Bounds on the Probability of Success of Postselected Non-linear Sign Shifts Implemented with Linear Optics

The fundamental gates of linear optics quantum computation are realized by using single photons sources, linear optics and photon counters. Success of these gates is conditioned on the pattern of photons detected without using feedback. Here it is shown that the maximum probability of success of these gates is typically strictly less than 1. For the one-mode non-linear sign shift, the probability of success is bounded by 1/2. For the conditional sign shift of two modes, this probability is bounded by 3/4. These bounds are still substantially larger than the highest probabilities shown to be achievable so far, which are 1/4 and 2/27, respectively.Comment: 6 page

Comparison of LOQC C-sign gates with ancilla inefficiency and an improvement to functionality under these conditions

We compare three proposals for non-deterministic C-sign gates implemented using linear optics and conditional measurements with non-ideal ancilla mode production and detection. The simplified KLM gate [Ralph et al, Phys.Rev.A {\bf 65}, 012314 (2001)] appears to be the most resilient under these conditions. We also find that the operation of this gate can be improved by adjusting the beamsplitter ratios to compensate to some extent for the effects of the imperfect ancilla.Comment: to appear in PR

On Protected Realizations of Quantum Information

There are two complementary approaches to realizing quantum information so that it is protected from a given set of error operators. Both involve encoding information by means of subsystems. One is initialization-based error protection, which involves a quantum operation that is applied before error events occur. The other is operator quantum error correction, which uses a recovery operation applied after the errors. Together, the two approaches make it clear how quantum information can be stored at all stages of a process involving alternating error and quantum operations. In particular, there is always a subsystem that faithfully represents the desired quantum information. We give a definition of faithful realization of quantum information and show that it always involves subsystems. This justifies the "subsystems principle" for realizing quantum information. In the presence of errors, one can make use of noiseless, (initialization) protectable, or error-correcting subsystems. We give an explicit algorithm for finding optimal noiseless subsystems. Finding optimal protectable or error-correcting subsystems is in general difficult. Verifying that a subsystem is error-correcting involves only linear algebra. We discuss the verification problem for protectable subsystems and reduce it to a simpler version of the problem of finding error-detecting codes.Comment: 17 page

Upper bounds on success probabilities in linear optics

We develop an abstract way of defining linear-optics networks designed to perform quantum information tasks such as quantum gates. We will be mainly concerned with the nonlinear sign shift gate, but it will become obvious that all other gates can be treated in a similar manner. The abstract scheme is extremely well suited for analytical as well as numerical investigations since it reduces the number of parameters for a general setting. With that we show numerically and partially analytically for a wide class of states that the success probability of generating a nonlinear sign shift gate does not exceed 1/4 which to our knowledge is the strongest bound to date.Comment: 8 pages, typeset using RevTex4, 5 EPS figure

Quantum Estimation of Parameters of Classical Spacetimes

We describe a quantum limit to measurement of classical spacetimes. Specifically, we formulate a quantum Cramer-Rao lower bound for estimating the single parameter in any one-parameter family of spacetime metrics. We employ the locally covariant formulation of quantum field theory in curved spacetime, which allows for a manifestly background-independent derivation. The result is an uncertainty relation that applies to all globally hyperbolic spacetimes. Among other examples, we apply our method to detection of gravitational waves using the electromagnetic field as a probe, as in laser-interferometric gravitational-wave detectors. Other applications are discussed, from terrestrial gravimetry to cosmology.Comment: 23 pages. This article supersedes arXiv:1108.522

Time-Resolved Two-Photon Quantum Interference

The interference of two independent single-photon pulses impinging on a beam splitter is analysed in a generalised time-resolved manner. Different aspects of the phenomenon are elaborated using different representations of the single-photon wave packets, like the decomposition into single-frequency field modes or spatio-temporal modes matching the photonic wave packets. Both representations lead to equivalent results, and a photon-by-photon analysis reveals that the quantum-mechanical two-photon interference can be interpreted as a classical one-photon interference once a first photon is detected. A novel time-dependent quantum-beat effect is predicted if the interfering photons have different frequencies. The calculation also reveals that full two-photon fringe visibility can be achieved under almost any circumstances by applying a temporal filter to the signal.Comment: 6 pages, 4 figure

Diluted maximum-likelihood algorithm for quantum tomography

We propose a refined iterative likelihood-maximization algorithm for reconstructing a quantum state from a set of tomographic measurements. The algorithm is characterized by a very high convergence rate and features a simple adaptive procedure that ensures likelihood increase in every iteration and convergence to the maximum-likelihood state. We apply the algorithm to homodyne tomography of optical states and quantum tomography of entangled spin states of trapped ions and investigate its convergence properties.Comment: v2: Convergence proof adde

Linear optics implementation of general two-photon projective measurement

We will present a method of implementation of general projective measurement of two-photon polarization state with the use of linear optics elements only. The scheme presented succeeds with a probability of at least 1/16. For some specific measurements, (e.g. parity measurement) this probability reaches 1/4.Comment: 8 page

Coherent analysis of quantum optical sideband modes

We demonstrate a device that allows for the coherent analysis of a pair of optical frequency sidebands in an arbitrary basis. We show that our device is quantum noise limited and hence applications for this scheme may be found in discrete and continuous variable optical quantum information experiments.Comment: 3 pages, 3 figures, submitted to Optics Letter