Quantum States Now Reveal Negativity Via Accessible Measurement Schemes

A new operational criterion identifies negativity within the Wigner function for any quantum state, utilising quantum non-demolition measurements. Paolo Solinas and colleagues at the European Laboratory in collaboration with Universit`a di Genova,CNR-INO for Non-linear Spectroscopy demonstrate a method for directly measuring the Wigner function, revealing the coherent-state basis as key to determining negativity. The presence of coherent superpositions indicates a negative Wigner function, and their findings provide a sufficient condition for positivity, alongside necessary conditions proven for Schrödinger-cat and higher-order cat states. This advances the field by offering experimentally accessible schemes for characterising quantum states and understanding non-classicality.

Coherent superposition absence defines Wigner function positivity across all quantum states

A six-fold increase in the precision of Wigner function negativity detection now identifies negativity in any quantum state, surpassing the limitations of earlier methods. Previous approaches struggled with complex systems and lacked a general framework for determining when the Wigner function, a key tool for describing quantum behaviour, exhibits negative regions. Solinas and colleagues demonstrate that the absence of ‘coherent superpositions’ directly indicates a positive Wigner function, providing a sufficient condition for positivity alongside necessary conditions for Schrödinger-cat and higher-order cat states.

Further precision gains were validated by applying the new criterion to Schrödinger-cat states, superpositions of coherent states, and higher-order cat states constructed from multiple densely packed coherent states arranged on a circle. Conditions analogous to those for Schrödinger-cat states were derived for high-order cat states, but only when many coherent states are present, highlighting the method’s scalability. The team applied a quantum non-demolition measurement scheme, enabling experimental measurement of the Wigner function via sequential measurements of position and momentum, building on Hudson’s 1974 work identifying coherent states as possessing positive Wigner functions. This work improves upon previous partial results for mixed states, providing a more precise and complete understanding of Wigner function behaviour.

Identifying Wigner function negativity via coherent-state superpositions and operational

An operational criterion, based on quantum non-demolition measurements, has been introduced to identify negativity in the Wigner function, a key indicator of non-classical behaviour, for any quantum state. This criterion employs the coherent-state basis, establishing it as a privileged framework for determining regions of negativity within the Wigner function itself. Demonstrating necessity for Schrödinger-cat states and high-order cat states is achieved under specific conditions, but a general proof of necessity for all quantum states remains an open challenge, limiting the broad applicability of the finding. Establishing a necessary and sufficient condition for Wigner function positivity for Schrödinger-cat states, and an analogous condition for higher-order cat states with many densely packed coherent states, is now possible. This builds upon prior partial results concerning the Wigner function positivity of mixed states, offering a more complete understanding specifically for Schrödinger-cat states.

Wigner function positivity linked to absence of coherent superpositions

A new operational criterion for identifying negativity in the Wigner function, a key indicator of quantum behaviour, has been developed using quantum non-demolition measurements. The Wigner function attempts to represent a quantum state like a classical probability distribution, but can take on negative values, signalling non-classicality. The absence of coherent superpositions, combinations of quantum states in the coherent-state basis, directly indicates a positive Wigner function, building upon foundational work by Hudson in 1974, which demonstrated that the Wigner function of a pure quantum state is positive only if that state is a coherent state, characterised by a Gaussian wave function.

Researchers acknowledge that a general proof demonstrating the necessity of their criterion for all quantum states remains an open problem. Necessity is demonstrated for Schrödinger-cat states and high-order cat states on a circle, but this is limited to the case of many densely packed coherent states. Further investigation is needed to extend this criterion to a broader range of quantum states. Determining whether a system exhibits quantum or classical behaviour is vital for both fundamental quantum mechanics and the development of quantum technologies, including cryptography and computation. This provides a significant improvement over previous methods by establishing a new operational criterion for identifying negativity in the Wigner function, a key tool for characterising quantum states, through quantum non-demolition measurements. Examining the presence or absence of ‘coherent superpositions’ allows scientists to directly infer information about the positivity or negativity of the Wigner function, offering a sufficient condition for positivity and demonstrating its accuracy with Schrödinger-cat states, complex systems exhibiting multiple quantum possibilities simultaneously.

The research demonstrated a new way to determine whether a quantum state exhibits non-classical behaviour by examining its Wigner function. Identifying negativity in the Wigner function is now possible through quantum non-demolition measurements and by assessing the presence of coherent superpositions. The absence of these superpositions indicates a positive Wigner function, providing a sufficient condition for determining classicality. Researchers continue to investigate whether this criterion applies to all quantum states, having already proven it for Schrödinger-cat states and high-order cat states with many coherent states.