Weak values and continuous-variable entanglement concentration

Abstract

We demonstrate a general weak measurement model which allows Gaussian preserving entanglement concentration of the two mode squeezed vacuum. The power of this simple and elegant protocol is through the constraints it places on possible ancilla states and measurement strategies that will allow entanglement concentration. In particular, it is shown how previously discovered protocols of this kind emerge as special examples of the general model described here. Finally, as evidence of its utility, we use it to provide another novel example of such a protocol.

Weak measurements with entangled probes

“…Furthermore, in conjunction with condition on K, we find the required properties of the interaction Hamiltonian to allow the desired effect. The capacity of Im(O W ) as a calculational tool in entanglement concentration protocols has been previous noted by us in [13] with the example of continuousvariable states. The current work here can be regarded as a generalization to arbitrary pure bipartite entangled states.…”

“…The entanglement content of the probe is altered if and only if S f = S i and so S f /S i = 1, which is true if both Im(O W ) and Tr( K(σ i − ω)) cannot be zero. The requirement that Im(O W ) = 0 is obvious from (13) as it accompanies a non-unitary transformation of the probe state. This follows from the properties of entanglement measures which are designed to be non-increasing under local unitary operations [10].…”

Quantum secret sharing with continuous-variable cluster states

“…Instead of conducting teleportation after each round of QQ QSS, we consider the extracted state is stored in quantum memories. After rounds of the QQ protocol, a more entangled state can be distilled from the stored extracted states through CV entanglement distillation [40][41][42][43][44]. Although distilling a maximally entangled CV state is impossible due to the infinite required energy, the enrichment of entanglement can enhance the fidelity of the teleportation.…”

Theory of “Weak Value" and Quantum Mechanical Measurements

“…The framework of weak values has been theoretically applied to foundations of quantum physics, e.g., the derivation of the Born rule from the alternative assumption for a priori measured value [74], the relationship to the uncertainty relationship [72], the quantum stochastic process [190], the tunneling traverse time [135,170,171], arrival time and time operator [21,39,146,147], the decay law [46,187], the non-locality [32,180,181], especially, quantum non-locality, which is characterized by the modular variable, consistent history [87,188], Bohmian quantum mechanics [98], semi-classical weak values on the tunneling [175], the quantum trajectory [192], and classical stochastic theory [177]. Also, in quantum information science, the weak value was analyzed on quantum computation [35,126], quantum communications [29,36], quantum estimation, e.g., state tomography [67][68][69]111,158] and the parameter estimation [70,73,157], the entanglement concentration [113], the quasi-probability distribution [24,61,148,183] and the cloning of the unknown quantum state with hint [161]. Furthermore, this was applied to the cosmological situations in quantum-mechanical region, e.g., the causality…”