arXiv:2507.15890

Quantum Complementarity ad Infinitum: Switching Higher-Order Coherence from Infinity to Zero

Arash Azizi

Published Jul 20, 2025• 0 citations

Abstract

We report a profound manifestation of quantum complementarity in the higher-order photon statistics of the ``Janus state,'' a coherent superposition of two squeezed vacua. We find that the state acts as a perfect quantum switch for multi-photon correlations, toggled by the availability of which-path information. Erasing this information activates quantum interference that can be tuned to be maximally destructive. This reveals a remarkable hierarchy of suppression: while two-photon correlations remain finite, we prove analytically and demonstrate numerically that it is possible to drive all higher-order correlations ($g^{(k)}$ for $k \ge 3$) to zero. This transition from the extreme bunching of the constituent states ($g^{(k)} \to \infty$) to a state of profound quantum order is visualized by the emergence of negativity in the state's Wigner function, an unambiguous signature of non-classicality. This work provides a foundational demonstration of quantum complementarity in multi-photon statistics and introduces a new paradigm for engineering highly ordered, non-classical light from Gaussian resources.

DOI: 10.48550/arxiv.2507.15890

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arXiv:2507.15890

Quantum Complementarity ad Infinitum: Switching Higher-Order Coherence from Infinity to Zero

Arash Azizi

Published Jul 20, 2025• 0 citations

arXiv HTML PDF

Abstract

g^{(k)}

for

k \ge 3

) to zero. This transition from the extreme bunching of the constituent states (

g^{(k)} \to \infty

) to a state of profound quantum order is visualized by the emergence of negativity in the state's Wigner function, an unambiguous signature of non-classicality. This work provides a foundational demonstration of quantum complementarity in multi-photon statistics and introduces a new paradigm for engineering highly ordered, non-classical light from Gaussian resources.

DOI: 10.48550/arxiv.2507.15890

Related papers

Quantum complementarity ad infinitum : Switching higher-order coherence from infinity to zero

Arash Azizi

We reveal a sharp form of complementarity in the \emph{Janus state}—a coherent superposition of two squeezed vacua. Using a compact generating-function formalism, we derive closed-form expressions for $g^{(k)}$ at all orders and introduce \emph{squeezing polynomials} $P_k(z)$ that factorize the moments and expose phase-dependent scaling. The Janus state operates as a phase-tunable quantum switch for multi-photon correlations: when which-path/which-state information is available (trivial interference), the higher-order coherences $g^{(k)}$ reproduce the single-squeezed limit and diverge; when path information is erased and genuine interference from coherent superposition is enabled, multi-photon events are extinguished, driving $g^{(k)}\!\to\!0$ for all $k\!\ge\!3$ . We obtain a hierarchy of suppression with exponents set by the interference phase and the parity of $k$ , and we visualize the mechanism via pronounced Wigner-function negativity. The framework is general and experimentally accessible, enabling engineered nonclassical light with tailored higher-order statistics.We reveal a sharp form of complementarity in the \emph{Janus state}—a coherent superposition of two squeezed vacua. Using a compact generating-function formalism, we derive closed-form expressions for $g^{(k)}$ at all orders and introduce \emph{squeezing polynomials} $P_k(z)$ that factorize the moments and expose phase-dependent scaling. The Janus state operates as a phase-tunable quantum switch for multi-photon correlations: when which-path/which-state information is available (trivial interference), the higher-order coherences $g^{(k)}$ reproduce the single-squeezed limit and diverge; when path information is erased and genuine interference from coherent superposition is enabled, multi-photon events are extinguished, driving $g^{(k)}\!\to\!0$ for all $k\!\ge\!3$. We obtain a hierarchy of suppression with exponents set by the interference phase and the parity of $k$, and we visualize the mechanism via pronounced Wigner-function negativity. The framework is general and experimentally accessible, enabling engineered nonclassical light with tailored higher-order statistics.

