Abstract
In quantum theory, the retrodiction problem is not as clear as its classical counterpart because of the uncertainty principle of quantum mechanics. In classical physics, the measurement outcomes of the present state can be used directly for predicting the future events and inferring the past events which is known as retrodiction. However, as a probabilistic theory, quantum-mechanical retrodiction is a nontrivial problem that has been investigated for a long time, of which the Mean King Problem is one of the most extensively studied issues. Here, we present the first experimental test of a variant of the Mean King Problem, which has a more stringent regulation and is termed “Tracking the King.” We demonstrate that Alice, by harnessing the shared entanglement and controlled-not gate, can successfully retrodict the choice of King's measurement without knowing any measurement outcome. Our results also provide a counterintuitive quantum communication to deliver information hidden in the choice of measurement.
Highlights
The thought experiment, named the Mean King Problem (MKP), is a quantum-mechanical retrodiction problem, which originates from the paper in 1987 by Vaidman et al [1]
What if the King does not tell Alice his choice? This question leads to another extension of the MKP termed “Tracking the King Problem” (TKP)
By sharing maximally entangled photon pairs and employing a controllednot gate (C-NOT) as Alice’s control measurement, we show that it is possible for Alice to retrodict the choice of King’s measurement without knowing any measurement outcome
Summary
The thought experiment, named the Mean King Problem (MKP), is a quantum-mechanical retrodiction problem, which originates from the paper in 1987 by Vaidman et al [1]. This question leads to another extension of the MKP termed “Tracking the King Problem” (TKP) In this new problem, Alice is not informed by the King’s choice (nor the outcome). The counterintuitive part of this problem is that in classical physics, measurements without outcomes being recorded carry no information and cannot be used for communication Such a measurement in quantum mechanics causes traceable disturbance to the measured system so that Alice’s control measurement can retrieve the King’s choice. By sharing maximally entangled photon pairs and employing a controllednot gate (C-NOT) as Alice’s control measurement, we show that it is possible for Alice to retrodict the choice of King’s measurement without knowing any measurement outcome The realization of this thought experiment unravels the intrinsic characteristics of quantum measurement and deepens our understanding of quantum theory.
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