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Register a new userCounterfactual computation revisited
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Mitchison and Jozsa recently suggested that the chained-Zeno counterfactual computation protocol recently proposed by Hosten et al. is counterfactual for only one output of the computer. This claim was based on the existing abstract algebraic definition of counterfactual computation, and indeed according to this definition, their argument is correct. However, a more general definition (physically adequate) for counterfactual computation is implicitly assumed by Hosten et. al. Here we explain in detail why the protocol is counterfactual and how the history tracking method of the existing description inadequately represents the physics underlying the protocol. Consequently, we propose a modified definition of counterfactual computation. Finally, we comment on one of the most interesting aspects of the error-correcting protocol.
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The possibility of interaction-free measurements and counterfactual computations is a striking feature of quantum mechanics pointed out around 20 years ago. We implement such phenomena in actual 5-qubit, 15-qubit and 20-qubit IBM quantum computers by means of simple quantum circuits. The results are in general close to the theoretical expectations. For the larger circuits (with numerous gates and consequently larger errors) we implement a simple error mitigation procedure which improve appreciably the performance.
We present how basic logic gates including NAND, NOR and XOR gates can be implemented counterfactually. The two inputs (Bob and Charlie) and the output (Alice) of the proposed counterfactual logic gate are not within the same station but rather separated in three different locations. We show that there is no need to pre-arrange entanglement for the gate, and more importantly, there is no real physical particles traveling among Alice, Bob and Charlie during the information processing. Bob and Charlie only need to independently control the blocking and unblocking of the transmission channels that connect them to Alice. In this way, they can completely determine the state of a real photon at Alices end, thereby leading to implement a counterfactual logic gate. The functionality of a particular counterfactual logic gate is determined only by an appropriate design of Alices optical device. Furthermore, by utilizing the proposed counterfactual logic gates, we demonstrate how to counterfactually prepare the Greenberger-Horne-Zeilinger state and W state with three remote quantum objects, which are in superposition states of blocking and unblocking the transmission channel.
We explore a counterfactual protocol for energy transfer. A modified version of a Mach-Zehnder interferometer dissociates a photons position and energy into separate channels, resulting in a photoelectric effect in one channel without the absorption of a photon. We use the quantum Zeno effect to extend our results by recycling the same photon through the system and obtain a stream of photoelectrons. If dissociation of properties such as energy can be demonstrated experimentally, there may be a variety of novel energy-related applications that may arise from the capacity to do non-local work. The dissociation of intrinsic properties, like energy, from elementary particles may also lead to theoretical discussions of the constitution of quantum objects.
A recent quantum protocol for counterfactual communication [Y. Aharonov and L. Vaidman, Phys. Rev. A 99, 010103(R), 2019] relies on post-selection to eliminate the weak trace in the transmission channel. We show that the post-selection in this protocol also eliminates the flow of Fisher information from transmitter to receiver. However, we also show that a classical communication protocol with post-selection can be counterfactual. Hence, we argue that post-selection should not be allowed in genuine counterfactual communication. In the quantum counterfactual communication protocol, the probability of discarding an event by post-selection tends to zero with an increasing number of ideal optical components. But the counterfactual violation strength tends to infinity at a faster rate. Consequently, the quantum protocol is not counterfactual proper.
In counterfactual QKD information is transfered, in a secure way, between Alice and Bob even when no particle carrying the information is in fact transmitted between them. In this letter we fully implement the scheme for counterfactual QKD proposed in [T. Noh, PRL textbf{103}, 230501 (2009)], demonstrating for the first time that information can be transmitted between two parties without the transmission of a carrier.
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