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However, such rules would not affect our results. Assumption possibility of state estimation. Now it is time to state the main result of this work, which essentially tells us that the only possible measurement postulates are the quantum ones. Theorem measurement. The methods section provides a summary of the ideas and techniques used in the proof of this theorem. At first sight, the above theorem says nothing about the post-measurement state-update rule. In this section we present an example of alternative measurement postulate, which shows that it is possible to bypass the measurement theorem if we give up the associativity condition It also illustrates how a different choice of measurement postulate produces a different set of mixed states.
Definition non-quantum measurement postulate. This and other exotic properties of this theory are analyzed in detail in previous work 35 , Also, the validity of marginal and conditional states imposes additional constraints on the matrices F which are also worked out in It is easy to check that the above definition satisfies conditions 7—13 and violates associativity Therefore, this provides a perfectly valid toy theory of systems that encompass either one or two components, but not more.
As we have mentioned above, the structure of the mixed states depends on the measurement postulate. We stress that our results, unlike previous contributions 2 , 3 , 4 , 5 , 6 , 7 , 8 , 10 , 12 , do not assume this type of non-contextuality. It may seem that conditions 7—14 are a lot of assumptions to claim that we derive the measurement postulates from the non-measurement ones. But from the operational point of view, these conditions constitute the very definition of measurement, single and multi-partite physical system.
Analogously, the rules of probability calculus or the axioms of the real numbers are not explicitly included in the postulates of QM. Note that our results also apply to indistinguishable particles bosons and fermions , as long as we interpret the tensor product not as a composition of particles, but of the corresponding modes. It is rather remarkable that none of the three measurement postulates structure, probabilities and state-update can be modified without having to redesign the whole theory. In particular, the probability rule is deeply ingrained in the main structures of the theory.
This fact shows that one need not appeal to any supplementary principles beyond operational primitives to derive the Born rule, nor do we need to make any assumptions about the structure of measurements, unlike previous work 6 , 10 , 12 , 18 , 19 , Finally, having cleared up unnecessary postulates in the formulation of QM, we find ourselves closer to its core message. All these restricted representations were classified by some of the authors in ref. This amounts to a classification of all alternatives to the measurement postulate for single systems, that is, when the consistency constraints related to composite systems 9—14 are ignored.
The next steps take composition into account. Schwinger, J. The theory of quantized fields I. Gleason, A. Measures on the Closed Subspaces of a Hilbert Space.
The International Workshop on Quantum Communications and Measurement was held at the University of Nottingham from July , It followed the. Department of Electrical & Computer Engineering. Department of Physics. Quantum Communication, Computing, & Measurement Laboratory. (Quantum Physics.
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The solid lines constructive would refer the to detection at D 3 and the dashed lines destructive would refer to the detection before entering a big MZI. The experimental interference fringes of the outputs of each small group of MZIs for logic 0. The experimental a constructive solid lines and b destructive dashed lines interference at the output ports of each small MZI in the first MZIs group, and detected by D 3 is Here due to the dissipation, non-perfect mirrors and loss of other optical elements, the experimental value for the normalized intensity detected at D 3 is The phase is controlled via a computer controlled series of lock-in systems.
This process is similar with the lock-in system for two big MZIs, we inject a strong reference beam from vacuum input part, then with the aid of the interference fringes from upper HR N s, HR M s and D 1 , the interlinked MZIs are locked. Thereafter, we switch off the injected beam and lock-in system to detect the results. This results in the small violation between the theoretical and experimental values as a consequence of the inevitable losses of BS M 1,2 and light transmission in the path of MZIs. The detected normalized intensity for logic 0.
For logic 1, most of light comes throughout the output port at D 2 , on the contrary for logic 0, most of light comes throughout the output port at D 1. The results demonstrate, in principle, that the quantum communication could be realized via interaction-free measurement of quantum logic. It also shows that few light is transferring through the transmission channel, proving the idea of quantum counterfactual-like communication to be accessible.
Our experiment is the realization of interaction-free measurement with a large efficiency. This process corresponds to interaction-free measurement, which is clearly seen from Eq. Here P det is the probability of an interaction-free measurement and P abs is the probability that the light is absorbed by the block including other loss factors.
Therefore we have. In Fig. It is shown that P det increases and P abs decreases with the increase of N. In conclusion, we performed an experiment of the high-efficiency interaction-free measurement. Based on the measurement, the quantum counterfactual-like communication with few portion of light involved in the transmission channel can be reached in this scheme. We showed that the practical scheme of high-efficiency interaction-free measurement with low number of M and relatively higher number N is accessible.
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