An Operational Approach to Quantum State Reduction

正直 小澤

Masanao Ozawa

An operational approach to quantum state reduction, the state change of the measured system caused by a measurement of an observable conditional upon the outcome of measurement, is founded without assuming the projection postulate in any stages of the measuring process. Whereas the conventional formula assumes that the probe measurement satisfies the projection postulate, a new formula for determining the state reduction shows that the state reduction does not depend on how the probe observable is measured, or in particular does not depend on whether the probe measurement satisfies the projection postulate or not, contrary to the longstanding attempts in showing how the macroscopic nature of probe detection provokes state reduction. 1.

Changhao Yi, Xiaodi Li, Huangjun Zhu

In this paper, we combine the k -reduction map, the moment method, and randomized measurements into a practical protocol for certifying the entanglement dimensionality. Our approach is based on the observation that a state with entanglement dimensionality at most k must stay positive under the action of the k -reduction map. The core of our protocol utilizes the moment method to determine whether the k -reduced operator, i.e., the operator obtained after applying the k -reduction map on a quantum state, contains a negative eigenvalue or not. Notably, we propose a systematic method for constructing reduction moment criteria that apply to a broader range of states, including k -unfaithful states, compared with fidelity-based methods. The performance of our approach gets better and better with the moment order employed, which is corroborated by extensive numerical simulations. To apply our approach, it suffices to implement a unitary 3-design instead of a 4-design, which is more feasible in practice than the correlation matrix method. In the course of study, we show that the k -reduction negativity, the absolute sum of the negative eigenvalues of the k -reduced operator, is monotonic under local operations and classical communication for pure states.

Shan Gao

Masanao Ozawa

R. Srikanth

Is the quantum state real? Does the reduction of the state of a quantum system by a measurement on another system, entangled with it and distant, constitute a real disturbance? As is well acknowledged, there is a lack of consensus among physicists over such ontological questions concerning quantum mechanics (QM). Here we argue that it is possible, surprisingly, to address such questions on the basis of only operational considerations. More generally, we show that the operational perspective itself provides an intrinsic interpretation of QM. The theory's syntax supplies its semantics, as it were. This interpretational framework, which we call ``signaling ontology'', builds on the simple insight that unconditional quantum state reduction, namely the state change of a measured quantum system due to a nonselective measurement, can be used for signaling locally, and that this signal provides a natural, operational criterion for the reality of the state reduction. This argument is formalized in the framework of generalized probability theories and extended to multipartite systems. Among other consequences of this approach, the two questions posed above at the beginning are testably answered in the affirmative. In particular, a steering inequality is proposed whose violation, together with a local signaling condition, provides an experimental test for the reality of the remote disturbance referenced in the second question. Accordingly, quantum correlations that meet this criterion are nonlocal in an operationally real sense. A further ramification of our work is an elucidation of the contrast between quantum no-signaling and relativistic signal locality.