Naimark extension for the single-photon canonical phase measurement

Pozza, Nicola Dalla; Paris, Matteo G. A.

doi:10.1103/physreva.100.032126

Cited by 5 publications

(4 citation statements)

References 39 publications

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“…with M = 4, 8. In the Bloch sphere representation, these quantum states are equally spaced along the equator defined by the Tr[ρσ z ] = 0 plane, and because of this symmetry they are often used to test discrimination protocols [41,75]. We consider the models 2r−Mr−M, 2r−M−M and 2−M−M, whose performance are reported in Fig.…”

Section: B M-ary Discriminationmentioning

confidence: 99%

“…While in the latter the optimal measurement operators are projectors, here the optimal ones are given by POVM. We can realize these POVM via projectors in an extended Hilbert space using the Naimark theorem [41,[75][76][77], meaning that the optimal network will try to implement such extended projectors via its dynamics and the measurement on the sink nodes. We find that 2−M−M is the most general model and has the highest performance, approaching asymptotically the optimal P * c .…”

Section: B M-ary Discriminationmentioning

confidence: 99%

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Quantum state discrimination on reconfigurable noise-robust quantum networks

Pozza

Caruso

2020

Phys. Rev. Research

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A fundamental problem in quantum information processing is the discrimination among a set of quantum states of a system. In this paper, we address this problem on an open quantum system described by a graph, whose evolution is defined by a quantum stochastic walk. In particular, the structure of the graph mimics those of neural networks, with the quantum states to discriminate encoded on input nodes and with the discrimination obtained on the output nodes. We optimize the parameters of the network to obtain the highest probability of correct discrimination. Numerical simulations show that after a transient time the probability of correct decision approaches the theoretical optimal quantum limit. These results are confirmed analytically for small graphs. Finally, we analyze the robustness and reconfigurability of the network for different set of quantum states and show that this architecture can pave the way to experimental realizations of our protocol as well as novel quantum generalizations of deep learning.

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Section: B M-ary Discriminationmentioning

confidence: 99%

Section: B M-ary Discriminationmentioning

confidence: 99%

Quantum state discrimination on reconfigurable noise-robust quantum networks

Pozza

Caruso

2020

Phys. Rev. Research

Self Cite

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“…( 17) also reflects this fact by showing that the relative phase operator E can be expressed from the single-mode phase operators E 1 and E 2 . Concretely, the local POVMs associated with the single-mode phases j (φ j ) can be implemented experimentally as projective measurements following the prescription given by the Naimark extension [53][54][55].…”

Section: A Number and Phase Operatorsmentioning

confidence: 99%

Number-phase entanglement and Einstein-Podolsky-Rosen steering

et al. 2020

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We use the uncertainty relation between the operators associated with the total number of particles and with the relative phase of two bosonic modes to construct entanglement and Einstein-Podolsky-Rosen steering criteria. These can be tested experimentally in a variety of systems, such as optical fields, Bose-Einstein condensates, and mechanical oscillators. While known entanglement criteria involving the phase observable typically require us to perform interference measurements by recombining the two systems, our criteria can be tested through local measurements at two spatially distinct positions to investigate the nonlocal nature of quantum correlations. We present simple examples where our criteria are violated and show their robustness to noise. Apart from being useful for state characterization, they might find application in quantum information protocols, for example, based on number-phase teleportation.

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“…( 17) reflects also this fact by showing that the relative phase operator E can be expressed from the single mode phase operators E 1 and E 2 . Concretely, the local POVMs associated to the single mode phases, Π j (φ j ), can be implemented experimentally as projective measurements following the prescription given by the Naimark extension [52][53][54].…”

Section: Number-phase Observablesmentioning

confidence: 99%

Number-phase entanglement and Einstein-Podolsky-Rosen steering

Fadel,

Ares,

Luis

et al. 2020

Preprint

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We use the uncertainty relation between the operators associated to the total number of particles and to the relative phase of two bosonic modes to construct entanglement and Einstein-Podolsky-Rosen steering criteria. These can be tested experimentally in a variety of systems, such as optical fields, Bose-Einstein condensates or mechanical oscillators. While known entanglement criteria involving the phase observable typically require to perform interference measurements by recombining the two systems, our criteria can be tested through local measurements at two spatially distinct positions, to investigate the nonlocal nature of quantum correlations. We present simple examples where our criteria are violated, and show their robustness to noise. Apart from being useful for state characterization, they might find application in quantum information protocols, for example based on number-phase teleportation.

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Naimark extension for the single-photon canonical phase measurement

Cited by 5 publications

References 39 publications

Quantum state discrimination on reconfigurable noise-robust quantum networks

Quantum state discrimination on reconfigurable noise-robust quantum networks

Number-phase entanglement and Einstein-Podolsky-Rosen steering

Number-phase entanglement and Einstein-Podolsky-Rosen steering

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