Weighted complex projective 2-designs from bases: optimal state determination by orthogonal measurements

A unique quasi-probability for projective yes-no measurements

From an analysis of projective measurements, it is shown that the Wigner rule is the unique operational quasi-probability for the post-measurement state. A unique pre-measurement quasi-probability is derived from a principle of invariance of measurement disturbance under orthogonal projector complementation. Physical arguments for this principle are given. The informationally complete complex extension of the quasi-probability is also derived. Nonclassicality of this quasi-probability is due to measurement disturbance. The same quasi-probability follows from weak measurements.

Determination of weak values of quantum operators using only strong measurements

Weak values have been shown to be helpful especially when considering them as the outcomes of weak measurements. In this paper we show that in principle, the real and imaginary parts of the weak value of any operator may be elucidated from expectation values of suitably defined density, flux and hermitian commutator operators. Expectation values are the outcomes of strong (projective) measurements implying that weak values are general properties of operators in association with pre- and post-selection and they need not be preferentially associated with weak measurements. They should be conside…

Simple criteria for projective measurements with linear optics

We derive a set of criteria to decide whether a given projection measurement can be, in principle, exactly implemented solely by means of linear optics. The derivation can be adapted to various detection methods, including photon counting and homodyne detection. These criteria enable one to obtain easily No-Go theorems for the exact distinguishability of orthogonal quantum states with linear optics including the use of auxiliary photons and conditional dynamics.

保序条件用于投影测量的相干性度量及一个实例

Order-preserving condition for coherence measures of projective measurements with One Example

本文针对投影测量和正交子空间的相干性度量提出了保序条件，通过推广相干性的1/2-affinity验证其满足该条件及其他合理条件，并探讨了POVM情形下的保序条件。

Limitations to the determination of a Laguerre-Gauss spectrum via projective, phase-flattening measurement

One of the most widely used techniques for measuring the orbital angular momentum components of a light beam is to flatten the spiral phase front of a mode, in order to couple it to a single-mode optical fiber. This method, however, suffers from an efficiency that depends on the orbital angular momentum of the initial mode and on the presence of higher order radial modes. The reason is that once the phase has been flattened, the field retains its ringed intensity pattern and is therefore a nontrivial superposition of purely radial modes, of which only the fundamental one couples to a single mo…

非局域性无需纠缠的激活需要不完备性

Incompleteness is necessary for activation of nonlocality without entanglement

本文证明任何初始局域可区分的完备正交积基在保正交局域投影测量下保持可区分，从而排除通过此类测量激活非局域性，并引入“强局域集”概念刻画LOCC可区分性的不可逆损失边界。

Projective measurement of a single nuclear spin qubit by using two-mode cavity QED

We report the implementation of projective measurement on a single 1/2 nuclear spin of the 171Yb atom by measuring the polarization of cavity-enhanced fluorescence. To obtain cavity-enhanced fluorescence having a nuclear-spin-dependent polarization, we construct a two-mode cavity QED system, in which two cyclic transitions are independently coupled to each of the orthogonally polarized cavity modes, by manipulating the energy level of 171Yb. This system can associate the nuclear spin degrees of freedom with the polarization of photons, which will facilitate the development of hybrid quantum sy…

Distinguishing a set of full product bases needs only projective measurements and classical communication

Nonlocality without entanglement is an interesting field. A manifestation of quantum nonlocality without entanglement is the local indistinguishability of a set of orthogonal product states. In this paper we analyze the character of operators to distinguish a set of full product bases in a multi-partite system, and show that distinguishing perfectly a set of full product bases needs only local projective measurements and classical communication, and these measurements cannot damage each product basis. Employing these conclusions one can discuss local distinguishability of full product bases ea…

用两个可观测量确定所有未知纯量子态

Determination of All Unknown Pure Quantum States with Two Observables

本文研究用两个可观测量确定纯量子态的问题，证明两个正交基可将候选态限制到最多 2^{d-1} 个，并提出在中间自适应加入 POVM 后，几乎所有纯 qudit 都能被唯一确定。

Distinguishing between non-orthogonal quantum states of a single spin

An important task for quantum information processing is optimal discrimination between two non-orthogonal quantum states, which until now has only been realized optically. Here, we present and compare experimental realizations of optimal quantum measurements for distinguishing between two non-orthogonal quantum states encoded in a single ^14 N nuclear spin. Implemented measurement schemes are the minimum-error measurement (known as Helstrom measurement), unambiguous state discrimination using a standard projective measurement, and optimal unambiguous state discrimination (known as IDP measurem…

Establishing spin-network topologies by repeated projective measurements

It has been recently shown that in quantum systems, the complex time evolution typical of many-bodied coupled networks can be transformed into a simple, relaxation-like dynamics, by relying on periodic dephasings of the off-diagonal density matrix elements. This represents a case of "quantum Zeno effects", where unitary evolutions are inhibited by projective measurements. We present here a novel exploitation of these effects, by showing that a relaxation-like behaviour is endowed to the polarization transfers occurring within a N-spin coupled network. Experimental implementations and coupling …

An effective iterative method to build the Naimark extension of rank-n POVMs

We revisit the problem of finding the Naimark extension of a probability operator-valued measure (POVM), i.e. its implementation as a projective measurement in a larger Hilbert space. In particular, we suggest an iterative method to build the projective measurement from the sole requirements of orthogonality and positivity. Our method improves existing ones, as it may be employed also to extend POVMs containing elements with rank larger than one. It is also more effective in terms of computational steps.

Representations of Coherent States in Non-orthogonal Bases

Starting with the canonical coherent states, we demonstrate that all the so-called nonlinear coherent states, used in the physical literature, as well as large classes of other generalized coherent states, can be obtained by changes of bases in the underlying Hilbert space. This observation leads to an interesting duality between pairs of generalized coherent states, bringing into play a Gelfand triple of (rigged) Hilbert spaces. Moreover, it is shown that in each dual pair of families of nonlinear coherent states, at least one family is related to a (generally) non-unitary projective represen…

一种在复空间中生成最大正交标架的遗传算法

A genetic algorithm to generate maximally orthogonal frames in complex space

提出一种带局部优化的混合遗传算法，用于在复空间中生成最大正交标架，能高效产生高度对称的通用标架（如SIC-POVMs），适用于较高维度的配置。