We examine various manipulations of photon number states which can be implemented by teleportation technique with number-sum measurement. The preparations of the Einstein-Podolsky-Rosen resources as well as the number-sum measurement resulting in projection to certain Bell state may be done conditionally with linear optical elements, i.e., beam splitters, phase shifters, and zero-one-photon detectors. Squeezed vacuum states are used as primary entanglement resource, while single-photon sources are not required.
We propose a realizable experimental scheme to prepare superposition of the vacuum and one-photon states by truncating an input coherent state. The scheme is based on the quantum scissors device proposed by Pegg, Phillips, and Barnett [Phys. Rev. Lett. 81, 1604 (1998)] and uses photon-counting detectors, a single photon source, and linear optical elements. Realistic features of the photon counting and single-photon generation are taken into account and possible error sources are discussed together with their effect on the fidelity and efficiency of the truncation process. Wigner function and phase distribution of the generated states are given and discussed for the evaluation of the proposed scheme.
Linear-optical realizations of Bell state measurement (BSM) on two single-photon qubits succeed with probability
ps no higher than 0.5. However, predetection quadrature squeezing, i.e., quantum noise limited phase sensitive amplification, in the usual linear-optical BSM circuit, can yield ${p}_{s}\ensuremath{\approx}0.643$. The ability to achieve
ps>0.5 has been found to be critical in resource-efficient realizations of linear-optical quantum computing and all-photonic quantum repeaters. Yet, the aforesaid value of
ps>0.5 is not known to be the maximum achievable using squeezing, thereby leaving it open whether close-to-
100 efficient BSM might be achievable using squeezing as a resource. In this paper, we report insights on why squeezing-enhanced BSM achieves
ps>0.5. Using this, we show that the previously reported ${p}_{s}\ensuremath{\approx}0.643$ at single-mode squeezing strength
r=0.6585---for unambiguous state discrimination (USD) of all four Bell states---is an experimentally unachievable point result, which drops to ${p}_{s}\ensuremath{\approx}0.59$ with the slightest change in
r. We, however, show that squeezing-induced boosting of
ps with USD operation is still possible over a continuous range of
r, with an experimentally achievable maximum occurring at
r=0.5774, achieving ${p}_{s}\ensuremath{\approx}0.596$. Finally, deviating from USD operation, we explore a trade space between
ps, the probability with which the BSM circuit declares a ``success,'' versus the probability of error
pe, the probability of an input Bell state being erroneously identified given the circuit declares a success. Since quantum error correction could correct for some
pe>0, this tradeoff may enable better quantum repeater designs by potentially increasing the entanglement generation rates with
ps exceeding what is possible with traditionally studied USD operation of BSMs.
We present an experimental scheme that realizes joint measurement of photon-number sum and phase-difference operators on a two-mode field. The proposed scheme only involves linear optical elements and photon detectors with single-photon sensitivity. Furthermore, we demonstrate that such a measurement setup can be applied to generate two-mode N-photon entangled states from a pair of squeezed vacuum states. These N-photon entangled states are useful resources for quantum-information processing, high-precision frequency measurement, and quantum optical lithography.
We compare the standard 50%-efficient single beam splitter method for Bell-state measurement to a proposed 75%-efficient auxiliary-photon-enhanced scheme [W. P. Grice, Phys. Rev. A 84, 042331 (2011)] in light of realistic conditions. The two schemes are compared with consideration for high input state photon loss, auxiliary state photon loss, detector inefficiency and coupling loss, detector dark counts, and non-number-resolving detectors. We also analyze the two schemes when multiplexed arrays of non-number-resolving detectors are used. Furthermore, we explore the possibility of utilizing spontaneous parametric down-conversion as the auxiliary photon pair source required by the enhanced scheme. In these different cases, we determine the bounds on the detector parameters at which the enhanced scheme becomes superior to the standard scheme and describe the impact of the different imperfections on measurement success rate and discrimination fidelity. This is done using a combination of numeric and analytic techniques. For many of the cases discussed, the size of the Hilbert space and the number of measurement outcomes can be very large, which makes direct numerical solutions computationally costly. To alleviate this problem, all of our numerical computations are performed using pure states. This requires tracking the loss modes until measurement and treating dark counts as variations on measurement outcomes rather than modifications to the state itself. In addition, we provide approximate analytic expressions that illustrate the effect of different imperfections on the Bell-state analyzer quality.
Quantum state teleportation of optical number states is conspicuously absent from the list of experimental milestones achieved to date. Here we demonstrate analytically a teleportation scheme with fidelity
100% for optical number states of arbitrary dimension using linear optical elements only. To this end, we develop an EPR source to supply Bell-type states for the teleportation, and show how the same set-up can also be used as a Bell-state analyser (BSA) when implemented in a time-reversal manner. These two aspects are then brought together to complete the teleportation protocol in a scheme that can deliver perfect fidelity, albeit with an efficiency that decays exponentially as the occupation of the number states increases stepwise. The EPR source and BSA schemes both consist of two optical axes in a symmetrical V-shape experimental layout, along which beam-splitters are placed cross-beam fashion at regular intervals, with their transmittivities treated as variables for which the values are calculated ad hoc. In particular, we show the full treatment for the case of qutrit teleportation, and calculate the transmittivity values of the beam splitters required for teleporting qubits, qutrits, qupentits, quheptits and qunits. The general case for arbitrary-dimensional number state teleportation is demonstrated through a counting argument.