Effectively classically correlated state of a measured system and a bosonic measurement apparatus

Abstract

We consider a multilevel system coupled to a bosonic measurement apparatus. We derive exact expressions for the time-dependent expectation values of a large class of physically relevant observables that depend on degrees of freedom of both systems. We find that, for this class, though the two systems become entangled as a result of their interaction, they appear classically correlated for long enough times. The unique corresponding time-dependent separable state is determined explicitly. To better understand the physical parameters that control the time scale of this effective disentanglement process, we study a one-dimensional measurement apparatus.

Monogamy Inequality for Any Local Quantum Resource and Entanglement

“…Consider, for instance, that A is a twolevel system, which interacts with a large system, B. For a pure dephasing Hamiltonian, and if A and B are initially in pure states, their common pure state reads |ψ = √ p|0 |0 + √ 1 − p|1 |1 , where p ∈ [0, 1], {|0 , |1 } is a basis of H 2 , and the states |ĩ are such that |0 = |1 at ini- tial time, and 0 |1 goes to zero at long times [24,41]. In this long time regime, the relative entropy of coherence, for the basis {|0 , |1 }, and the state ρ A = tr B |ψ ψ|, vanishes, and the entanglement of formation, for ρ = |ψ ψ|, reaches h(p) ≡ −p log p − (1 − p) log(1 − p).…”

“…It shows that the entanglement between two systems, and the violation, by one of them, of a state-dependent noncontextuality inequality, constrain each other. In the context of open sytems, the development of the entanglement between a system and its environment, due to their mutual interaction, is commonly seen as playing an essential role in the decoherence of the system [23,24]. These influences on the quantum properties of a system, of its entanglement with another system, suggest that there may be a general monogamy relation between any local quantum resource and entanglement.…”

“…The coherence R d may vanish at long times, for a particular basis {|i }, whereas the entanglement with the environment, allows nonzero coherence for other bases. Consider, for instance, that A is a twolevel system, which interacts with a large system, B. tial time, and 0| 1 goes to zero at long times [24,41]. In this long time regime, the relative entropy of coherence, for the basis {|0 , |1 }, and the state ρ A = tr B |ψ ψ|, vanishes, and the entanglement of formation, for ρ = |ψ ψ|, reaches h(p) ≡ −p log p − (1 − p) log(1 − p).…”

Simple state preparation for contextuality tests with few observables

“…First, for some states, the noncontextuality inequality is satisfied with any set of observables obeying the required compatibility relations. Second, for the other states, the observables must be chosen according to the state, in order to violate the inequality [13][14][15][16][17]. A noncontextuality inequality involves a sum of expectation values.…”