We conjecture a new entropic uncertainty principle governing the entropy of complementary observations made on a system given side information in the form of quantum states, generalizing the entropic uncertainty relation of Maassen and Uffink [Phys. Rev. Lett. 60, 1103 (1988)]. We prove a special case for certain conjugate observables by adapting a similar result found by Christandl and Winter pertaining to quantum channels [IEEE Trans. Inf. Theory 51, 3159 (2005)], and discuss possible applications of this result to the decoupling of quantum systems and for security analysis in quantum cryptography.
We present an experimental implementation of the coined discrete-time quantum walk on a square using a three-qubit liquid-state nuclear-magnetic-resonance ͑NMR͒ quantum-information processor ͑QIP͒. Contrary to its classical counterpart, we observe complete interference after certain steps and a periodicity in the evolution. Complete state tomography has been performed for each of the eight steps, making a full period. The results have extremely high fidelity with the expected states and show clearly the effects of quantum interference in the walk. We also show and discuss the importance of choosing a molecule with a natural Hamiltonian well suited to a NMR QIP by implementing the same algorithm on a second molecule. Finally, we show experimentally that decoherence after each step makes the statistics of the quantum walk tend to that of the classical random walk.
We present two polarization-based protocols for quantum key distribution. The protocols encode key bits in noiseless subspaces or subsystems, and so can function over a quantum channel subjected to an arbitrary degree of collective noise, as occurs, for instance, due to rotation of polarizations in an optical fiber. These protocols can be implemented using only entangled photon-pair sources, single-photon rotations, and single-photon detectors. Thus, our proposals offer practical and realistic alternatives to existing schemes for quantum key distribution over optical fibers without resorting to interferometry or two-way quantum communication, thereby circumventing, respectively, the need for high precision timing and the threat of Trojan horse attacks. Quantum key distribution (QKD), such as the BB84 protocol proposed by Bennett and Brassard in 1984, allows two parties (Alice and Bob) to generate an arbitrarily long random secret key provided that they initially share a short secret key and that they have access to a quantum channel [1]. As opposed to classical key distribution, the secrecy of the generated key does not rely on computational assumptions but simply on the laws of physics: as long as quantum mechanics holds, the information available to an eavesdropper (Eve) can be made arbitrarily small.Photons are obvious candidates for mediators of quantum information since they are fast, cheap, and interact weakly with the environment. Both free air and optical fiber based QKD have been realized experimentally; see [2] and [3] for reviews. Any experimental implementation of QKD naturally has to deal with the issue of noise in the quantum channel, which substantially complicates the security of QKD, as Eve may attempt to disguise her eavesdropping as noise from another source. Standard security proofs deal with channel noise, including photon loss, and show that Eve acquires essentially no information provided the noise rate is not too high. Higher noise rates mandate lower key generation rates, and once it becomes too large, secure key generation is impossible.Building a viable quantum cryptographic system therefore depends on ensuring that the noise rate is low. The degree of freedom used to encode the information can be the polarization of the photon, its phase, or some combination of both. Purely phase-based schemes have been realized experimentally [4] but require complex interferometric setups, high precision timing, and stable low temperatures. Interferometry becomes even more challenging with multi-photon states because of the difficulty of keeping phase coherence between the photons. A scheme which escapes some of these limitations using a clever encoding of key bits was proposed recently [5].Polarization-based schemes also come with a disadvantage as optical fibers rotate polarizations of transmitted photons, and the degree of rotation fluctuates over time. If left untreated, this would result in an unacceptably high error rate. A number of proposals have been made to handle this source of errors; we ...
Quantum key distribution (QKD) protocols are cryptographic techniques with security based only on the laws of quantum mechanics. Two prominent QKD schemes are the Bennett-Brassard 1984 and Bennett 1992 protocols that use four and two quantum states, respectively. In 2000, Phoenix et al. proposed a new family of three-state protocols that offers advantages over the previous schemes. Until now, an error rate threshold for security of the symmetric trine spherical code QKD protocol has been shown only for the trivial intercept-resend eavesdropping strategy. In this Letter, we prove the unconditional security of the trine spherical code QKD protocol, demonstrating its security up to a bit error rate of 9.81%. We also discuss how this proof applies to a version of the trine spherical code QKD protocol where the error rate is evaluated from the number of inconclusive events.
Noise and imperfection of realistic devices are major obstacles for implementing quantum cryptography. In particular, birefringence in optical fibers leads to decoherence of qubits encoded in photon polarization. We show how to overcome this problem by doing single qubit quantum communication without a shared spatial reference frame and precise timing. Quantum information will be encoded in pairs of photons using tag operations, which corresponds to the time delay of one of the polarization modes. This method is robust against the phase instability of the interferometers despite the use of time bins. Moreover synchronized clocks are not required in the ideal no photon loss case as they are necessary only to label the different encoded qubits.
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