We investigate the role of inefficiency in quantum measurements in the quantum-to-classical transition, and consistently observe the quantum-to-classical transition by coarsening the references of the measurements (e.g., when and where to measure). Our result suggests that the definition of measurement precision in quantum theory should include the degree of the observer's ability to precisely control the measurement references.PACS numbers: 03.67. Mn, 42.50.Dv, 03.65.Ud, Introduction.-Typical quantum phenomena observed on microscopic scales somehow disappear on macroscopic scales. There have been trials to explain the quantumto-classical transition. Decoherence is one of the well known and successful attempts to explain such a revelation of a classical world out of quantum mechanical rules [1]. There are two crucial elements in the framework of quantum mechanics: one is the state of a physical system represented by a wave function, and the other is the measurement represented by non-negative operators. The decoherence program focuses on the evolution of the state: it describes a transition of a quantum state to a classical one due to its interactions with environments.Recently, a different point of view was presented [2], where coarsening of measurements is attributed to the cause of the quantum-to-classical transition. Along this line, it was also pointed out that coarsening of measurements makes it hard to detect micro-macro entanglement in optical systems [3]. However, there exist seemingly contradicting results where even fuzzy measurements allow to observe severe violations of the Bell inequality [4, 13] and also of the Leggett-Garg inequality [6]. It means that fuzziness in measurements do not always result in the quantum-to-classical transition.There is yet another example in which coarsening measurements results in local realism under stronger restrictions [7]. There have been extensive attempts to clarify sophisticated conditions of the quantum-to-classical transition [8][9][10][11][12] and it has been found that the quantumto-classical transition does not always occur when it is expected [9, 11, 12]. Indeed, a condition of the measurement process in which the quantum-to-classical transition is definitely forced to occur is yet to be found.In fact, a complete measurement process is composed of two parts: the one is to set a measurement reference and control it while the other is the final detection with the corresponding projection operator. The aforementioned works to explain the quantum-to-classical transition have focused on the role of inefficiency in the final detection by coarsening its measuring resolution. On the other hand, the control of the measurement reference is
There have been several upper bounds on the quantum capacity of the single-mode Gaussian channels with thermal noise, such as thermal attenuator and amplifier. We consider a class of attenuator and amplifier with more general noises, including squeezing or even non-Gaussian one. We derive new upper bounds on the energy-constrained quantum capacity of those channels by using the quantum conditional entropy power inequality. Also, we obtain lower bounds for the same channels by means of Gaussian optimizer with fixed input entropy. They give narrow bounds when the transmissivity is near unity and the energy of input state is low.
We propose a scheme of loss-resilient entanglement swapping between two distant parties via an imperfect optical channel. In this scheme, two copies of hybrid entangled states are prepared and the continuous-variable parts propagate through lossy media. In order to perform successful entanglement swapping, several different measurement schemes are considered for the continuousvariable parts such as single-photon detection for ideal cases and a homodyne detection for practical cases. We find that the entanglement swapping using hybrid states with small amplitudes offers larger entanglement than the discrete-variable entanglement swapping in the presence of large losses. Remarkably, this hybrid scheme still offers excellent robustness of entanglement to the detection inefficiency. Thus, the proposed scheme could be used for the practical quantum key distribution in hybrid optical states under photon losses.
We find that the purifications of several Gaussian maximally mixed states (GMMSs) correspond to some Gaussian maximally entangled states (GMESs) in the continuous-variable regime. Here, we consider a two-mode squeezed vacuum (TMSV) state as a purification of the thermal state and construct a general formalism of the Gaussian purification process. Moreover, we introduce other kind of GMESs via the process. All of our purified states of the GMMSs exhibit Gaussian profiles; thus, the states show maximal quantum entanglement in the Gaussian regime.Comment: 6 pages, 2 figures; Close to published versio
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