Adan Cabello

Quantum key distribution in the Holevo limit.

A theorem by Shannon and the Holevo theorem impose that the efficiency of any protocol for quantum key distribution, E, defined as the number of secret (i.e., allowing eavesdropping detection) bits per transmitted bit plus qubit, is E < or = 1. The problem addressed here is whether the limit E = 1 can be achieved. It is showed that it can be done by splitting the secret bits between several qubits and forcing Eve to have only a sequential access to the qubits, as proposed by Goldenberg and Vaidman. A protocol with E = 1 based on polarized photons and in which Bobs state discrimination can be implemented with linear optical elements is presented.

Bell-Kochen-Specker theorem: A proof with 18 vectors

Abstract We present a “state-independent” proof of the Bell-Kochen-Specker theorem using only 18 four-dimensional vectors, which is a record for this kind of proof. This set of vectors contains subses which allow us to develop a “state-specific” proof with ten vectors (also a record) and a “probabilistic” proof with seven vectors which reflects the algebraic structure of Hardys nonlocality theorem.

State-independent experimental test of quantum contextuality

The question of whether quantum phenomena can be explained by classical models with hidden variables is the subject of a long-lasting debate. In 1964, Bell showed that certain types of classical models cannot explain the quantum mechanical predictions for specific states of distant particles, and some types of hidden variable models have been experimentally ruled out. An intuitive feature of classical models is non-contextuality: the property that any measurement has a value independent of other compatible measurements being carried out at the same time. However, a theorem derived by Kochen, Specker and Bell shows that non-contextuality is in conflict with quantum mechanics. The conflict resides in the structure of the theory and is independent of the properties of special states. It has been debated whether the Kochen–Specker theorem could be experimentally tested at all. First tests of quantum contextuality have been proposed only recently, and undertaken with photons and neutrons. But these tests required the generation of special quantum states and left various loopholes open. Here we perform an experiment with trapped ions that demonstrates a state-independent conflict with non-contextuality. The experiment is not subject to the detection loophole and we show that, despite imperfections and possible measurement disturbances, our results cannot be explained in non-contextual terms.

Experimentally Testable State-Independent Quantum Contextuality

We show that there are Bell-type inequalities for noncontextual theories that are violated by any quantum state. One of these inequalities between the correlations of compatible measurements is particularly suitable for testing this state-independent violation in an experiment.

Experimental Test of Quantum Contextuality in Neutron Interferometry

We performed an experimental test of the Kochen-Specker theorem based on an inequality derived from the Peres-Mermin proof, using spin-path (momentum) entanglement in a single neutron system. Following the strategy proposed by Cabello et al. [Phys. Rev. Lett. 100, 130404 (2008)10.1103/PhysRevLett.100.130404], a Bell-like state was generated, and three expectation values were determined. The observed violation 2.291 +/- 0.008 not less, dbl equals1 clearly shows that quantum mechanical predictions cannot be reproduced by noncontextual hidden-variable theories.

Decoherence-free quantum information processing with four-photon entangled states

Decoherence-free states protect quantum information from collective noise, the predominant cause of decoherence in current implementations of quantum communication and computation. Here we demonstrate that spontaneous parametric down conversion can be used to generate four-photon states which enable the encoding of one qubit in a decoherence-free subspace. The immunity against noise is verified by quantum state tomography of the encoded qubit. We show that particular states of the encoded qubit can be distinguished by local measurements on the four photons only.

Quantum key distribution without alternative measurements

Entanglement swapping between Einstein-Podolsky-Rosen ~EPR! pairs can be used to generate the same sequence of random bits in two remote places. A quantum key distribution protocol based on this idea is described. The scheme exhibits the following features. ~a! It does not require that Alice and Bob choose between alternative measurements, therefore improving the rate of generated bits by transmitted qubit. ~b! It allows Alice and Bob to generate a key of arbitrary length using a single quantum system ~three EPR pairs!, instead of a long sequence of them. ~c! Detecting Eve requires the comparison of fewer bits. ~d! Entanglement is an essential ingredient. The scheme assumes reliable measurements of the Bell operator. PACS number~s!: 03.67.Dd, 03.67.Hk, 03.65.Bz The two main goals of cryptography are for two distant parties, Alice and Bob, to be able to communicate in a form that is unintelligible to a third party, Eve, and to prove that the message was not altered in transit. Both of these goals can be accomplished securely if both Alice and Bob are in possession of the same secret random sequence of bits, a ‘‘key’’ @1#. Therefore, one of the main problems of cryptography is the key distribution problem, that is, how do Alice and Bob, who initially share no secret information, come into the possession of a secret key, while being sure that Eve cannot acquire even partial information about it. This problem cannot be solved by classical means, but it can be solved using quantum mechanics @2#. The security of protocols for quantum key distribution ~QKD! such as the BennettBrassard 1984 ~BB84 !@ 2#, E91 @3#, B92 @4#, and other protocols @5,6#, is assured by the fact that while information stored in classical form can be examined and copied without altering it in any detectable way, it is impossible to do that when information is stored in unknown quantum states, because an unknown quantum state cannot be reliably cloned ~‘‘no-cloning’’ theorem @7#!. In these protocols security is assured by the fact that both Alice and Bob must choose randomly between two possible measurements. In this paper I introduce a QKD scheme which does not require that Alice and Bob choose between alternative measurements. This scheme is based on ‘‘entanglement swapping’’ @8‐10# between two pairs of ‘‘qubits’’ ~quantum two-level systems!, induced by a Bell operator measurement @11#. The Bell operator is a nondegenerate operator which acts on a pair of qubits i and j, and projects their combined state onto one of the four Bell states

State-Independent Quantum Contextuality with Single Photons

We present an experimental state-independent violation of an inequality for noncontextual theories on single particles. We show that 20 different single-photon states violate an inequality which involves correlations between results of sequential compatible measurements by at least 419 standard deviations. Our results show that, for any physical system, even for a single system, and independent of its state, there is a universal set of tests whose results do not admit a noncontextual interpretation. This sheds new light on the role of quantum mechanics in quantum information processing.

Graph-Theoretic Approach to Quantum Correlations

Correlations in Bell and noncontextuality inequalities can be expressed as a positive linear combination of probabilities of events. Exclusive events can be represented as adjacent vertices of a graph, so correlations can be associated to a subgraph. We show that the maximum value of the correlations for classical, quantum, and more general theories is the independence number, the Lovász number, and the fractional packing number of this subgraph, respectively. We also show that, for any graph, there is always a correlation experiment such that the set of quantum probabilities is exactly the Grötschel-Lovász-Schrijver theta body. This identifies these combinatorial notions as fundamental physical objects and provides a method for singling out experiments with quantum correlations on demand.

Experimental Demonstration of a Quantum Protocol for Byzantine Agreement and Liar Detection

We introduce a new quantum protocol for solving detectable Byzantine agreement (also called detectable broadcast) between three parties, and also for solving the detectable liar detection problem. The protocol is suggested by the properties of a four-qubit entangled state, and the classical part of the protocol is simpler than that of previous proposals. In addition, we present an experimental implementation of the protocol using four-photon entanglement.