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arXiv:quant-ph/9908006 · Physical Review A

Quantum-communication protocol employing weak measurements

Alonso Botero, Benni Reznik

Published Mar 31, 2000• 16 citations
arXivHTMLPDF

Abstract

We propose a communication protocol exploiting correlations between two events with a definite time ordering: (a) the outcome of a weak measurement on a spin, and (b) the outcome of a subsequent ordinary measurement on the spin. In our protocol, Alice first generates a ``code'' by performing weak measurements on a sample of N spins. The sample is sent to Bob, who later performs a postselection by measuring the spin along either of two certain directions. The results of the postselection define the ``key,'' which he then broadcasts publicly. Using both her previously generated code and this key, Alice is able to infer the direction chosen by Bob in the postselection. Alternatively, if Alice broadcasts publicly her code, Bob is able to infer from the code and the key the direction chosen by Alice for her weak measurement. Two possible experimental realizations of the protocols are briefly mentioned.

DOI
10.1103/physreva.61.050301

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We propose a communication protocol exploiting correlations between two events with a definite time ordering: (a) the outcome of a weak measurement on a spin, and (b) the outcome of a subsequent ordinary measurement on the spin. In our protocol, Alice first generates a code'' by performing weak measurements on a sample of N spins. The sample is sent to Bob, who later performs a postselection by measuring the spin along either of two certain directions. The results of the postselection define the key,'' which he then broadcasts publicly. Using both her previously generated code and this key, Alice is able to infer the direction chosen by Bob in the postselection. Alternatively, if Alice broadcasts publicly her code, Bob is able to infer from the code and the key the direction chosen by Alice for her weak measurement. Two possible experimental realizations of the protocols are briefly mentioned.
The classical theories of communication rely on the assumption that there has to be a flow of particles from Bob to Alice in order for him to send a message to her. We develop a quantum protocol that allows Alice to perceive Bob's message ``counterfactually''; that is, without Alice receiving any particles that have interacted with Bob. By utilizing a setup built on results from interaction-free measurements, we outline a communication protocol whereby the information travels in the opposite direction of the emitted particles. In comparison to previous attempts on such protocols, this one is such that a weak measurement at the message source would not leave a weak trace that could be detected by Alice's receiver. While some interaction-free schemes require a large number of carefully aligned beam splitters, our protocol is realizable with two or more beam splitters. We demonstrate this protocol by numerically solving the time-dependent Schr\"odinger equation for a Hamiltonian that implements this quantum counterfactual phenomenon.
We propose a new protocol for the weak measurement of any observable with remote pre and postselections. We show that if two parties share a pure entangled state, then by using local operations and classical communication they can preselect and postselect at distant locations leading to the weak value of an observable as a shift in the pointer of the apparatus at one location in the process of the weak measurement. This can be achieved with either sharing of a pure maximally or non-maximally entangled state. We generalize the protocol for realizing the weak value of any observable with remote pre and postselection of mixed states. Finally, we show how the weak value is modified in the remote pre and postselection setting if Alice and Bob share a mixed entangled state.
We present a scheme for quantum communication, where a set of EPR pairs, initially shared by the sender Alice and the receiver Bob, functions as a quantum channel. After insuring the safety of the quantum channel, Alice applies local measurement on her particles of the EPR pairs and informs Bob the encoding classical information publicly. According to Alice's classical information and his measurement outcomes on the EPR pairs Bob can infer the secret messages directly. In this scheme, to transmit one bit secret message, the sender Alice only needs to send one bit classical information to the receiver Bob. We also show that this scheme is completely secure if perfect quantum channel is used.
Based on an EPR pair of qubits and allowing asymptotically secure key distribution, a secure communication protocol is presented. Bob sends either of the EPR pair qubits to Alice. Alice receives the travel qubit. Then she can encode classical information by local unitary operations on this travel qubit. Alice send the qubit back to Bob. Bob can get Alice's information by measurement on the two photons in Bell operator basis. If Eve in line, she has no access to Bob's home qubit. All her operations are restricted to the travel qubit. In order to find out which opeartion Alice performs, Eve's operation must include measurements. The EPR pair qubits are destroyed. Bob's measurement on the two photons in Bell operator basis can help him to judge whether Eve exist in line or not. In this protocal, a public channel is not necessary.
Assume Alice and Bob share some bipartite d-dimensional quantum state. A well-known result in quantum mechanics says that by performing two-outcome measurements, Alice and Bob can produce correlations that cannot be obtained locally, i.e., with shared randomness alone. We show that by using only two bits of communication, Alice and Bob can classically simulate any such correlations. All previous protocols for exact simulation required the communication to grow to infinity with the dimension d. Our protocol and analysis are based on a power series method, resembling Krivine's bound on Grothendieck's constant, and on the computation of volumes of spherical tetrahedra.
Assume Alice and Bob share some bipartite ddd-dimensional quantum state. A well-known result in quantum mechanics says that by performing two-outcome measurements, Alice and Bob can produce correlations that cannot be obtained locally, i.e., with shared randomness alone. We show that by using only two bits of communication, Alice and Bob can classically simulate any such correlations. All previous protocols for exact simulation required the communication to grow to infinity with the dimension ddd. Our protocol and analysis are based on a power series method, resembling Krivine's bound on Grothendieck's constant, and on the computation of volumes of spherical tetrahedra.