Resource theory of asymmetric distinguishability

This paper systematically develops the resource theory of asymmetric distinguishability, as initiated roughly a decade ago [K. Matsumoto, arXiv:1010.1030 (2010)]. The key constituents of this resource theory are quantum boxes, consisting of a pair of quantum states, which can be manipulated for free by means of an arbitrary quantum channel. We introduce bits of asymmetric distinguishability as the basic currency in this resource theory, and we prove that it is a reversible resource theory in the asymptotic limit, with the quantum relative entropy being the fundamental rate of resource interconversion. The distillable distinguishability is the optimal rate at which a quantum box consisting of independent and identically distributed (i.i.d.) states can be converted to bits of asymmetric distinguishability, and the distinguishability cost is the optimal rate for the reverse transformation. Both of these quantities are equal to the quantum relative entropy. The exact one-shot distillable distinguishability is equal to the min-relative entropy, and the exact one-shot distinguishability cost is equal to the max-relative entropy. Generalizing these results, the approximate one-shot distillable distinguishability is equal to the smooth min-relative entropy, and the approximate one-shot distinguishability cost is equal to the smooth max-relative entropy. As a notable application of the former results, we prove that the optimal rate of asymptotic conversion from a pair of i.i.d. quantum states to another pair of i.i.d. quantum states is fully characterized by the ratio of their quantum relative entropies.Comment: v3: 28 page

Positive-partial-transpose distinguishability for lattice-type maximally entangled states

We study the distinguishability of a particular type of maximally entangled states -- the "lattice states" using a new approach of semidefinite program. With this, we successfully construct all sets of four ququad-ququad orthogonal maximally entangled states that are locally indistinguishable and find some curious sets of six states having interesting property of distinguishability. Also, some of the problems arose from \cite{CosentinoR14} about the PPT-distinguishability of "lattice" maximally entangled states can be answered.Comment: It's rewritten. We deleted the original section II about PPT-distinguishability of three ququad-ququad MESs. Moreover, we have joined new section V which discuss PPT-distinguishability of lattice MESs for cases $t=3$ and $t=4$ . As a result, the sequence of the theorems in our article has been changed. And we revised the title of our articl

Wigner-Araki-Yanase theorem on Distinguishability

The presence of an additive conserved quantity imposes a limitation on the measurement process. According to the Wigner-Araki-Yanase theorem, the perfect repeatability and the distinguishability on the apparatus cannot be attained simultaneously. Instead of the repeatability, in this paper, the distinguishability on both systems is examined. We derive a trade-off inequality between the distinguishability of the final states on the system and the one on the apparatus. The inequality shows that the perfect distinguishability of both systems cannot be attained simultaneously.Comment: To be published in Phys.Rev.

Local and Global Distinguishability in Quantum Interferometry

A statistical distinguishability based on relative entropy characterises the fitness of quantum states for phase estimation. This criterion is employed in the context of a Mach-Zehnder interferometer and used to interpolate between two regimes, of local and global phase distinguishability. The scaling of distinguishability in these regimes with photon number is explored for various quantum states. It emerges that local distinguishability is dependent on a discrepancy between quantum and classical rotational energy. Our analysis demonstrates that the Heisenberg limit is the true upper limit for local phase sensitivity. Only the `NOON' states share this bound, but other states exhibit a better trade-off when comparing local and global phase regimes.Comment: 4 pages, in submission, minor revision

Optimal depth-dependent distinguishability bounds for electrical impedance tomography in arbitrary dimension

The inverse problem of electrical impedance tomography is severely ill-posed. In particular, the resolution of images produced by impedance tomography deteriorates as the distance from the measurement boundary increases. Such depth dependence can be quantified by the concept of distinguishability of inclusions. This paper considers the distinguishability of perfectly conducting ball inclusions inside a unit ball domain, extending and improving known two-dimensional results to an arbitrary dimension $d \geq 2$ with the help of Kelvin transformations. The obtained depth-dependent distinguishability bounds are also proven to be optimal.Comment: 20 pages, 2 figure

Distinguishability of hyperentangled Bell state by linear evolution and local projective measurement

Measuring an entangled state of two particles is crucial to many quantum communication protocols. Yet Bell state distinguishability using a finite apparatus obeying linear evolution and local measurement is theoretically limited. We extend known bounds for Bell-state distinguishability in one and two variables to the general case of entanglement in $n$ two-state variables. We show that at most $2^{n+1}-1$ classes out of $4^n$ hyper-Bell states can be distinguished with one copy of the input state. With two copies, complete distinguishability is possible. We present optimal schemes in each case.Comment: 5 pages, 2 figure