Realizing quantum advantage without entanglement in single-photon states
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| Number of Parts | 40 | |
| Author | 0000-0003-2131-6090 (ORCID) 0000-0001-8724-9885 (ORCID) | |
| License | CC Attribution 3.0 Unported: You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor. | |
| Identifiers | 10.5446/38429 (DOI) | |
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Transcript: English(auto-generated)
00:03
Quantum advantage without entanglement. Quantum mechanics offers advantage in games and communication, even when there is no entanglement present. Our paper shows how this could be demonstrated with an optical interferometer. In this work, we studied a communication protocol in which the sender,
00:25
Alice, probabilistically encodes two bits of information on one of her two qubits. Then, she challenged the receiver, Bob, to estimate the bits by applying a decoding mechanism. We studied how much advantage Bob can get when he is able to perform decoding protocols that make use of quantum mechanics.
00:45
In particular, we studied the cases when there is a quantum advantage even when there is no entanglement in the system. Let me describe how the protocol works. Alice has access to a two-qubit mixed state described by the density matrix Rho S P, where S and P can refer to any two independent qubits.
01:05
In our proposed implementation, they stand for the spin and path of a photon. She sends qubit P to Bob. Now, how does Alice encode the bits? To encode the pair b1, b2, she applies the single qubit gate, uk, with probability pk.
01:25
After encoding b1 and b2, Alice sends qubit B to Bob and challenges him to guess which pair of bits she encoded. Now is when we begin to analyze how good is for Bob to make use of quantum mechanics.
01:41
We quantify his performance through the mutual information between what he estimated and what Alice sent. Let's analyze what are Bob's options. A classical decoding machine. In this case, the decoding protocols that Bob can implement are restricted by the interaction between the two qubits.
02:01
He can only apply single qubit gates and classical communication. We call the corresponding mutual information IC. A quantum decoding machine. In this case, he has access to a machine that allows him to implement any decoding protocol. Specifically, he can apply two qubit quantum gates.
02:24
We call the mutual information IQ. This is the maximum amount of information that Bob can extract in a perfect scenario. In this work, we quantify the quantum advantage as the difference between the mutual information that Bob can get with a quantum machine versus a classical one.
02:43
This is delta I equals IQ minus IC. In our work, we show that even when there is no entanglement, there is an advantage for Bob when he uses a quantum machine. When Alice encode the bits by applying the four unit operations with the same probability, the encoding is called optimal.
03:05
In this encoding, she has to implement the three Pauli matrices. We found that in the absence of entanglement, the maximal advantage that Bob can obtain when the encoding is done optimally is one over three bits. We also found that when Alice encodes only using sigma C, Bob can obtain a similar advantage of 0.3111 bits.