Physical Review ADec 6, 20250 citations

The Janus state: a universal lower bound for second-order coherence

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arXiv:2506.06397Optics LettersDec 17, 20250 citations

Tunable non-Gaussianity and exact higher-order coherences for quantum advantage

Arash Azizi

Non-Gaussian states are essential for achieving a quantum advantage in continuous-variable (CV) information processing. Among these, coherent superpositions of squeezed states are a foundational resource. While exact higher-order statistics are available in the undisplaced case, a complete and analytically tractable treatment with a common displacement has been missing. We introduce and solve the displaced Janus state---a coherent superposition of two squeezed coherent states that share the same displacement---and develop an analytical framework, based on a family of generalized squeezing polynomials, that yields closed-form expressions for arbitrary-order factorial moments and coherence functions ${g}^{(k)}(0)$ , the full Wigner function, and the quantum Fisher information. The analysis shows how interference at a fixed mean, driven by a mismatch of the component covariances rather than by mean separation, can be precisely engineered to transform the extreme photon bunching of the constituents into strong sub-Poissonian and even perfect multiphoton suppression. We further provide a rigorous quantum Fisher information analysis, proving that parameters encoded by linear generators (for example, the number operator) are bounded by the standard quantum limit, whereas parameters encoded by quadratic generators (for example, squeezing transformations) achieve Heisenberg-limited scaling. Together, these results furnish a complete analytical toolkit for a versatile class of non-Gaussian states, establishing the displaced Janus state as a key primitive for hybrid quantum protocols, quantum metrology, and fault-tolerant continuous-variable computation.Non-Gaussian states are essential for achieving a quantum advantage in continuous-variable (CV) information processing. Among these, coherent superpositions of squeezed states are a foundational resource. While exact higher-order statistics are available in the undisplaced case, a complete and analytically tractable treatment with a common displacement has been missing. We introduce and solve the displaced Janus state---a coherent superposition of two squeezed coherent states that share the same displacement---and develop an analytical framework, based on a family of generalized squeezing polynomials, that yields closed-form expressions for arbitrary-order factorial moments and coherence functions ${g}^{(k)}(0)$, the full Wigner function, and the quantum Fisher information. The analysis shows how interference at a fixed mean, driven by a mismatch of the component covariances rather than by mean separation, can be precisely engineered to transform the extreme photon bunching of the constituents into strong sub-Poissonian and even perfect multiphoton suppression. We further provide a rigorous quantum Fisher information analysis, proving that parameters encoded by linear generators (for example, the number operator) are bounded by the standard quantum limit, whereas parameters encoded by quadratic generators (for example, squeezing transformations) achieve Heisenberg-limited scaling. Together, these results furnish a complete analytical toolkit for a versatile class of non-Gaussian states, establishing the displaced Janus state as a key primitive for hybrid quantum protocols, quantum metrology, and fault-tolerant continuous-variable computation.

arXiv:2508.09234Physical Review ANov 10, 20250 citations

Tuning photon statistics with coherent fields

Eduardo Zubizarreta Casalengua, Juan Camilo López Carreño, Fabrice P. Laussy +1 more

Photon correlations, as measured by Glauber's $n\mathrm{th}$ -order coherence functions ${g}^{(n)}$ , are highly sought to be minimized and/or maximized. In systems that are coherently driven, so-called blockades can give rise to strong correlations according to two scenarios based on level repulsion (conventional blockade) or interferences (unconventional blockade). Here, we show how these two approaches relate to the admixing of a coherent state with a quantum state such as a squeezed state for the simplest and most recurrent case. The emission from a variety of systems, such as resonance fluorescence, the Jaynes-Cummings model, or microcavity polaritons, as a few examples of a large family of quantum optical sources, are shown to be particular cases of such admixtures, that can further be doctored up externally by adding an amplitude- and phase-controlled coherent field with the effect of tuning the photon statistics from exactly zero to infinity. We show how such an understanding also allows to classify photon statistics throughout platforms according to conventional and unconventional features, with the effect of optimizing the correlations and with possible spectroscopic applications. In particular, we show how configurations that can realize simultaneously conventional and unconventional antibunching bring the best of both worlds: huge antibunching (unconventional) with large populations and being robust to dephasing (conventional).Photon correlations, as measured by Glauber's $n\mathrm{th}$-order coherence functions ${g}^{(n)}$, are highly sought to be minimized and/or maximized. In systems that are coherently driven, so-called blockades can give rise to strong correlations according to two scenarios based on level repulsion (conventional blockade) or interferences (unconventional blockade). Here, we show how these two approaches relate to the admixing of a coherent state with a quantum state such as a squeezed state for the simplest and most recurrent case. The emission from a variety of systems, such as resonance fluorescence, the Jaynes-Cummings model, or microcavity polaritons, as a few examples of a large family of quantum optical sources, are shown to be particular cases of such admixtures, that can further be doctored up externally by adding an amplitude- and phase-controlled coherent field with the effect of tuning the photon statistics from exactly zero to infinity. We show how such an understanding also allows to classify photon statistics throughout platforms according to conventional and unconventional features, with the effect of optimizing the correlations and with possible spectroscopic applications. In particular, we show how configurations that can realize simultaneously conventional and unconventional antibunching bring the best of both worlds: huge antibunching (unconventional) with large populations and being robust to dephasing (conventional).

