Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Higher-order criteria for nonclassical effects in photon statistics

Ching Tsung Lee

Published Feb 1, 1990• 114 citations
Publisher

Abstract

Based on inequalities derived from the partial ordering by majorization, some higher-order criteria for the existence of nonclassical effects in photon statistics are introduced. These generalize the well-known concept of two-photon antibunching to many-photon antibunching. The photon-number distribution of the famous two-photon coherent state is used to illustrate these new criteria.

DOI
10.1103/physreva.41.1721

Related papers

General criteria for nonclassical photon statistics in multimode radiations

C. T. Lee

Using Muirhead's inequality based on the concept of majorization, general criteria for nonclassical photon statistics of arbitrary orders and involving any number of modes of radiations are derived. For the case of second-order correlations, it implies that both intramode antibunching and intermode bunching can contribute toward making multimode radiations nonclassical.

Optics Letters•Dec 1, 1990•14 citations

Nonclassical photon statistics of two-mode squeezed states

Ching Tsung Lee

The concept of photon antibunching as a manifestation of nonclassical character in single-mode radiation is extended to two-mode radiation. A simple criterion for the existence of nonclassical effects in two-mode radiation is established. It implies that the intermode photon bunching, rather than antibunching, can play a key role in rendering two-mode radiation nonclassical. The two-mode squeezed vacuum states are used as simple examples to illustrate the essential point of the criterion. The criterion is then used to study the nonclassical properties of two types of two-mode squeezed states. A state generated by applying the squeeze operator to the two-mode vacuum first, followed by the displacement operator, is called a two-mode coherent squeezed state. If the order of the two operators is reversed, a two-mode squeezed coherent state is obtained. It is found that the latter has a much stronger tendency to become a nonclassical state than the former, assuming that the parameters involved are all the same. A measure of nonclassical depth of radiation is adopted. It is found that, according to this measure, the effect of squeezing in making two-mode coherent squeezed states nonclassical is not monotonic. Such phenomena do not occur in squeezed coherent states.

Physical Review A•Aug 1, 1990•73 citations

General criteria for nonclassical photon statistics in multimode radiation

C. T. Lee

The criterion for photon antibunching manifested in the second-order correlation function of a single-mode radiation can be established by the relation1

•May 21, 1990•0 citations

Higher-order nonclassicality criteria for photon-subtracted and photon-added states via the normalization constant

Jhordan Santiago

We show that any nonclassicality criterion based on factorial moments, including several higher-order parameters such as the Mandel $Q^{(\ell)}$ parameter, the Lee antibunching function $d^{(\ell-1)}_h$, and the Agarwal--Tara parameter $A_3$, can be computed straightforwardly for photon-subtracted and photon-added states by performing operator reordering of the factorial moments. Within this approach, all relevant quantities depend solely on the normalization constant of the given state.

quant-pharXiv:2511.21801•Nov 27, 2025•0 citations

Lower-vs-Higher Order Non-classicality of Photon-added Bell-type Entangled Coherent States

Deepak Deepak, Arpita Chatterjee

We compare the lower and higher order non-classicality of a class of the photon-added Bell-type entangled coherent states (PBECS) got from Bell-type entangled coherent states using creation operators. We obtained lower and higher order criteria namely Mandel's $Q_m^l$, antibunching $d_h^{l-1}$, Subpoissioning photon statistics $D_h(l-1)$ and Squeezing $S(l)$ for the states obtained. Further we observe that first three criteria does not gives non-classicality for any state and higher order criteria gives very high positive values for all values of parameters. Also the fourth or last criterion $S(l)$ gives non-classicality for lower order as well as higher order.

arXiv:2305.18123•May 29, 2023•0 citations

Higher-order sub-Poissonian-like nonclassical fields: Theoretical and experimental comparison

Jan Peřina, Václav Michálek, Ondřej Haderka

Criteria defining higher-order sub-Poissonian-like fields are given using five different quantities: moments of (I) integrated intensity, (II) photon number, (III) integrated-intensity fluctuation, (IV) photon-number fluctuation, and (V) elements of photocount and photon-number distributions. Relations among the moment criteria are revealed. Performance of the criteria is experimentally investigated using a set of potentially sub-Poissonian fields obtained by post-selection from a twin beam. The criteria based on moments of integrated intensity and photon number and those using the elements of photocount distribution are found as the most powerful. States nonclassical up to the fifth order are experimentally reached in the former case, even the ninth-order nonclassicality is observed in the latter case.

arXiv:1709.08406•Physical Review A•Sep 28, 2017•37 citations
Based on inequalities derived from the partial ordering by majorization, some higher-order criteria for the existence of nonclassical effects in photon statistics are introduced. These generalize the well-known concept of two-photon antibunching to many-photon antibunching. The photon-number distribution of the famous two-photon coherent state is used to illustrate these new criteria.
The concept of photon antibunching as a manifestation of nonclassical character in single-mode radiation is extended to two-mode radiation. A simple criterion for the existence of nonclassical effects in two-mode radiation is established. It implies that the intermode photon bunching, rather than antibunching, can play a key role in rendering two-mode radiation nonclassical. The two-mode squeezed vacuum states are used as simple examples to illustrate the essential point of the criterion. The criterion is then used to study the nonclassical properties of two types of two-mode squeezed states. A state generated by applying the squeeze operator to the two-mode vacuum first, followed by the displacement operator, is called a two-mode coherent squeezed state. If the order of the two operators is reversed, a two-mode squeezed coherent state is obtained. It is found that the latter has a much stronger tendency to become a nonclassical state than the former, assuming that the parameters involved are all the same. A measure of nonclassical depth of radiation is adopted. It is found that, according to this measure, the effect of squeezing in making two-mode coherent squeezed states nonclassical is not monotonic. Such phenomena do not occur in squeezed coherent states.
We show that any nonclassicality criterion based on factorial moments, including several higher-order parameters such as the Mandel Q(ℓ)Q^{(\ell)}Q(ℓ) parameter, the Lee antibunching function dh(ℓ−1)d^{(\ell-1)}_hdh(ℓ−1)​, and the Agarwal--Tara parameter A3A_3A3​, can be computed straightforwardly for photon-subtracted and photon-added states by performing operator reordering of the factorial moments. Within this approach, all relevant quantities depend solely on the normalization constant of the given state.
We compare the lower and higher order non-classicality of a class of the photon-added Bell-type entangled coherent states (PBECS) got from Bell-type entangled coherent states using creation operators. We obtained lower and higher order criteria namely Mandel's QmlQ_m^lQml​, antibunching dhl−1d_h^{l-1}dhl−1​, Subpoissioning photon statistics Dh(l−1)D_h(l-1)Dh​(l−1) and Squeezing S(l)S(l)S(l) for the states obtained. Further we observe that first three criteria does not gives non-classicality for any state and higher order criteria gives very high positive values for all values of parameters. Also the fourth or last criterion S(l)S(l)S(l) gives non-classicality for lower order as well as higher order.
Criteria defining higher-order sub-Poissonian-like fields are given using five different quantities: moments of (I) integrated intensity, (II) photon number, (III) integrated-intensity fluctuation, (IV) photon-number fluctuation, and (V) elements of photocount and photon-number distributions. Relations among the moment criteria are revealed. Performance of the criteria is experimentally investigated using a set of potentially sub-Poissonian fields obtained by post-selection from a twin beam. The criteria based on moments of integrated intensity and photon number and those using the elements of photocount distribution are found as the most powerful. States nonclassical up to the fifth order are experimentally reached in the former case, even the ninth-order nonclassicality is observed in the latter case.