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Entangled quantum states, such as N00N states, are of major importance for quantum technologies due to their quantum-enhanced performance. At the same time, their quantum correlations are relatively vulnerable when they are subjected to imperfections. Therefore, it is crucial to determine under which circumstances their distinct quantum features can be exploited. In this paper, we study the entanglement property of noisy N00N states. This class of states is a generalization of N00N states including various attenuation effects, such as mixing, constant or fluctuating losses, and dephasing. To verify their entanglement, we pursue two strategies: detection-based entanglement witnesses and entanglement quasiprobabilities. Both methods result from our solution of so-called separability eigenvalue equations. In particular, the entanglement quasiprobabilities allow for a full entanglement characterization. As examples of our general treatment, the cases of N00N states subjected to Gaussian dephasing and fluctuating atmospheric losses are explicitly studied. In any correlated fluctuating loss channel, entanglement is found to survive for non-zero transmissivity. In addition, an extension of our approach to multipartite systems is given, and the relation to the quantum-optical nonclassicality in phase-space is discussed.
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Quantum metrology and quantum information necessitate a profound study of suitable states. Attenuations induced by free-space communication links or fluctuations in the generation of such states limit the quantum enhancement in possible applications. For this reason we investigate quantum features of mixtures of so-called N00N states propagating in atmospheric channels. First, we show that noisy N00N states can still yield a phase resolution beyond classical limitations. Second, we identify entanglement of noisy N00N states after propagation in fluctuating loss channels. To do so, we apply the partial transposition criterion. Our theoretical analysis formulates explicit bounds which are indispensable for experimental verification of quantum entanglement and applications in quantum metrology.
Two qubits in pure entangled states going through separate paths and interacting with their own individual environments will gradually lose their entanglement. Here we show that the entanglement change of a two-qubit state due to amplitude damping noises can be recovered by entanglement swapping. Some initial states can be asymptotically purified into maximally entangled states by iteratively using our protocol.
We describe a phase transition for long-range entanglement in a three-dimensional cluster state affected by noise. The partially decohered state is modeled by the thermal state of a suitable Hamiltonian. We find that the temperature at which the entanglement length changes from infinite to finite is nonzero. We give an upper and lower bound to this transition temperature.
In this paper we examine the N-photon absorption properties of N00N states, a subclass of path entangled number states. We consider two cases. The first involves the N-photon absorption properties of the ideal N00N state, one that does not include spectral information. We study how the N-photon absorption probability of this state scales with N. We compare this to the absorption probability of various other states. The second case is that of two-photon absorption for an N = 2 N00N state generated from a type II spontaneous down conversion event. In this situation we find that the absorption probability is both better than analogous coherent light (due to frequency entanglement) and highly dependent on the optical setup. We show that the poor production rates of quantum states of light may be partially mitigated by adjusting the spectral parameters to improve their two-photon absorption rates. This work has application to quantum imaging, particularly quantum lithography, where the N-photon absorbing process in the lithographic resist must be optimized for practical applications.
The N00N state, which was introduced as a resource for quantum-enhanced metrology, is in fact a special case of a superposition of two SU(2) coherent states. We show here explicitly the derivation of the N00N state from the superposition state. This derivation makes clear the connection between these seemingly disparate states as well as shows how the N00N state can be generalized to a superposition of SU(2) coherent states.
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