Many-particle interference beyond many-boson and many-fermion statistics

The collective interference of partially distinguishable bosons in multi-mode networks is studied via double-sided Feynman diagrams. The probability for many-body scattering events becomes a multi-dimensional tensor-permanent, which interpolates between distinguishable particles and identical bosons, and easily extends to mixed initial states. The permanent of the distinguishability matrix, composed of all mutual scalar products of the single-particle mode-functions, emerges as a natural measure for the degree of interference: It yields a bound on the difference between event probabilities for partially distinguishable bosons and the idealized species, and exactly quantifies the degree of bosonic bunching.

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“…. , r m ) [49], where r j particles populate input mode j. We are interested in the probability to find the final state s = (s 1 , .…”

Section: A Scattering Scenariomentioning

confidence: 99%

“…. d n ) [49], which indicates the mode in which the jth particle resides, the effective scattering matrix becomes…”

Section: A Scattering Scenariomentioning

confidence: 99%

Sampling of partially distinguishable bosons and the relation to the multidimensional permanent

2015

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“…For the interpretation of (30), we can apply an intuitive picture of many-particle paths [50], which is also illustrated in Fig. 3: Many distinct many-particle paths contribute to post-selected events with one particle per group of modes, and the entanglement in the final state originates from this superposition of distinct paths [61] (see Fig.…”

Section: B Polarizing and Polarization-manipulating Setupsmentioning

confidence: 99%

“…We propose a treatment of entanglement-generating setups which accommodates virtually all possible schemes that use identical particles. The created state can then be understood as a coherent superposition of many-particle paths [50,51], which can be traced back to the state representation. In particular, we find a combinatorial bound for the generalized Schmidt number [52], which generalizes a theorem for two particles [41].…”

Section: Introductionmentioning

confidence: 99%

Limits to multipartite entanglement generation with bosons and fermions

2013

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Many-photon interference in linear-optics setups can be exploited to generate and detect multipartite entanglement. Without recurring to any inter-particle interaction, many entangled states have been created experimentally, and a panoply of theoretical schemes for the generation of various classes of entangled states is available. Here, we present a unifying framework that accommodates the present experiments and theoretical protocols for the creation of multiparticle entanglement via interference. A general representation of the states that can be created is provided for bosons and fermions, for any particle number, and for any dimensionality of the entangled degree of freedom. Using this framework, we derive an upper bound on the generalized Schmidt number of the states that can be generated, and we establish bounds on the dimensionality of the manifold of these states. We show that -at the expense of a smaller success probability -more states can be created with bosons than with fermions, and give an intuitive interpretation of the state representation and of the established bounds in terms of superimposed many-particle paths.

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“…Remarkably, the visibility of the (2, 1)-signal  (2,1) 2:1 can fully vanish for non-vanishing values of the decoherence parameters, due to the competition of the different phase-dependent terms of opposite sign in equation (26) [28]. In general, full dephasing does not lead to the classical behavior of distinguishable particles: even though both visibilities vanish for γ → 0 phase , bosonic statistics survive, favouring the(3, 0) and (0, 3) signal over the(2, 1) and (1, 2) signal [19].…”

Section: Double-fock Superposition|mentioning

confidence: 99%

Time-bin entangled photon pairs from spontaneous parametric down-conversion pumped by a cw multi-mode diode laser

Kwon

Park

et al. 2015

Advances in Photonics of Quantum Computing, Memory, and Communication VIII

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Interferometric signals are degraded by decoherence, which encompasses dephasing, mixing and any distinguishing which-path information. These three paradigmatic processes are fundamentally different, but, for coherent, single-photon and N N 00 -states, they degrade interferometric visibility in the very same way, which impedes the diagnosis of the cause for reduced visibility in a single experiment. We introduce a versatile formalism for many-boson interferometry based on double-sided Feynman diagrams, which we apply to a protocol for differential decoherence diagnosis: twin-Fock states | 〉 N N , with ⩾ N 2 reveal to what extent decoherence is due to path distinguishability or to mixing, while double-Fock superpositions|( , , ) 2 with > > N M 0 additionally witness the degree of dephasing. Hence, double-Fock superposition interferometry permits the differential diagnosis of decoherence processes in a single experiment, indispensable for the assessment of interferometers.

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Many-particle interference beyond many-boson and many-fermion statistics

Cited by 90 publications

References 34 publications

Sampling of partially distinguishable bosons and the relation to the multidimensional permanent

Sampling of partially distinguishable bosons and the relation to the multidimensional permanent

Limits to multipartite entanglement generation with bosons and fermions

Time-bin entangled photon pairs from spontaneous parametric down-conversion pumped by a cw multi-mode diode laser

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