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S. S. Nazin

Publications and source records attributed to S. S. Nazin.

14 recordsLinked to original sources

Role of causality in ensuring unconditional security of relativistic quantum cryptography

The problem of unconditional security of quantum cryptography (i.e. the security which is guaranteed by the fundamental laws of nature rather than by technical limitations) is one of the central points in quantum information theory. We propose a relativistic quantum cryptosystem and prove its unconditional security against any eavesdropping attempts. Relativistic causality arguments allow to demonstrate the security of the system in a simple way. Since the proposed protocol does not employ collective measurements and quantum codes, the cryptosystem can be experimentally realized with the present state-of-art in fiber optics technologies. The proposed cryptosystem employs only the individual measurements and classical codes and, in addition, the key distribution problem allows to postpone the choice of the state encoding scheme until after the states are already received instead of choosing it before sending the states into the communication channel (i.e. to employ a sort of ``antedate'' coding).

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Relativistic Restrictions on the Distinguishability of Orthogonal Quantum States

We analyze the restrictions on the distinguishability of quantum states imposed by special relativity. An explicit expression relating the error probability for distinguishing between two orthogonal single-photon states with the time $T$ elapsed from the start of the measurement procedure until the measurement result is obtained by the observer.

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Quantum Bit Commitment in a Noisy Channel

Under rather general assumptions about the properties of a noisy quantum channel, a first quantum protocol is proposed which allows to implement the secret bit commitment with the probability arbitrarily close to unity.

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A simple proof of the unconditional security of relativistic quantum cryptography

A simple proof of the unconditional security of a relativistic quantum cryptosystem based on orthogonal states is proposed. Restrictions imposed by special relativity allow to substantially simplify the proof compared with the non-relativistic cryptosystems involving non-orthogonal states. Important for the proposed protocol is the spatio-temporal structure of the quantum states which is actually ignored in the non-relativistic protocols employing only the structure of the state space of the information carriers. As a consequence, the simplification arises because of the inefficiency of collective measurements which constitute the major problem in the non-relativistic case.

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Relativistic quantum protocols: "Bit Commitment" and "Coin Tossing"

The relativistic quantum protocols realizing the bit commitment and distant coin tossing schemes are proposed. The protocols are based on the fact that the non-stationary orthogonal extended quantum states cannot be reliably distinguished if they are not fully accessible for the measurement. As the states propagate from the domain controlled by one of the user to the domain accessible for the measurements performed by the other user, they become reliably distinguishable for the second user. Important for the protocol are both the quantum nature of the states and the existence of a finite maximum speed of the signal propagation imposed by the special relativity.

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On the Distinguishability of Relativistic Quantum States in Quantum Cryptography

Relativistic quantum field theory imposes additional fundamental restrictions on the distinguishability of quantum states. Because of the unavoidable delocalization of the quantum field states in the Minkowski space-time, the reliable (with unit probability) distinguishability of orthogonal states formally requires infinite time. For the cryptographic protocols which are finite in time the latter means that the effective ``noise'' is present even in the ideal communication channel because of the non-localizability of the quantum field states.

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Teleportation of the Relativistic Quantum Field

The process of teleportation of a completely unknown one-particle state of a free relativistic quantum field is considered. In contrast to the non-relativistic quantum mechanics, the teleportation of an unknown state of the quantum field cannot be in principle described in terms of a measurement in a tensor product of two Hilbert spaces to which the unknown state and the state of the EPR-pair belong. The reason is of the existence of a cyclic (vacuum) state common to both the unknown state and the EPR-pair. Due to the common vacuum vector and the microcausality principle (commutation relations for the field operators), the teleportation amplitude contains inevitably contributions which are irrelevant to the teleportation process. Hence in the relativistic theory the teleportation in the sense it is understood in the non-relativistic quantum mechanics proves to be impossible because of the impossibility of the realization of the appropriate measurement as a tensor product of the measurements related to the individual subsystems so that one can only speak of the amplitude of the propagation of the field as a whole.

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On Teleportation of a Completely Unknown State of Relativistic Photon

The process of teleportation of a completely unknown single-photon relativistic state is considered. Analysis of the relativistic case reveals that the teleportation as it is understood in the non-relativistic quantum mechanics is impossible if no {\it a priori} information on the state to be teleported is available. It is only possible to speak of the amplitude of the propagation of the field (taking into account the measurement procedure) since the existence of a common vacuum state together with the microcausality principle (the field operators commutation relations) make the concept of the propagation amplitude for the individual subsystems physically meaningless. When partial {\it a priori} information is available (for example, only the polarization state of the photon is unknown while its spatial state is specified beforehand), the teleportation does become possible in the relativistic case. In that case the {\it a priori} information can be used to ``label'' the identical particles to make them effectively distinguishable.

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Unconditionally Secure Relativistic Quantum Bit Commitment

A new relativistic quantum protocol is proposed allowing to implement the bit commitment scheme. The protocol is based on the idea that in the relativistic case the field propagation to the region of space accessible to measurement requires, contrary to the non-relativistic case, a finite non-zero time which depends on the structure of the particular state of the field. In principle, the secret bit can be stored for arbitrarily long time with the probability arbitrarily close to unit.

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Relativistic quantum coin tossing

A relativistic quantum information exchange protocol is proposed allowing two distant users to realize ``coin tossing'' procedure. The protocol is based on the point that in relativistic quantum theory reliable distinguishing between the two orthogonal states generally requires a finite time depending on the structure of these states.

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Single Spin State Detection for the Kane Model of Silicon-Based Quantum Computer

The scheme for measurement of the state of a single spin (or a few spin system) based on the single-electron turnstile and injection of spin polarized electrons from magnetic metal contacts is proposed. Applications to the recent proposal concerning the spin gates based on a silicon matrix (B.Kane, Nature, {\bf 393}, 133 (1998)) are discussed.

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On the Teleportation of Continuous Variable

The measurement procedures used in quantum teleportation are analyzed from the viewpoint of the general theory of quantum-mechanical measurements. It is shown that to find the teleported state one should only know the identity resolution (positive operator-valued measure) generated by the corresponding instrument (quantum operation describing the system state change caused by the measurement) rather than the instrument itself. A quantum teleportation protocol based on a measurement associated with a non-orthogonal identity resolution is proposed for a system with non-degenerate continuous spectrum.

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Photon Frequency Entanglement Swapping

We propose a simple non-linear crystal based optical scheme for experimental realization of the frequency entanglement swapping between the photons belonging to two independent biphotons.

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