Jianxin Chen

Superactivation of the Asymptotic Zero-Error Classical Capacity of a Quantum Channel

The zero-error classical capacity of a quantum channel is the asymptotic rate at which it can be used to send classical bits perfectly so that they can be decoded with zero probability of error. We show that there exist pairs of quantum channels, neither of which individually have any zero-error capacity whatsoever (even if arbitrarily many uses of the channels are available), but such that access to even a single copy of both channels allows classical information to be sent perfectly reliably. In other words, we prove that the zero-error classical capacity can be superactivated. This result is the first example of superactivation of a classical capacity of a quantum channel.

Uniqueness of quantum states compatible with given measurement results

We discuss the uniqueness of quantum states compatible with given measurement results for a set of observables. For a given pure state, we consider two different types of uniqueness: (1) no other pure state is compatible with the same measurement results and (2) no other state, pure or mixed, is compatible with the same measurement results. For case (1), it was known that for a

No-go Theorem For One-way Quantum Computing On Naturally Occurring Two-level Systems

d

Discontinuity of maximum entropy inference and quantum phase transitions

-dimensional Hilbert space, there exists a set of

Pure-state tomography with the expectation value of Pauli operators

4d\ensuremath{-}5

The Minimum Size of Unextendible Product Bases in the Bipartite Case (and Some Multipartite Cases)

observables that uniquely determines any pure state. We show that for case (2),

Comment on some results of Erdahl and the convex structure of reduced density matrices

5d\ensuremath{-}7

From Ground States to Local Hamiltonians

observables suffice to uniquely determine any pure state. Thus, there is a gap between the results for (1) and (2), and we give some examples to illustrate this. Unique determination of a pure state by its reduced density matrices (RDMs), a special case of determination by observables, is also discussed. We improve the best-known bound on local dimensions in which almost all pure states are uniquely determined by their RDMs for case (2). We further discuss circumstances where (1) can imply (2). We use convexity of the numerical range of operators to show that when only two observables are measured, (1) always implies (2). More generally, if there is a compact group of symmetries of the state space which has the span of the observables measured as the set of fixed points, then (1) implies (2). We analyze the possible dimensions for the span of such observables. Our results extend naturally to the case of low-rank quantum states.

Existence of Universal Entangler

One-way quantum computing achieves the full power of quantum computation by performing single particle measurements on some many-body entangled state, known as the resource state. As single particle measurements are relatively easy to implement, the preparation of the resource state becomes a crucial task. An appealing approach is simply to cool a strongly correlated quantum many-body system to its ground state. In addition to requiring the ground state of the system to be universal for one-way quantum computing, we also want the Hamiltonian to have non-degenerate ground state protected by a fixed energy gap, to involve only two-body interactions, and to be frustration-free so that measureme nts in the course of the computation leave the remaining particles in the ground space. Recently, significant eff orts have been made to the search of resource states that appear naturally as ground states in spin lattice syste ms. The approach is proved to be successful in spin- 5 and spin- 3 systems. Yet, it remains an open question whether there could be such a natural resource state in a spin- 1 , i.e., qubit system. Here, we give a negative answer to this question by proving that it is impossible for a genuinely entangled qubit states to be a non-degenerate ground state of any two-body frustration-free Hamiltonian. What is more, we prove that every spin- 1 frustration-free Hamiltonian with two-body interaction always has a ground state that is a product of single- or two-qubit st ates, a stronger result that is interesting independent of the context of one-way quantum computing.

Ground-state spaces of frustration-free Hamiltonians

In this paper, we discuss the connection between two genuinely quantum phenomena --- the discontinuity of quantum maximum entropy inference and quantum phase transitions at zero temperature. It is shown that the discontinuity of the maximum entropy inference of local observable measurements signals the non-local type of transitions, where local density matrices of the ground state change smoothly at the transition point. We then propose to use the quantum conditional mutual information of the ground state as an indicator to detect the discontinuity and the non-local type of quantum phase transitions in the thermodynamic limit.