Bipartite subspaces having no LOCC-distinguishable bases

  title={Bipartite subspaces having no LOCC-distinguishable bases},
  author={John Watrous},
It is proved that there exist subspaces of bipartite tensor product spaces that have no or-thonormal bases that can be perfectly distinguished by means of LOCC protocols. A corollary of this fact is that there exist quantum channels having sub-optimal classical capacity even when the receiver may communicate classically with a third party that represents the channel's environment. 
9 Citations
Reliably distinguishing states in qutrit channels using one-way LOCC
We present numerical evidence showing that any three-dimensional subspace of C^3 \otimes C^n has an orthonormal basis which can be reliably distinguished using one-way LOCC, where a measurement is
Quantum nonlocality without entanglement: explicit dependence on prior probabilities of nonorthogonal mirror-symmetric states
In the case of a multi-party system, through local operations and classical communication (LOCC), each party may not perform perfect discrimination of quantum states that are separable and
Using entanglement more efficiently in distinguishing orthogonal product states by LOCC
This paper presents a method to locally distinguish a set of \(2n-1\) orthogonal product states in a \(m \otimes n\) bipartite system with an ancillary two-qubit maximally entangled state, and generalize the discrimination method to Orthogonal Product states in even-partite system.
Quantum nonlocality without entanglement depending on nonzero prior probabilities in optimal unambiguous discrimination
It is shown that even in optimal unambiguous discrimination, the occurrence of NLWE can depend on nonzero prior probabilities, and the results provide new insights into classifying sets of multipartite quantum states in terms of quantum state discrimination.
Nonlocality of tripartite orthogonal product states
It is proved that a three-qubit GHZ state is sufficient as a resource to distinguish each of the above classes of states.
Strong quantum nonlocality for multipartite entangled states
A general definition of strong quantum nonlocality based on the local indistinguishability is presented and it is shown that a set of orthogonal entangled states is locally reducible but locally indistinguishable in all bipartitions, which means the states have strong nonLocality.


Local distinguishability of multipartite orthogonal quantum states
The protocol outlined is both completely reliable and completely general; it will correctly distinguish any two orthogonal states 100% of the time.
Unextendible product bases and bound entanglement
An unextendible product basis( UPB) for a multipartite quantum system is an incomplete orthogonal product basis whose complementary subspace contains no product state. We give examples of UPBs, and
Quantum nonlocality without entanglement
We exhibit an orthogonal set of product states of two three-state particles that nevertheless cannot be reliably distinguished by a pair of separated observers ignorant of which of the states has
Distinguishability and indistinguishability by local operations and classical communication.
  • H. Fan
  • Mathematics
    Physical review letters
  • 2004
A set of linearly independent quantum states, where U(m,n) are generalized Pauli matrices, cannot be discriminated deterministically or probabilistically by local operations and classical communication, but any l maximally entangled states from this set are locally distinguishable if l(l-1)< or =2d.
Nonlocality, asymmetry, and distinguishing bipartite states.
A fundamental asymmetry to nonlocality is revealed, which is the origin of "nonlocality without entanglement," and a very simple proof of this phenomenon is presented.
Local indistinguishability: more nonlocality with less entanglement.
The method shows that probabilistic local distinguishing is possible for a complete multipartite orthogonal basis if and only if all vectors are product, and leads to local indistinguishability of a set of Orthogonal pure states of 3 multiply sign in circle 3, which shows that one can have more nonlocality with less entanglement.
Distinguishability of maximally entangled states
In 2x2, more than two orthogonal Bell states with a single copy can never be discriminated with certainty if only local operations and classical communication (LOCC) are allowed. We show here that
Orthogonality and distinguishability: Criterion for local distinguishability of arbitrary orthogonal states
We consider the relation between the orthogonality and the distinguishability of a set of arbitrary states (including multipartite states). It is shown that if a set of arbitrary states can be
Correcting quantum channels by measuring the environment
It is shown that (i) all qu bit channels have corrected capacity log 2, (ii) a product of N qubit channels has corrected capacity N log 2; and (iii) all channels have correcting capacity at least log 2.
Entanglement measures and purification procedures
It is argued that the statistical basis of the measure of entanglement determines an upper bound to the number of singlets that can be obtained by any purification procedure.