arXiv:2004.11885Physical Review AJun 18, 202035 citations

Manipulating the Spatial Structure of Second-Order Quantum Coherence Using Entangled Photons

Shuang‐Yin Huang, Jing 菁 Gao 高, Zhi‐Cheng Ren +10 more

Abstract High-order quantum coherence reveals the statistical correlation of quantum particles. Manipulation of quantum coherence of light in the temporal domain enables the production of the single-photon source, which has become one of the most important quantum resources. High-order quantum coherence in the spatial domain plays a crucial role in a variety of applications, such as quantum imaging, holography, and microscopy. However, the active control of second-order spatial quantum coherence remains a challenging task. Here we predict theoretically and demonstrate experimentally the first active manipulation of second-order spatial quantum coherence, which exhibits the capability of switching between bunching and anti-bunching, by mapping the entanglement of spatially structured photons. We also show that signal processing based on quantum coherence exhibits robust resistance to intensity disturbance. Our findings not only enhance existing applications but also pave the way for broader utilization of higher-order spatial quantum coherence.Abstract High-order quantum coherence reveals the statistical correlation of quantum particles. Manipulation of quantum coherence of light in the temporal domain enables the production of the single-photon source, which has become one of the most important quantum resources. High-order quantum coherence in the spatial domain plays a crucial role in a variety of applications, such as quantum imaging, holography, and microscopy. However, the active control of second-order spatial quantum coherence remains a challenging task. Here we predict theoretically and demonstrate experimentally the first active manipulation of second-order spatial quantum coherence, which exhibits the capability of switching between bunching and anti-bunching, by mapping the entanglement of spatially structured photons. We also show that signal processing based on quantum coherence exhibits robust resistance to intensity disturbance. Our findings not only enhance existing applications but also pave the way for broader utilization of higher-order spatial quantum coherence.

Chinese Physics LettersJun 21, 20248 citations

Two-Mode Janus States: non-Gaussian generalizations of thermofield double

Arash Azizi

We introduce the Two-Mode Janus State (TMJS), a non-Gaussian quantum state defined as a coherent superposition of two distinct Two-Mode Squeezed States (TMSS). This construction serves as a direct, non-Gaussian generalization of the canonical thermofield double (TFD) state, which is itself a single, Gaussian TMSS. We develop a complete analytical framework for the TMJS's arbitrary $k$ -th order photon statistics, identifying a new family of "squeezing polynomials" that govern all diagonal and off-diagonal moments. Our central result is that the state's non-Gaussianity is dynamically steerable via an external "Janus phase." This phase acts as a switch, allowing the higher-order coherences ( $g^{(k)}$ ) to be tuned from perfectly thermal (matching the TFD marginal) to deeply sub-Poissonian, a regime marked by strong Wigner negativity. We further establish a physical realization for the TMJS, proposing its generation via coherently superposed Dynamical Casimir Effect (DCE) trajectories, distinguishing it from the static, observer-dependent Unruh effect. The TMJS provides a versatile, interference-enhanced platform for engineering Unruh-DeWitt detector responses and probing non-Gaussian physics in relativistic settings.We introduce the Two-Mode Janus State (TMJS), a non-Gaussian quantum state defined as a coherent superposition of two distinct Two-Mode Squeezed States (TMSS). This construction serves as a direct, non-Gaussian generalization of the canonical thermofield double (TFD) state, which is itself a single, Gaussian TMSS. We develop a complete analytical framework for the TMJS's arbitrary $k$-th order photon statistics, identifying a new family of "squeezing polynomials" that govern all diagonal and off-diagonal moments. Our central result is that the state's non-Gaussianity is dynamically steerable via an external "Janus phase." This phase acts as a switch, allowing the higher-order coherences ($g^{(k)}$) to be tuned from perfectly thermal (matching the TFD marginal) to deeply sub-Poissonian, a regime marked by strong Wigner negativity. We further establish a physical realization for the TMJS, proposing its generation via coherently superposed Dynamical Casimir Effect (DCE) trajectories, distinguishing it from the static, observer-dependent Unruh effect. The TMJS provides a versatile, interference-enhanced platform for engineering Unruh-DeWitt detector responses and probing non-Gaussian physics in relativistic settings.

