Multi-mode Gaussian State Analysis with Total Photon Counting

The continuing improvement in the qualities of photon-number-resolving detectors opens new possibilities for measuring quantum states of light. In this work we consider the question of what properties of an arbitrary multimode Gaussian state are determined by a single photon-number-resolving detector that measures total photon number. We find an answer to this question in the ideal case where the exact photon-number probabilities are known. We show that the quantities determined by the total photon number distribution are the spectrum of the covariance matrix, the absolute displacement in each eigenspace of the covariance matrix, and nothing else. In the case of pure Gaussian states, the spectrum determines the squeezing parameters

Improving quantum state detection with adaptive sequential observations

For many quantum systems intended for information processing, one detects the logical state of a qubit by integrating a continuously observed quantity over time. For example, ion and atom qubits are typically measured by driving a cycling transition and counting the number of photons observed from the resulting fluorescence. Instead of recording only the total observed count in a fixed time interval, one can observe the photon arrival times and get a state detection advantage by using the temporal structure in a model such as a Hidden Markov Model. We study what further advantage may be achieved by applying pulses to adaptively transform the state during the observation. We give a three-state example where adaptively chosen transformations yield a clear advantage, and we compare performances on an ion example, where we see improvements in some regimes. We provide a software package that can be used for exploration of temporally resolved strategies with and without adaptively chosen transformations.Comment: Submitted for publication in Quantum Science and Technology. 26 pages, 8 figures. Corrected typos in appendix, updated acknowledgement

The statistical strength of experiments to reject local realism with photon pairs and inefficient detectors

Because of the fundamental importance of Bell's theorem, a loophole-free demonstration of a violation of local realism (LR) is highly desirable. Here, we study violations of LR involving photon pairs. We quantify the experimental evidence against LR by using measures of statistical strength related to the Kullback-Leibler (KL) divergence, as suggested by van Dam et al. [W. van Dam, R. Gill and P. Grunwald, IEEE Trans. Inf. Theory. 51, 2812 (2005)]. Specifically, we analyze a test of LR with entangled states created from two independent polarized photons passing through a polarizing beam splitter. We numerically study the detection efficiency required to achieve a specified statistical strength for the rejection of LR depending on whether photon counters or detectors are used. Based on our results, we find that a test of LR free of the detection loophole requires photon counters with efficiencies of at least 89.71%, or photon detectors with efficiencies of at least 91.11%. For comparison, we also perform this analysis with ideal unbalanced Bell states, which are known to allow rejection of LR with detector efficiencies above 2/3.Comment: 18 pages, 3 figures, minor changes (add more references, replace the old plots, etc.)

Constraints on Gaussian Error Channels and Measurements for Quantum Communication

Joint Gaussian measurements of two quantum systems can be used for quantum communication between remote parties, as in teleportation or entanglement swapping protocols. Many types of physical error sources throughout a protocol can be modeled by independent Gaussian error channels acting prior to measurement. In this work we study joint Gaussian measurements on two modes $\mathsf{A}$ and $\mathsf{B}$ that take place after independent single-mode Gaussian error channels, for example loss with parameters $l_\mathsf{A}$ and $l_\mathsf{B}$ followed by added noise with parameters $n_\mathsf{A}$ and $n_\mathsf{B}$. We show that, for any Gaussian measurement, if $l_\mathsf{A} + l_\mathsf{B} + n_\mathsf{A} + n_\mathsf{B} \geq 1$ then the effective total measurement is separable and unsuitable for teleportation or entanglement swapping of arbitrary input states. If this inequality is not satisfied then there exists a Gaussian measurement that remains inseparable. We extend the results and determine the set of pairs of single-mode Gaussian error channels that render all Gaussian measurements separable

Imperfect Detectors in Linear Optical Quantum Computers

We discuss the effects of imperfect photon detectors suffering from loss and noise on the reliability of linear optical quantum computers. We show that for a given detector efficiency, there is a maximum achievable success probability, and that increasing the number of ancillary photons and detectors used for one controlled sign flip gate beyond a critical point will decrease the probability that the computer will function correctly. We have also performed simulations of some small logic gates and estimate the efficiency and noise levels required for the linear optical quantum computer to function properly.Comment: 13 pages, 5 figure