In classical mechanics, performing a measurement without reading the measurement outcome is equivalent to not exploiting the measurement at all. A nonselective measurement in the classical realm carries no information. Here we show that the situation is remarkably different when quantum mechanical systems are concerned. A nonselective measurement on one part of a maximally entangled pair can allow communication between two parties. In the proposed protocol, the signal is encoded in the choice of the measurement basis of one of the communicating parties, while the outcomes of the measurement are irrelevant for the communication and therefore may be discarded. Different choices for the (nonselective) measurement correspond to different signals. The implication of the study of measurements in quantum mechanics is considered. The scheme is studied in a Hilbert space of prime dimension.
In classical mechanics, performing a measurement without reading the measurement outcome is equivalent to not exploiting the measurement at all. A nonselective measurement in the classical realm carries no information. Here we show that the situation is remarkably different when quantum mechanical systems are concerned. A nonselective measurement on one part of a maximally entangled pair can allow communication between two parties. In the proposed protocol, the signal is encoded in the choice of the measurement basis of one of the communicating parties, while the outcomes of the measurement are irrelevant for the communication and therefore may be discarded. Different choices for the (nonselective) measurement correspond to different signals. The implication of the study of measurements in quantum mechanics is considered. The scheme is studied in a Hilbert space of prime dimension.
It is shown that, with respect to the outcomes of two entangled quantum systems, the choices of measurement basis cannot be independent from each other. Two parties share maximally entangled states and bases chosen between Z and X with P=1/2 are used to perform measurements at each end. With the assumption that an element of physical reality for the choice made at one end is not a function of the outcome of an entangled state at the other end, we derive a contradiction to this assumption and show that elements of physical reality for the choice of measurement basis at each end cannot be independent from each other.
Unlike classical measurements, quantum measurements may be useful even without reading the outcome. Such so called nonselective measurements are exploited in this paper to design a quantum dialogue protocol that allows exchanging secret data without prior key distributions. The relevant data to be exchanged are in terms of the high-dimensional mutually unbiased bases of quantum measurements. Appropriate modes of bidirectional controlling are devised to ensure the protocol security which is asymptotic.
It has been found that the signal can be encoded in the choice of the measurement basis of one of the communicating parties, while the outcomes of the measurement are irrelevant for the communication and therefore may be discarded. The proposed protocol was novel and interesting, but it wasn't secure for communication. The eavesdropper can obtain the information without being detected. We utilize the outcomes of the measurement to propose a secure communication protocol. And the error correction code is used to increase the fault tolerance in the noise.
The topic of this thesis is Quantum Cryptography. Based on the laws of Quantum Mechanics, this allows two parties to share a secure key, by using quantum states to carry classical information. Namely, the Quantum Key Distribution (QKD) process, completed with the classical algorithm One Time Pad, leads to an unconditionally secure cryptosystem. Most QKD protocols, like the famous BB84, are realized on unidirectional quantum channels and have probabilistic character. Recently, a new protocol, named LM05, has been proposed, which works on bidirectional quantum channels and in a deterministic way. This thesis is mainly concerned with protocols extending LM05 from binary to d-ary alphabets (dmajor2), by using multi-level quantum systems in d-dimensional Hilbert spaces. The construction of such protocols relies on the notion of Mutually Unbiased Bases (MUB). But the total number of MUB in a Hilbert space of dimension d is known only if d is a prime power. Accordingly, the new protocols are realized under this assumption. As a preliminary step, an explicit expression for MUB encompassing powers of both even and odd primes is discussed. The first proposed extension, called EM09, uses shift operators on MUB to encode information and the usual quantum measurement to realize the control procedure. This guarantees maximal security for dimension d=3 against a powerful individual attack. The second extension, named EM11, is characterized by an innovative control strategy based on a suitable unitary transformation rather than on quantum measurement. Such protocol only works for d an odd prime power, due to the particular choice of the control operator, which is proved to be the only possible with the required properties. The EM11 protocol leads to a relevant improvement. In fact, the security against the same attack is much better than in the EM09 and it increases in terms of the dimension d. Some partial results are also obtained about the possible extensions of the probabilistic protocol called SARG04 to higher dimensions. Finally, it is considered the use of the EM09 and EM11 protocols in the Quantum Direct Communication, where the meaningful message is transmitted without any encryption, as allowed by their deterministic character. In this context, the asymptotic security turns out to be optimal in dimension d=2 for EM09 and in dimension d=3 for EM11.
An analysis of quantum measurement is presented that relies on an information-theoretic description of quantum entanglement. In a consistent quantum information theory of entanglement, entropies (uncertainties) conditional on measurement outcomes can be negative, implying that measurement can be described via unitary, entropy-conserving, interactions, while still producing randomness in a measurement device. In such a framework, quantum measurement is not accompanied by a wave-function collapse, or a quantum jump. The theory is applied to the measurement of incompatible variables, giving rise to a stronger entropic uncertainty relation than heretofore known. It is also applied to standard quantum measurement situations such as the Stern-Gerlach and double-slit experiments to illustrate how randomness, inherent in the conventional quantum probabilities, arises in a unitary framework. Finally, the present view clarifies the relationship between classical and quantum concepts.
Recently, Kalev et al. [A. Kalev, A. Mann, and M. Revzen, Phys. Rev. Lett. 110, 260502 (2013).] proposed a quantum (public) communication protocol with an interesting encoding style, where the signal is encoded in the choice of the measurement basis of one of the communicating parties (Bob) and Bob's measurement results are irrelevant for the communication. As we know, one of the main advantages of quantum technique in communication over the classical one is the higher security. Therefore, as Kalev et al. have mentioned in their paper, an interesting open question is whether one could and how to utilize this new encoding style to design a secure communication protocol, i.e., translate the choice of measurement into the secret. Here we propose a quantum key distribution protocol, which is a secure communication protocol, with this encoding style, where Bob's measurement results are still irrelevant. Furthermore, the security of the proposed protocol in the zero-error case has been proved.