Scott M. Cohen

Atemporal Diagrams for Quantum Circuits

A system of diagrams is introduced that allows the representation of various elements of a quantum circuit, including measurements, in a form which makes no reference to time (hence “atemporal”). It can be used to relate quantum dynamical properties to those of entangled states (map-state duality), and suggests useful analogies, such as the inverse of an entangled ket. Diagrams clarify the role of channel kets, transition operators, dynamical operators (matrices), and Kraus rank for noisy quantum channels. Positive (semidefinite) operators are represented by diagrams with a symmetry that aids in understanding their connection with completely positive maps. The diagrams are used to analyze standard teleportation and dense coding, and for a careful study of unambiguous (conclusive) teleportation. A simple diagrammatic argument shows that a Kraus rank of 3 is impossible for a one-qubit channel modeled using a one-qubit environment in a mixed state.

Efficient implementation of bipartite nonlocal unitary gates using prior entanglement and classical communication

Any bipartite nonlocal unitary operation can be carried out by teleporting a quantum state from one party to the other, performing the unitary gate locally, and teleporting a state back again. This paper investigates unitaries which can be carried out using less prior entanglement and classical communication than are needed for teleportation. Large families of such unitaries are constructed using (projective) representations of finite groups. Among the tools employed are: a diagrammatic approach for representing entangled states, a theorem on the necessary absence of information at certain times and locations, and a representation of bipartite unitaries based on a group Fourier transform.

Understanding entanglement as resource : Locally distinguishing unextendible product bases

It is known that the states in an unextendible product basis (UPB) cannot be distinguished perfectly when the parties are restricted to local operations and classical communication (LOCC). Previous discussions of such bases have left open the following question: What entanglement resources are necessary and/or sufficient for this task to be possible with LOCC? In this paper, I present protocols which use entanglement more efficiently than teleportation to distinguish certain classes of UPBs. The ideas underlying my approach to this problem offer rather general insight into why entanglement is useful for such tasks.

Sickle hemoglobin fibers: mechanisms of depolymerization.

We examined the depolymerization of hemoglobin (Hb) S fibers in the presence of CO by using photolysis of COHbS to create and isolate individual fibers, then removing photolysis to induce depolymerization. Depolymerization occurs at two sites, fiber ends and fiber sides, with different kinetics and by different mechanisms. At low partial pressure of CO (pCO), end-depolymerization is dominant, proceeding at approximately 1 microm s(-1), whereas at high pCO fibers vanish very rapidly, in much less than one second, by side-depolymerization. Each kind of depolymerization could occur by a ligand-independent path, in which deoxyHb depolymerizes and then is prevented from returning to the polymer by liganding with CO, or by a ligand-dependent path in which CO binds to the polymer inducing dissociation of the newly liganded molecules from it. We find that ligand-independent depolymerization is the dominant path for end-depolymerization and ligand-dependent depolymerization dominates, at least at high pCO, for side-depolymerization. On the basis of our kinetic results and electron micrographs of depolymerizing fibers, we propose a model for side-depolymerization in which a hole is nucleated by cooperative loss of a few molecules from fiber sides, followed by rapid depolymerization from the newly created fiber ends abutting the hole. Potential significance of these results for the pathophysiology of sickle cell disease is discussed.

Deterministic and Unambiguous Dense Coding

Optimal dense coding using a partially-entangled pure state of Schmidt rank ¯ D and a noiseless quantum channel of dimension D is studied both in the deterministic case where at most Ld messages can be transmitted with perfect fidelity, and in the unambiguous case where when the protocol succeeds (probabilityx) Bob knows for sure that Alice sent message x, and when it fails (probability 1 − �x) he knows it has failed. Alice is allowed any single-shot (one use) encoding procedure, and Bob any single-shot measurement. For ¯ D ≤ D a bound is obtained for Ld in terms of the largest Schmidt coefficient of the entangled state, and is compared with published results by Mozes et al. For ¯ D > D it is shown that Ld is strictly less than D 2 unless ¯ D is an integer multiple of D, in which case uniform (maximal) entanglement is not needed to achieve the optimal protocol. The unambiguous case is studied for ¯

Aspects of Relativistic Sum Rules

Abstract The status of our understanding of relativistic sum rules is reviewed. The recent development of new theoretical methods for the evaluation of these sum rules offers hope for further advances in this challenging field. These new techniques are described, along with a discussion of the source of difficulties inherent in such relativistic calculations. A connection is pointed out between certain sum rules for atomic interactions with charged particles and those for interactions with photons.

When a quantum measurement can be implemented locally, and when it cannot

In the absence of quantum channels, local operations on subsystems and classical communication between parties (LOCC) constitute the most general protocols available on spatially separated quantum systems. Every LOCC protocol implements a separable quantum measurement, but it is known that there exist separable measurements that cannot be implemented by LOCC. A longstanding problem in quantum information theory is to understand the difference between LOCC and the full set of separable measurements. Toward this end, we show in this paper how to construct an LOCC protocol to implement an arbitrary separable measurement whenever such a protocol exists. In addition, given a measurement that cannot be implemented by LOCC within some fixed maximum number of rounds, the method shows explicitly that this is the case.

Optimizing local protocols implementing nonlocal quantum gates

We present a method of optimizing recently designed protocols for implementing an arbitrary nonlocal unitary gate acting on a bipartite system. These protocols use only local operations and classical communication with the assistance of entanglement, and are deterministic while also being “one-shot”, in that they use only one copy of an entangled resource state. The optimization is in the sense of minimizing the amount of entanglement used, and it is often the case that less entanglement is needed than with an alternative protocol using two-way teleportation.

Phase boundaries in deterministic dense coding

We consider dense coding with partially entangled states on bipartite systems of dimension

Almost every set ofN≥d+1orthogonal states ond⊗nis locally indistinguishable

d\times d