29,420 research outputs found
Four-level and two-qubit systems, sub-algebras, and unitary integration
Four-level systems in quantum optics, and for representing two qubits in
quantum computing, are difficult to solve for general time-dependent
Hamiltonians. A systematic procedure is presented which combines analytical
handling of the algebraic operator aspects with simple solutions of classical,
first-order differential equations. In particular, by exploiting and sub-algebras of the full SU(4)
dynamical group of the system, the non-trivial part of the final calculation is
reduced to a single Riccati (first order, quadratically nonlinear) equation,
itself simply solved. Examples are provided of two-qubit problems from the
recent literature, including implementation of two-qubit gates with Josephson
junctions.Comment: 1 gzip file with 1 tex and 9 eps figure files. Unpack with command:
gunzip RSU05.tar.g
Secure bit commitment from relativistic constraints
We investigate two-party cryptographic protocols that are secure under
assumptions motivated by physics, namely relativistic assumptions
(no-signalling) and quantum mechanics. In particular, we discuss the security
of bit commitment in so-called split models, i.e. models in which at least some
of the parties are not allowed to communicate during certain phases of the
protocol. We find the minimal splits that are necessary to evade the
Mayers-Lo-Chau no-go argument and present protocols that achieve security in
these split models. Furthermore, we introduce the notion of local versus global
command, a subtle issue that arises when the split committer is required to
delegate non-communicating agents to open the commitment. We argue that
classical protocols are insecure under global command in the split model we
consider. On the other hand, we provide a rigorous security proof in the global
command model for Kent's quantum protocol [Kent 2011, Unconditionally Secure
Bit Commitment by Transmitting Measurement Outcomes]. The proof employs two
fundamental principles of modern physics, the no-signalling property of
relativity and the uncertainty principle of quantum mechanics.Comment: published version, IEEE format, 18 pages, 8 figure
The Measurement Calculus
Measurement-based quantum computation has emerged from the physics community
as a new approach to quantum computation where the notion of measurement is the
main driving force of computation. This is in contrast with the more
traditional circuit model which is based on unitary operations. Among
measurement-based quantum computation methods, the recently introduced one-way
quantum computer stands out as fundamental.
We develop a rigorous mathematical model underlying the one-way quantum
computer and present a concrete syntax and operational semantics for programs,
which we call patterns, and an algebra of these patterns derived from a
denotational semantics. More importantly, we present a calculus for reasoning
locally and compositionally about these patterns.
We present a rewrite theory and prove a general standardization theorem which
allows all patterns to be put in a semantically equivalent standard form.
Standardization has far-reaching consequences: a new physical architecture
based on performing all the entanglement in the beginning, parallelization by
exposing the dependency structure of measurements and expressiveness theorems.
Furthermore we formalize several other measurement-based models:
Teleportation, Phase and Pauli models and present compositional embeddings of
them into and from the one-way model. This allows us to transfer all the theory
we develop for the one-way model to these models. This shows that the framework
we have developed has a general impact on measurement-based computation and is
not just particular to the one-way quantum computer.Comment: 46 pages, 2 figures, Replacement of quant-ph/0412135v1, the new
version also include formalization of several other measurement-based models:
Teleportation, Phase and Pauli models and present compositional embeddings of
them into and from the one-way model. To appear in Journal of AC
Enhanced No-Go Theorem for Quantum Position Verification
Based on the instantaneous nonlocal quantum computation (INQC), Buhrman et
al. proposed an excellent attack strategy to quantum position verification
(QPV) protocols in 2011, and showed that, if the colluding adversaries are
allowed to previously share unlimited entangled states, it is impossible to
design an unconditionally secure QPV protocol in the previous model. Here,
trying to overcome this no-go theorem, we find some assumptions in the INQC
attack, which are implicit but essential for the success of this attack, and
present three different QPV protocols where these assumptions are not
satisfied. We show that for the general adversaries, who execute the attack
operations at every common time slot or the time when they detect the arrival
of the challenge signals from the verifiers, secure QPV is achievable. This
implies practically secure QPV can be obtained even if the adversaries is
allowed to share unlimited entanglement previously. Here by "practically" we
mean that in a successful attack the adversaries need launch a new round of
attack on the coming qubits with extremely high frequency so that none of the
possible qubits, which may be sent at random time, will be missed. On the other
side, using such Superdense INQC (SINQC) attack, the adversaries can still
attack the proposed protocols successfully in theory. The particular attack
strategies to our protocols are presented respectively. On this basis, we
demonstrate the impossibility of secure QPV with looser assumptions, i.e. the
enhanced no-go theorem for QPV.Comment: 19 pages, single column, 3 tables, 6 figure
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