Positivity restrictions to the transverse polarization of the inclusively detected spin-half baryons in unpolarized electron-positron annihilation

The positivity constraints to the structure functions for the inclusive spin-half baryon production by a time-like photon fragmentation are investigated. One conclusion is that $\hat F$, which arises from the hadronic final-state interactions, is subjected to an inequality between its absolute value and the two spin-independent structure functions. On the basis of this finding, we derive a formula through which the upper limits can be given for the transverse polarization of the inclusively detected spin-half baryons in unpolarized electron-positron annihilation. The derived upper bound supplies a consistency check for the judgement of reliability of experimental data and model calculations.Comment: final version to appear in Z. Phys. C, references update

Topological and Error-Correcting Properties for Symmetry-Protected Topological Order

We discuss the symmetry-protected topological (SPT) orders for bosonic systems from an information-theoretic viewpoint. We show that with a proper choice of the onsite basis, the degenerate ground-state space of SPT orders (on a manifold with boundary) is a quantum error-correcting code with macroscopic classical distance, hence is stable against any local bit-flip errors. We show that this error-correcting property of the SPT orders has a natural connection to that of the symmetry-breaking orders, whose degenerate ground-state space is a classical error-correcting code with a macroscopic distance, providing a new angle for the hidden symmetry-breaking properties in SPT orders. We propose new types of topological entanglement entropy that probe the STP orders hidden in their symmetric ground states, which also signal the topological phase transitions protected by symmetry. Combined with the original definition of topological entanglement entropy that probes the 'intrinsic topological orders', and the recent proposed one that probes the symmetry-breaking orders, the set of different types of topological entanglement entropy may hence distinguish topological orders, SPT orders, and symmetry-breaking orders, which may be mixed up in a single system.Comment: 5 pages, 7 figure

Extending PPTL for Verifying Heap Evolution Properties

In this paper, we integrate separation logic with Propositional Projection Temporal Logic (PPTL) to obtain a two-dimensional logic, namely PPTL^{\tiny\mbox{SL}}. The spatial dimension is realized by a decidable fragment of separation logic which can be used to describe linked lists, and the temporal dimension is expressed by PPTL. We show that PPTL and PPTL^{\tiny\mbox{SL}} are closely related in their syntax structures. That is, for any PPTL^{\tiny\mbox{SL}} formula in a restricted form, there exists an "isomorphic" PPTL formula. The "isomorphic" PPTL formulas can be obtained by first an equisatisfiable translation and then an isomorphic mapping. As a result, existing theory of PPTL, such as decision procedure for satisfiability and model checking algorithm, can be reused for PPTL^{\tiny\mbox{SL}}

Linearly-independent quantum states can be cloned

A fundamental question in quantum mechanics is, whether it is possible to replicate an arbitrary unknown quantum state. Then famous quantum no-cloning theorem [Nature 299, 802 (1982)] says no to the question. But it leaves open the following question: If the state is not arbitrary, but secretly chosen from a certain set $\$={ | \Psi _1> ,| \Psi_2> ,... ,| \Psi _n> }$, whether is the cloning possible? This question is of great practical significance because of its applications in quantum information theory. If the states $| \Psi_1>, | \Psi_2>,...$ and $| \Psi_n>$ are linearly-dependent, similar to the proof of the no-cloning theorem, the linearity of quantum mechanics forbids such replication. In this paper, we show that, if the states $| \Psi_1>, | \Psi _2>, ...$ and $| \Psi_n>$ are linearly-independent, they do can be cloned by a unitary-reduction process.Comment: 9 pages, no figures, Late

Optimal Perfect Distinguishability between Unitaries and Quantum Operations

We study optimal perfect distinguishability between a unitary and a general quantum operation. In 2-dimensional case we provide a simple sufficient and necessary condition for sequential perfect distinguishability and an analytical formula of optimal query time. We extend the sequential condition to general d-dimensional case. Meanwhile, we provide an upper bound and a lower bound for optimal sequential query time. In the process a new iterative method is given, the most notable innovation of which is its independence to auxiliary systems or entanglement. Following the idea, we further obtain an upper bound and a lower bound of (entanglement-assisted) q-maximal fidelities between a unitary and a quantum operation. Thus by the recursion in [1] an upper bound and a lower bound for optimal general perfect discrimination are achieved. Finally our lower bound result can be extended to the case of arbitrary two quantum operations.Comment: 11 pages, 0 figures. Comments are welcom

Decoherence of quantum registers

We consider decoherence of quantum registers, which consist of the qubits sited approximately periodically in space. The sites of the qubits are permitted to have a small random variance. We derive the explicit conditions under which the qubits can be assumed decohering independently. In other circumstances, the qubits are decohered cooperatively. We describe two kinds of collective decoherence. In each case, a scheme is proposed for reducing the collective decoherence. The schemes operate by encoding the input states of the qubits into some ''subdecoherent'' states.Comment: 12 pages, no figures, Late

Certification of Boson Sampling Devices with Coarse-Grained Measurements

A boson sampling device could efficiently sample from the output probability distribution of noninteracting bosons undergoing many-body interference. This problem is not only classically intractable, but its solution is also believed to be classically unverifiable. Hence, a major difficulty in experiment is to ensure a boson sampling device performs correctly. We present an experimental friendly scheme to extract useful and robust information from the quantum boson samplers based on coarse-grained measurements. The procedure can be applied to certify the equivalence of boson sampling devices while ruling out alternative fraudulent devices. We perform numerical simulations to demonstrate the feasibility of the method and consider the effects of realistic noise. Our approach is expected to be generally applicable to other many-body certification tasks beyond the boson sampling problem.Comment: 8 pages including Supplemental Materials, 7 figures, 3 table

Fault Tolerant Quantum Random Number Generator Certified by Majorana Fermions

Braiding of Majorana fermions gives accurate topological quantum operations that are intrinsically robust to noise and imperfection, providing a natural method to realize fault-tolerant quantum information processing. Unfortunately, it is known that braiding of Majorana fermions is not sufficient for implementation of universal quantum computation. Here we show that topological manipulation of Majorana fermions provides the full set of operations required to generate random numbers by way of quantum mechanics and to certify its genuine randomness through violation of a multipartite Bell inequality. The result opens a new perspective to apply Majorana fermions for robust generation of certified random numbers, which has important applications in cryptography and other related areas.Comment: 4pages of the main text+5 pages of supplementary informatio

Reply to the comment "quant-ph/9710002"

In the comment, Zanardi and Rasetti argue that several claims in our recent letter (Phys. Rev. Lett. 79, 1953, 1997) are questionable. The reply shows these claims remain true.Comment: 2 pages, Late

Two non-orthogonal states can be cloned by a unitary-reduction process

We show that, there are physical means for cloning two non-orthogonal pure states which are secretly chosen from a certain set % \$={ | \Psi_0 > , | \Psi_1 > }. The states are cloned through a unitary evolution together with a measurement. The cloning efficiency can not attain 100%. With some negative measurement results, the cloning fails.Comment: 9 pages, no figures, Late