quant-pharXiv:2511.09704Nov 14, 20250 citations

g^{(k)}

for

k \ge 3

) to zero. This transition from the extreme bunching of the constituent states (

g^{(k)} \to \infty

g^{(k)}

at all orders and introduce \emph{squeezing polynomials}

P_k(z)

that factorize the moments and expose phase-dependent scaling. The Janus state operates as a phase-tunable quantum switch for multi-photon correlations: when which-path/which-state information is available (trivial interference), the higher-order coherences

g^{(k)}

reproduce the single-squeezed limit and diverge; when path information is erased and genuine interference from coherent superposition is enabled, multi-photon events are extinguished, driving

g^{(k)}\!\to\!0

for all

k\!\ge\!3

. We obtain a hierarchy of suppression with exponents set by the interference phase and the parity of

k

, and we visualize the mechanism via pronounced Wigner-function negativity. The framework is general and experimentally accessible, enabling engineered nonclassical light with tailored higher-order statistics.

{g}^{(k)}(0)

, the full Wigner function, and the quantum Fisher information. The analysis shows how interference at a fixed mean, driven by a mismatch of the component covariances rather than by mean separation, can be precisely engineered to transform the extreme photon bunching of the constituents into strong sub-Poissonian and even perfect multiphoton suppression. We further provide a rigorous quantum Fisher information analysis, proving that parameters encoded by linear generators (for example, the number operator) are bounded by the standard quantum limit, whereas parameters encoded by quadratic generators (for example, squeezing transformations) achieve Heisenberg-limited scaling. Together, these results furnish a complete analytical toolkit for a versatile class of non-Gaussian states, establishing the displaced Janus state as a key primitive for hybrid quantum protocols, quantum metrology, and fault-tolerant continuous-variable computation.

Photon correlations, as measured by Glauber's

n\mathrm{th}

-order coherence functions

{g}^{(n)}

, are highly sought to be minimized and/or maximized. In systems that are coherently driven, so-called blockades can give rise to strong correlations according to two scenarios based on level repulsion (conventional blockade) or interferences (unconventional blockade). Here, we show how these two approaches relate to the admixing of a coherent state with a quantum state such as a squeezed state for the simplest and most recurrent case. The emission from a variety of systems, such as resonance fluorescence, the Jaynes-Cummings model, or microcavity polaritons, as a few examples of a large family of quantum optical sources, are shown to be particular cases of such admixtures, that can further be doctored up externally by adding an amplitude- and phase-controlled coherent field with the effect of tuning the photon statistics from exactly zero to infinity. We show how such an understanding also allows to classify photon statistics throughout platforms according to conventional and unconventional features, with the effect of optimizing the correlations and with possible spectroscopic applications. In particular, we show how configurations that can realize simultaneously conventional and unconventional antibunching bring the best of both worlds: huge antibunching (unconventional) with large populations and being robust to dephasing (conventional).

k

-th order photon statistics, identifying a new family of "squeezing polynomials" that govern all diagonal and off-diagonal moments. Our central result is that the state's non-Gaussianity is dynamically steerable via an external "Janus phase." This phase acts as a switch, allowing the higher-order coherences (

g^{(k)}

) to be tuned from perfectly thermal (matching the TFD marginal) to deeply sub-Poissonian, a regime marked by strong Wigner negativity. We further establish a physical realization for the TMJS, proposing its generation via coherently superposed Dynamical Casimir Effect (DCE) trajectories, distinguishing it from the static, observer-dependent Unruh effect. The TMJS provides a versatile, interference-enhanced platform for engineering Unruh-DeWitt detector responses and probing non-Gaussian physics in relativistic settings.