Measuring microwave quantum states: Tomogram and moments

Filippov, S.; Man’ko, Vladimir I.

doi:10.1103/physreva.84.033827

Cited by 19 publications

(23 citation statements)

References 58 publications

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“…Finally, based on the operator moments (â † ) nâm , we calculate the covariance matrix σ of the signal mode, and reconstruct the Wigner function of the propagating signal incident at the input of the hybrid ring. We verify that the reconstructed states comply with the Heisenberg principle for the 2-nd and the 4-th order moments (â † ) nâm [23], and with a Gaussianity criterion based on cumulants [3,24,25]. We characterize the squeezing level of the reconstructed quantum state in decibels as S = −10 log 10 [(∆X sq ) 2 /0.25], where (∆X sq ) 2 is the variance of the squeezed quadrature and the chosen vacuum reference is (∆X vac ) 2 ≡ 0.25.…”

supporting

confidence: 54%

Displacement of Propagating Squeezed Microwave States

et al. 2016

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Displacement of propagating quantum states of light is a fundamental operation for quantum communication. It enables fundamental studies on macroscopic quantum coherence and plays an important role in quantum teleportation protocols with continuous variables. In our experiments, we have successfully implemented this operation for propagating squeezed microwave states. We demonstrate that, even for strong displacement amplitudes, there is no degradation of the squeezing level in the reconstructed quantum states. Furthermore, we confirm that path entanglement generated by using displaced squeezed states remains constant over a wide range of the displacement power.

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supporting

confidence: 54%

Displacement of Propagating Squeezed Microwave States

et al. 2016

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“…The extraction procedure of the anti normally ordered moments for the case in which was described in detail in [20].…”

Section: Experimental Determinationmentioning

confidence: 99%

Evolution of microwave quantum states in terms of measurable ordered moments of creation and annihilation operators

Filippov

Man’ko

2012

Opt. Spectrosc.

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The detection of microwave states is complicated by strong thermal noise, which is inevitably introduced by linear amplifiers. We show how to extract from measured data normally or anti normally ordered moments of photon creation and annihilation operators, the set of which contains complete infor mation on the quantum state of an electromagnetic field. Equations for the evolution of the quantum state are derived in terms of moments. Using this approach, we consider in detail issues of decoherence and ther malization of microwave quantum states. Results are illustrated using the examples of Fock, coherent, squeezed, thermal, and even and odd coherent states (Schrödinger cat states).

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“…The photon creation and annihilation operators are extensively used in quantum optics [3] because many physical operators and characteristics are be expressed through them, for instance in terms of the moments tr[̺(a † ) m a n ], Refs. [4][5][6]. Conditional transformations of quantum states in a measurement are conventionally described by a mapping I : (Ω, F ) → O that is also referred to as instrument [2,[7][8][9].…”

Section: Introductionmentioning

confidence: 99%

On Quantum Operations of Photon Subtraction and Photon Addition

Filippov

2019

Lobachevskii J Math

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The conventional photon subtraction and photon addition transformations, ̺ → ta̺a † and ̺ → ta † ̺a, are not valid quantum operations for any constant t > 0 since these transformations are not trace nonincreasing. For a fixed density operator ̺ there exist fair quantum operations, N− and N+, whose conditional output states approximate the normalized outputs of former transformations with an arbitrary accuracy. However, the uniform convergence for some classes of density operators ̺ has remained essentially unknown. Here we show that, in the case of photon addition operation, the uniform convergence takes place for the energy-second-moment-constrained states such that tr[̺H 2 ] ≤ E2 < ∞, H = a † a. In the case of photon subtraction, the uniform convergence takes place for the energy-second-moment-constrained states with nonvanishing energy, i.e., the states ̺ such that tr[̺H] ≥ E1 > 0 and tr[̺H 2 ] ≤ E2 < ∞. We prove that these conditions cannot be relaxed and generalize the results to the cases of multiple photon subtraction and addition.

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Measuring microwave quantum states: Tomogram and moments

Cited by 19 publications

References 58 publications

Displacement of Propagating Squeezed Microwave States

Displacement of Propagating Squeezed Microwave States

Evolution of microwave quantum states in terms of measurable ordered moments of creation and annihilation operators

On Quantum Operations of Photon Subtraction and Photon Addition

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