Amplifying hybrid entangled states and superpositions of coherent states 2409 16562v1

Подписаться 77

50% 1

Potcast by Google NotebookLM(20241009수)
Amplifying Nonclassical States of Light: A Comparative Analysis
Excerpts from "Amplifying Hybrid Entangled States and Superpositions of Coherent States" (InU Jeon, Sungjoo Cho, and Hyunseok Jeong)
I. Introduction:
Introduces hybrid entangled states (HESs) and superpositions of coherent states (SCSs) as significant nonclassical states in quantum information processing.
Highlights the importance of large amplitudes in these states for practical applications.
Discusses the use of two amplification schemes, photon addition and then subtraction (ˆaˆa†) and successive photon addition (ˆa†2).
Introduces fidelity, gain, and quantum Fisher information as measures for comparing the effectiveness of amplification schemes.
II. Preliminary:
A. Hybrid Entangled States:
Defines HESs as entangled states between discrete-variable (DV) and continuous-variable (CV) systems, using a qubit basis for illustration.
Generalizes HES qubits to qudits, demonstrating their orthonormality and noting their photon number statistics are identical to coherent states of equal amplitude.
Explains the effect of photon addition/subtraction on HES qudits, mapping them to other HES qudits with potential amplitude changes.
B. Superposition of Coherent States:
Defines SCSs as linear combinations of coherent states with distinct phases, exemplified by even/odd cat states.
Explains the normalization factor dependence on amplitude due to non-orthogonal coherent components, and the phase-dependent orthogonality of SCSs.
Generalizes SCS qubits to qudits, demonstrating their orthonormality and highlighting their pseudo-number state property.
III. Amplification of Hybrid States:
Compares ââ† and â†2 amplification schemes applied to HESs, noting their non-unitary nature and probabilistic implementation via quantum channels.
Establishes the independence of normalization factors from dimension and qudit index due to HES structure, simplifying expectation value calculations.
Proposes that expectation values of bosonic operator polynomials with equal creation/annihilation operator degrees in HESs are identical to those in coherent states of equal amplitude.
Compares fidelity and gain for both schemes, finding ââ† yields higher fidelity, while â†2 provides higher gain for all amplitudes.
Extends the fidelity agreement between HES and coherent state amplification to general schemes, demonstrating its dependence on both DV orthogonality and specific phase relationships.
Discusses the limitations of defining gain via quadrature operator ratios in HESs due to zero expectation values, highlighting the potential inadequacy of equivalent input noise (EIN) as a performance measure.
Employs quantum Fisher information for phase estimation as an alternative performance indicator, supporting its relevance due to its connection with amplitude gain and noiseless properties.
Analyzes quantum Fisher information for both schemes, revealing ââ† superiority for small amplitudes and â†2 dominance for larger amplitudes, with minimal difference at asymptotically large amplitudes.
IV. Amplification of Superpositions of Coherent States:
Compares ââ† and â†2 schemes applied to SCSs, highlighting the dependence of normalization factors on dimension and qudit number, contrasting with HESs.
Derives fidelity expressions for both schemes, noting the complexity hindering closed-form gain solutions and requiring numerical analysis.
Analyzes fidelity and gain for different dimensions and qudit numbers, revealing unique behaviors for specific states under (â†)2 due to the pseudo-number property and the mapping of qudit numbers.
Investigates quantum Fisher information for SCSs and amplified SCSs, observing non-monotonic behavior challenging its interpretation as a performance measure for high dimensions.
Concludes quantum Fisher information is suitable for assessing phase estimation performance in SCSs, highlighting the limitations of its generalization for overall amplification performance.
Discusses the impact of pseudo-number property on quantum Fisher information fluctuations, emphasizing the interplay between amplitude growth and Fock state concentration.
Compares quantum Fisher information for both schemes across dimensions, identifying regions where ââ† surpasses â†2 performance, particularly at specific amplitudes and higher dimensions.
Analyzes the ratio of amplified SCSs' quantum Fisher information to that of original SCSs, demonstrating amplification effectiveness for small amplitudes and highlighting the need for scheme selection based on experimental goals and SCS conditions.