Quantum States Made to Order

O. M. Sotnikov, E. A. Stepanov, Mikhail I. Katsnelson +2 more

In certain magnetic systems, one superposition of quantum eigenstates leads to a particular classical order, demonstrating that quantum-classical connections can be made via not only observables but also quantum states.

Yasunobu Nakamura

Blind Review

It is typically thought that indefinite causal order and some variants of holographic gravity are incompatible with the conventional quantum circuit model. These theoretic developments are saved from incompatibility when temporal (which can be causal order or 'time') postselection is introduced. To be natural, these require introducing time as a state in the quantum circuit framework, if no modification of the framework is to be made. Temporal postselection is not really different from spatial entanglement - once we have some knowledge of time or causal order information, a collapsed quantum state must be compatible with this knowledge. At least for all known cases, right before quantum measurements are made, causal order or time of an observer is fixed, which naturally leads to temporal postselection. If the 'time as a state' view is correct, then the postselection variants of quantum complexity classes become more central notions than the original classes. Despite this, an increasing difficulty level of physical implementations of computation models may be conjectured - heavy utilization of gravitational physics may be required for a temporal postselection-based quantum computation model to be physically realized.

Jan de Boer, Giuseppe Di Giulio, Esko Keski-Vakkuri +1 more

In quantum resource theory, one is often interested in identifying which states serve as the best resources for particular quantum tasks. If a relative comparison between quantum states can be made, this gives rise to a partial order, where states are ordered according to their suitability to act as a resource. In the literature, various different partial orders for a variety of quantum resources have been proposed. In discrete variable systems, vector majorization of Wigner functions in discrete phase space provides a natural partial order between quantum states. In the continuous variable case, a natural counterpart would be continuous majorization of Wigner functions in quantum phase space. Indeed, this concept was recently proposed and explored (mostly restricting to the single-mode case) by Van Herstraeten []. In this work, we develop the theory of continuous majorization in the general N -mode case. In addition, we propose extensions to include states with finite Wigner negativity. For the special case of the convex hull of N -mode Gaussian states, we prove a conjecture made by Van Herstraeten, Jabbour, and Cerf. We also prove a phase space counterpart of Uhlmann's theorem of majorization.

Ian T. Durham