| negativity | |
|---|---|
| Name | Negativity (quantum) |
| Field | Quantum physics |
| Introduced | 20th century |
| Related | Wigner function, quasiprobability, entanglement |
negativity
Negativity is a term used in quantum physics to denote the presence of negative values in representations of quantum states or processes where classical probabilistic descriptions would be nonnegative. It is an operational and mathematical signature of nonclassicality that affects quantum interference, entanglement, and resource theories for quantum information processing.
Negativity refers to negative values appearing in quasiprobability representations, operator expansions, or spectrum-based measures that describe quantum systems. In contrast to classical probability theory, where probabilities are nonnegative, quantum mechanics permits phase-space distributions and superoperator kernels that take negative values; these are taken as indicators of incompatibility with any underlying classical stochastic model. The concept is tied to foundational results such as the Bell's theorem and the Kochen–Specker theorem by highlighting where classical realist descriptions fail. Historically, negativity has been discussed in the context of phase-space methods introduced by Eugene Wigner and later formalized in relation to quantum optics by researchers at institutions such as Bell Labs and Caltech.
Negativity is most commonly examined in quasiprobability distributions on phase space, notably the Wigner function introduced by Eugene Wigner in 1932. The Wigner function W(x,p) can take negative values for nonclassical states such as Fock states and Schrödinger cat states, providing a visual and quantitative signature of quantum interference. The Glauber–Sudarshan P representation (Glauber–Sudarshan P representation) can be highly singular or negative for nonclassical optical fields, while the Husimi Q function (Husimi Q function) is always nonnegative but less sensitive to fine nonclassical features. Extensions like the Wigner–Weyl transform and the family of s-parameterized quasiprobabilities link these distributions; negativity typically decreases as smoothing (larger s) is applied. Experimental reconstructions of these functions often reference methods developed at National Institute of Standards and Technology and in quantum optics groups at Harvard University and Max Planck Society.
In composite systems, the term "negativity" is also the name of a computable entanglement measure: the negativity defined via the trace norm of the partial transpose of a density matrix. The related logarithmic negativity quantifies bipartite entanglement and is widely used in studies by groups at MIT and University of Oxford. Conceptually, these measures link the algebraic property of having negative eigenvalues under partial transposition (the Peres–Horodecki criterion) to the presence of quantum correlations that lack separable classical analogues. Negativity as an entanglement monotone is used in resource theories and in comparing entanglement generation across platforms such as ion trap experiments, superconducting qubits, and photonic quantum information.
Negativity has operational implications in measurement outcomes and state reconstruction. Quantum state tomography techniques reconstruct the density matrix or Wigner function from measurement data; negative regions in reconstructions are treated as evidence for nonclassicality. Experiments at laboratories like CERN (in quantum simulation efforts), IBM Quantum (superconducting processors), and academic groups (for example Yale University's circuit QED group) have reported Wigner negativity for microwave cavity states and itinerant photonic states. Negativity affects tasks such as quantum metrology and quantum sensing, where nonclassical states can surpass classical limits (for example, beating the standard quantum limit). Practical measurement protocols must account for noise and finite sampling, which can mask or produce spurious negativities, leading to the use of bootstrapping and maximum likelihood methods developed in statistical communities.
Mathematically, negativity is quantified in various ways depending on context: by the integral of the absolute value minus one for quasiprobabilities (the "negativity volume"), by the sum of negative eigenvalues for partial transposes (entanglement negativity), or by robustness measures within resource theories. Techniques such as semidefinite programming (SDP), convex optimization, and spectral analysis are standard tools to compute or bound negativity in realistic models. Formal connections exist between negativity and nonclassical distance measures like the trace distance and relative entropy of nonclassicality; researchers at institutes such as Stanford University and University of Cambridge have developed analytic bounds and numerical algorithms to evaluate these quantities for states used in quantum technologies.
Negativity is treated as a resource in many quantum information protocols. Wigner-negativity is necessary for universal quantum computation in some continuous-variable models and for quantum advantage in sampling tasks such as boson sampling (studied at University of Bristol and Caltech). In discrete-variable circuits, entanglement negativity correlates with the ability to perform quantum teleportation, dense coding, and error correction in codes developed by Peter Shor and groups at Microsoft Research and IBM Research. Resource theories formalize how negativity can be consumed or distilled, influencing protocols for state conversion in networks and for benchmarking near-term quantum devices.
Negativity is fragile under environmental coupling; decoherence tends to smooth phase-space distributions, removing negative features as systems approach classical behavior. Models of open quantum systems (e.g., Lindblad master equations) show exponential suppression of Wigner negativity under typical thermalization and noise channels. This decay underlies experimental efforts to protect nonclassicality via error correction, dynamical decoupling, or engineered reservoirs (studied in groups at NEC Laboratories America and NIST). The transition from quantum to classical, as exemplified by the emergence of nonnegative, coarse-grained quasiprobabilities, remains an active area connecting foundations, quantum thermodynamics, and experimental quantum technologies.
Category:Quantum mechanics Category:Quantum information theory