Quantum Key Distribution Based on Arbitrarily Weak Distillable Entangled States (original) (raw)
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IEEE Transactions on Information Theory, 2000
We prove unconditional security for a quantum key distribution (QKD) protocol based on distilling pbits (twisted ebits) [1] from an arbitrary untrusted state that is claimed to contain distillable key. Our main result is that we can verify security using only public communication -via parameter estimation of the given untrusted state. The technique applies even to bound entangled states, thus extending QKD to the regime where the available quantum channel has zero quantum capacity. We also show how to convert our purification-based QKD schemes to prepare-measure schemes.
Provable entanglement and information cost for qubit-based quantum key-distribution protocols
European Physical Journal D, 2006
Provable entanglement has been shown to be a necessary precondition for unconditionally secure key generation in the context of quantum cryptographic protocols. We estimate the maximal threshold disturbance up to which the two legitimate users can prove the presence of quantum correlations in their data, in the context of the four- and six-state quantum key-distribution protocols, under the assumption of coherent attacks. Moreover, we investigate the conditions under which an eavesdropper can saturate these bounds, by means of incoherent and two-qubit coherent attacks. A direct connection between entanglement distillation and classical advantage distillation is also presented.
Low-Dimensional Bound Entanglement With One-Way Distillable Cryptographic Key
IEEE Transactions on Information Theory, 2008
We provide a class of bound entangled states that have positive distillable secure key rate. The smallest state of this kind is 4 ⊗ 4, which shows that peculiar security contained in bound entangled states does not need high dimensional systems. We show, that for these states a positive key rate can be obtained by one-way Devetak-Winter protocol. Subsequently the volume of bound entangled keydistillable states in arbitrary dimension is shown to be nonzero. We provide a scheme of verification of cryptographic quality of experimentally prepared state in terms of local observables. Proposed set of 7 collective settings is proven to be optimal in number of settings.
Unconditional Privacy over Channels which Cannot Convey Quantum Information
Physical Review Letters, 2008
By sending systems in specially prepared quantum states, two parties can communicate without an eavesdropper being able to listen. The technique, called quantum cryptography, enables one to verify that the state of the quantum system has not been tampered with, and thus one can obtain privacy regardless of the power of the eavesdropper. All previous protocols relied on the ability to faithfully send quantum states. In fact, until recently, they could all be reduced to a single protocol where security is ensured though sharing maximally entangled states. Here we show this need not be the case -one can obtain verifiable privacy even through some channels which cannot be used to reliably send quantum states.
Quantum Privacy Amplification and the Security of Quantum Cryptography over Noisy Channels
Physical Review Letters, 1996
Existing quantum cryptographic schemes are not, as they stand, operable in the presence of noise on the quantum communication channel. Although they become operable if they are supplemented by classical privacy-amplification techniques, the resulting schemes are difficult to analyse and have not been proved secure. We introduce the concept of quantum privacy amplification and a cryptographic scheme incorporating it which is provably secure over a noisy channel. The scheme uses an 'entanglement purification' procedure which, because it requires only a few quantum Controlled-Not and singlequbit operations, could be implemented using technology that is currently being developed. The scheme allows an arbitrarily small bound to be placed on the information that any eavesdropper may extract from the encrypted 1 message. 89.70.+c, 03.65.Bz, 89.80.+h Typeset using REVT E X
Security of Quantum Key Distribution with entangled quNits
2003
We consider a generalisation of Ekert's entanglement-based quantum cryptographic protocol where qubits are replaced by qu$N$its (i.e., N-dimensional systems). In order to study its robustness against optimal incoherent attacks, we derive the information gained by a potential eavesdropper during a cloning-based individual attack. In doing so, we generalize Cerf's formalism for cloning machines and establish the form of the most general cloning machine that respects all the symmetries of the problem. We obtain an upper bound on the error rate that guarantees the confidentiality of quNit generalisations of the Ekert's protocol for qubits.
Secret-Key Distillation across a Quantum Wiretap Channel under Restricted Eavesdropping
Physical Review Applied
The theory of quantum cryptography aims to guarantee unconditional information-theoretic security against an omnipotent eavesdropper. In many practical scenarios, however, the assumption of an allpowerful adversary is excessive and can be relaxed considerably. In this paper we study secret-key distillation across a lossy and noisy quantum wiretap channel between Alice and Bob, with a separately parameterized realistically lossy quantum channel to the eavesdropper Eve. We show that under such restricted eavesdropping, the key rates achievable can exceed the secret-key-distillation capacity against an unrestricted eavesdropper in the quantum wiretap channel. Furthermore, we show upper bounds on the key rates based on the relative entropy of entanglement. This simple restricted eavesdropping model is widely applicable, for example, to free-space quantum optical communication, where realistic collection of light by Eve is limited by the finite size of her optical aperture. Future work will include calculating bounds on the amount of light Eve can collect under various realistic scenarios.
Security of quantum key distributions with entangled qudits
Physical Review A, 2004
We consider a generalisation of Ekert's entanglement-based quantum cryptographic protocol where qubits are replaced by quN its (i.e., N -dimensional systems). In order to study its robustness against optimal incoherent attacks, we derive the information gained by a potential eavesdropper during a cloning-based individual attack. In doing so, we generalize Cerf's formalism for cloning machines and establish the form of the most general cloning machine that respects all the symmetries of the problem. We obtain an upper bound on the error rate that guarantees the confidentiality of quN it generalisations of the Ekert's protocol for qubits.
Quantum key distribution using intra-particle entanglement
We propose the use of intra-particle entanglement to enhance the security of a practical implementation of the Bennett-Brassard-1984 (BB84) quantum key distribution scheme. Intra-particle entanglement is an attractive resource since it can be easily generated using only linear optics. Security is studied under a simple model of incoherent attack for protocols involving two or all five mutually unbiased bases. In terms of efficiency of secret key generation and tolerable error rate, the latter is found to be superior to the former. We find that states that allow secrecy distillation are necessarily entangled, though they may be local. Since more powerful attacks by Eve obviously exist, our result implies that security is a strictly stronger condition than entanglement for these protocols.
Quantum cryptography using partially entangled states
Optics Communications, 2010
We show that non-maximally entangled states can be used to build a quantum key distribution (QKD) scheme where the key is probabilistically teleported from Alice to Bob. This probabilistic aspect of the protocol ensures the security of the key without the need of non-orthogonal states to encode it, in contrast to other QKD schemes. Also, the security and key transmission rate of the present protocol is nearly equivalent to those of standard QKD schemes and these aspects can be controlled by properly harnessing the new free parameter in the present proposal, namely, the degree of partial entanglement. Furthermore, we discuss how to build a controlled QKD scheme, also based on partially entangled states, where a third party can decide whether or not Alice and Bob are allowed to share a key.