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We identify proper quantum computation with computational processes that cannot be efficiently simulated on a classical computer. For optical quantum computation, we establish no-go theorems for classes of quantum optical experiments that cannot yield proper quantum computation, and we identify requirements for optical proper quantum computation that correspond to violations of assumptions underpinning the no-go theorems.
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Although universal continuous-variable quantum computation cannot be achieved via linear optics (including squeezing), homodyne detection and feed-forward, inclusion of ideal photon counting measurements overcomes this obstacle. These measurements are sometimes described by arrays of beam splitters to distribute the photons across several modes. We show that such a scheme cannot be used to implement ideal photon counting and that such measurements necessarily involve nonlinear evolution. However, this requirement of nonlinearity can be moved off-line, thereby permitting universal continuous-variable quantum computation with linear optics.
We show that the sender (Alice) and the receiver (Bob) each require coherent devices in order to achieve unconditional continuous variable quantum teleportation (CVQT), and this requirement cannot be achieved with conventional laser sources, even in principle. The appearance of successful CVQT in recent experiments is due to interpreting the measurement record fallaciously in terms of one preferred ensemble (or decomposition) of the correct density matrix describing the state. Our analysis is unrelated to technical problems such as laser phase drift or finite squeezing bandwidth.
We study the procedure for sequential unambiguous state discrimination. A qubit is prepared in one of two possible states, and measured by two observers Bob and Charlie sequentially. A necessary condition for the state to be unambiguously discriminated by Charlie is the absence of entanglement between the principal qubit, prepared by Alice, and Bobs auxiliary system. In general, the procedure for both Bob and Charlie to recognize between two nonorthogonal states conclusively relies on the availability of quantum discord which is precisely the quantum dissonance when the entanglement is absent. In Bobs measurement, the left discord is positively correlated with the information extracted by Bob, and the right discord enhances the information left to Charlie. When their product achieves its maximum the probability for both Bob and Charlie to identify the state achieves its optimal value.
In topological quantum computation, quantum information is stored in states which are intrinsically protected from decoherence, and quantum gates are carried out by dragging particle-like excitations (quasiparticles) around one another in two space dimensions. The resulting quasiparticle trajectories define world-lines in three dimensional space-time, and the corresponding quantum gates depend only on the topology of the braids formed by these world-lines. We show how to find braids that yield a universal set of quantum gates for qubits encoded using a specific kind of quasiparticle which is particularly promising for experimental realization.
It has been argued [T. Rudolph and B.C. Sanders, Phys. Rev. Lett. 87, 077903 (2001)] that continuous-variable quantum teleportation at optical frequencies has not been achieved because the source used (a laser) was not `truly coherent. Here I show that `true coherence is always illusory, as the concept of absolute time on a scale beyond direct human experience is meaningless. A laser is as good a clock as any other, even in principle, and this objection to teleportation experiments is baseless.
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