By Akira Furusawa
Particular in that it truly is together written via an experimentalist and a theorist, this monograph provides common quantum computation in line with quantum teleportation as an simple subroutine and multi-party entanglement as a common source. Optical ways to measurement-based quantum computation also are defined, together with schemes for quantum mistakes correction, with many of the experiments conducted by means of the authors themselves. starting from the theoretical historical past to the main points of the experimental attention, the publication describes effects and advances within the box, subsidized via a variety of illustrations of the authors' experimental setups.Aimed at researchers, physicists, and graduate and PhD scholars in physics, theoretical quantum optics, quantum mechanics, and quantum details.
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Additional info for Quantum Teleportation and Entanglement: A Hybrid Approach to Optical Quantum Information Processing
Moreover, similar to the two-qubit stabilizers, the two-qumode stabilizers here are useful to construct so-called entanglement witnesses. These witnesses would enable one to detect the entanglement of the physical, ﬁnitely correlated, and possibly even noisy mixed-state approximations of the EPR state. How to ﬁnd such witnesses for qubits and qumodes will be discussed in Chapter 3. At this point, we shall proceed by looking at the entanglement of mixed states, inseparability criteria, and the deﬁnition of entanglement witnesses.
O0 D E ( O). For this linear map to be physical, it must satisfy the mathematical notion of complete positivity. 73) AO k O AO k . k The sum may be ﬁnite or go to inﬁnity and the summation over k may also be replaced by an integral. The operators AO k are usually referred to as Kraus operators. † When the corresponding set of positive operators AO k AO k sums up to the identiP † ty, AO AO k D 1, we have a CP trace-preserving (CPTP) map. Otherwise, when P k† k O O k A k A k < 1, the CP map is trace-decreasing (CPTD).
The vectors fju µ ig are unnormalized, possibly non-orthogonal state vectors in the Hilbert space K. We may write EO µ D ju µ ihu µ j . 86) PN These are the POVM operators of an N-valued POVM with µD1 EO µ D 1. The vectors fjN µ ig are deﬁned in the complementary space K? orthogonal to K, with the total Hilbert space H D K ˚ K? If the dimension of the signal space is n, Pn with ju µ i D complex coefﬁcients b µ i , and fjv i ig niD1 as a baiD1 b µ i jv i i, some PN sis in K, we have jN µ i D iDnC1 b µ i jv i i with some complex coefﬁcients b µ i , ?
Quantum Teleportation and Entanglement: A Hybrid Approach to Optical Quantum Information Processing by Akira Furusawa