomena, including quantum criticality and topological order. We present two results for the entanglement negativity: a disentangling theorem, which allows the use of this entanglement measure as a means to detect whether a wave function of three subsystems $A,\phantom{\rule{0.28em}{0ex}}B$ , and $C$ factorizes into a product state for parts $A{B}_{1}$ and ${B}_{2}C$ ; and a monogamy relation conjecture based on entanglement negativity, which states that if $A$ is very entangled with $B$ , then $A$ cannot be simultaneously very entangled also with $C$ .Entanglement negativity is a measure of mixed-state entanglement increasingly used to investigate and characterize emerging quantum many-body phenomena, including quantum criticality and topological order. We present two results for the entanglement negativity: a disentangling theorem, which allows the use of this entanglement measure as a means to detect whether a wave function of three subsystems $A,\phantom{\rule{0.28em}{0ex}}B$, and $C$ factorizes into a product state for parts $A{B}_{1}$ and ${B}_{2}C$; and a monogamy relation conjecture based on entanglement negativity, which states that if $A$ is very entangled with $B$, then $A$ cannot be simultaneously very entangled also with $C$.

arXiv:1401.5843Physical Review AJan 28, 201577 citations

Pre-management of disentanglement

Xiao-Feng Qian

We define threshold disentanglement as the level above which entanglement must be maintained for later use and calculate the values of quantum system parameters at t = 0 that will ensure that the threshold is not crossed in a specified time. An important issue is the possibility of non-smooth, typically non-exponential, decay of entanglement into the state of complete disentanglement. Given a specified operation time τ, we determine phase diagrams showing entanglement preservation during the evolution of a generic two-qubit mixed state as a function of selected initial parameters such as concurrence and excitation probabilities. In other words, disentanglement can be pre-managed through these parameters. Three common relaxation processes—amplitude, phase and depolarization—are considered.We define threshold disentanglement as the level above which entanglement must be maintained for later use and calculate the values of quantum system parameters at t = 0 that will ensure that the threshold is not crossed in a specified time. An important issue is the possibility of non-smooth, typically non-exponential, decay of entanglement into the state of complete disentanglement. Given a specified operation time τ, we determine phase diagrams showing entanglement preservation during the evolution of a generic two-qubit mixed state as a function of selected initial parameters such as concurrence and excitation probabilities. In other words, disentanglement can be pre-managed through these parameters. Three common relaxation processes—amplitude, phase and depolarization—are considered.

arXiv:1211.7001Journal of Physics A Mathematical and TheoreticalJun 13, 20144 citations

A,\phantom{\rule{0.28em}{0ex}}B

, and

C

factorizes into a product state for parts

A{B}_{1}

and

{B}_{2}C

; and a monogamy relation conjecture based on entanglement negativity, which states that if

A

is very entangled with

B

, then

A

cannot be simultaneously very entangled also with

C